               Persistence of Vision (tm) Ray-Tracer
                                
                     POV-Ray (tm) Version 3.1g
                                
                      User's Documentation
                            May 1999
                                
                    Copyright 1999 POV-Team (tm)
                                
POV-Ray (tm) is based on DKBTrace 2.12 by David K. Buck and Aaron A.
                            Collins.
                                
   POV-Ray, POV-Help, POV-Team, and Persistence of Vision are
                   trademarks of the POV-Team.


1  Introduction
 1.1  Program Description
 1.2  What is Ray-Tracing?
 1.3  What is POV-Ray?
 1.4  How Do I Begin?
 1.5  Notation and Basic Assumptions
 1.6  What's New in POV-Ray 3.1?
  1.6.1  Media Replaces Halo & Atmosphere
  1.6.2  New #macro Feature
  1.6.3  Arrays Added
  1.6.4  File I/O and other Directives
  1.6.5  Additional New Features

2  Beginning Tutorial
 2.1  Our First Image
  2.1.1  Understanding POV-Ray's Coordinate System
  2.1.2  Adding Standard Include Files
  2.1.3  Adding a Camera
  2.1.4  Describing an Object
  2.1.5  Adding Texture to an Object
  2.1.6  Defining a Light Source
 2.2  Simple Shapes
  2.2.1  Box Object
  2.2.2  Cone Object
  2.2.3  Cylinder Object
  2.2.4  Plane Object
 2.3  CSG Objects
  2.3.1  What is CSG?
  2.3.2  CSG Union
  2.3.3  CSG Intersection
  2.3.4  CSG Difference
  2.3.5  CSG Merge
  2.3.6  CSG Pitfalls
    2.3.6.1  Coincidence Surfaces
 2.4  Advanced Shapes
  2.4.1  Bicubic Patch Object
  2.4.2  Blob Object
    2.4.2.1  Component Types and Other New Features
    2.4.2.2  Complex Blob Constructs and Negative Strength
  2.4.3  Height Field Object
  2.4.4  Lathe Object
    2.4.4.1  Understanding The Concept of Splines
  2.4.5  Mesh Object
  2.4.6  Polygon Object
  2.4.7  Prism Object
    2.4.7.1  Teaching An Old Spline New Tricks
    2.4.7.2  Smooth Transitions
    2.4.7.3  Multiple Sub-Shapes
    2.4.7.4  Conic Sweeps And The Tapering Effect
  2.4.8  Superquadric Ellipsoid Object
  2.4.9  Surface of Revolution Object
  2.4.10  Text Object
  2.4.11  Torus Object
 2.5  The Light Source
  2.5.1  The Pointlight Source
  2.5.2  The Spotlight Source
  2.5.3  The Cylindrical Light Source
  2.5.4  The Area Light Source
  2.5.5  The Ambient Light Source
  2.5.6  Light Source Specials
    2.5.6.1  Using Shadowless Lights
    2.5.6.2  Assigning an Object to a Light Source
    2.5.6.3  Using Light Fading
 2.6  Simple Texture Options
  2.6.1  Surface Finishes
  2.6.2  Adding Bumpiness
  2.6.3  Creating Color Patterns
  2.6.4  Pre-defined Textures
 2.7  Advanced Texture Options
  2.7.1  Pigments
    2.7.1.1  Using Color List Pigments
    2.7.1.2  Using Pigment and Patterns
    2.7.1.3  Using Pattern Modifiers
    2.7.1.4  Using Transparent Pigments and Layered Textures
    2.7.1.5  Using Pigment Maps
  2.7.2  Normals
    2.7.2.1  Using Basic Normal Modifiers
    2.7.2.2  Blending Normals
  2.7.3  Finishes
    2.7.3.1  Using Ambient
    2.7.3.2  Using Surface Highlights
    2.7.3.3  Using Reflection and Metallic
    2.7.3.4  Using Iridescence
  2.7.4  Working With Pigment Maps
  2.7.5  Working With Normal Maps
  2.7.6  Working With Texture Maps
  2.7.7  Working With List Textures
  2.7.8  What About Tiles?
  2.7.9  Average Function
  2.7.10  Working With Layered Textures
    2.7.10.1  Declaring Layered Textures
    2.7.10.2  Another Layered Textures Example
  2.7.11  When All Else Fails: Material Maps
  2.7.12  Limitations Of Special Textures
 2.8  Using the Camera
  2.8.1  Using Focal Blur
 2.9  Using Atmospheric Effects
  2.9.1  The Background
  2.9.2  The Sky Sphere
    2.9.2.1  Creating a Sky with a Color Gradient
    2.9.2.2  Adding the Sun
    2.9.2.3  Adding Some Clouds
  2.9.3  The Fog
    2.9.3.1  A Constant Fog
    2.9.3.2  Setting a Minimum Translucency
    2.9.3.3  Creating a Filtering Fog
    2.9.3.4  Adding Some Turbulence to the Fog
    2.9.3.5  Using Ground Fog
    2.9.3.6  Using Multiple Layers of Fog
    2.9.3.7  Fog and Hollow Objects
  2.9.4  The Rainbow
    2.9.4.1  Starting With a Simple Rainbow
    2.9.4.2  Increasing the Rainbow's Translucency
    2.9.4.3  Using a Rainbow Arc
  2.9.5  Animation
    2.9.5.1  The Clock Variable: Key To It All
    2.9.5.2  Clock Dependant Variables And Multi-Stage
               Animations
    2.9.5.3  The Phase Keyword
    2.9.5.4  Do Not Use Jitter Or Crand
    2.9.5.5  INI File Settings

3  POV-Ray Options
 3.1  Setting POV-Ray Options
  3.1.1  Command Line Switches
  3.1.2  Using INI Files
  3.1.3  Using the POVINI Environment Variable
 3.2  Options Reference
  3.2.1  Animation Options
    3.2.1.1  External Animation Loop
    3.2.1.2  Internal Animation Loop
    3.2.1.3  Subsets of Animation Frames
    3.2.1.4  Cyclic Animation
    3.2.1.5  Field Rendering
  3.2.2  Output Options
    3.2.2.1  General Output Options
     3.2.2.1.1  Height and Width of Output
     3.2.2.1.2  Partial Output Options
     3.2.2.1.3  Interrupting Options
     3.2.2.1.4  Resuming Options
    3.2.2.2  Display Output Options
     3.2.2.2.1  Display Hardware Settings
     3.2.2.2.2  Display Related Settings
     3.2.2.2.3  Mosaic Preview
    3.2.2.3  File Output Options
     3.2.2.3.1  Output File Type
     3.2.2.3.2  Output File Name
     3.2.2.3.3  Output File Buffer
    3.2.2.4  CPU Utilization Histogram
     3.2.2.4.1  File Type
     3.2.2.4.2  File Name
     3.2.2.4.3  Grid Size
  3.2.3  Scene Parsing Options
    3.2.3.1  Input File Name
    3.2.3.2  Library Paths
    3.2.3.3  Language Version
  3.2.4  Shell-out to Operating System
    3.2.4.1  String Substitution in Shell Commands
    3.2.4.2  Shell Command Sequencing
    3.2.4.3  Shell Command Return Actions
  3.2.5  Text Output
    3.2.5.1  Text Streams
    3.2.5.2  Console Text Output
    3.2.5.3  Directing Text Streams to Files
    3.2.5.4  Help Screen Switches
  3.2.6  Tracing Options
    3.2.6.1  Quality Settings
    3.2.6.2  Radiosity Setting
    3.2.6.3  Automatic Bounding Control
    3.2.6.4  Removing User Bounding
    3.2.6.5  Anti-Aliasing Options

4  Scene Description Language
 4.1  Language Basics
  4.1.1  Identifiers and Keywords
  4.1.2  Comments
  4.1.3  Float Expressions
    4.1.3.1  Float Literals
    4.1.3.2  Float Identifiers
    4.1.3.3  Float Operators
    4.1.3.4  Built-in Float Identifiers
    4.1.3.5  Boolean Keywords
    4.1.3.6  Float Functions
  4.1.4  Vector Expressions
    4.1.4.1  Vector Literals
    4.1.4.2  Vector Identifiers
    4.1.4.3  Vector Operators
    4.1.4.4  Operator Promotion
    4.1.4.5  Built-in Vector Identifiers
    4.1.4.6  Vector Functions
  4.1.5  Specifying Colors
    4.1.5.1  Color Vectors
    4.1.5.2  Color Keywords
    4.1.5.3  Color Identifiers
    4.1.5.4  Color Operators
    4.1.5.5  Common Color Pitfalls
  4.1.6  Strings
    4.1.6.1  String Literals
    4.1.6.2  String Identifiers
    4.1.6.3  String Functions
  4.1.7  Array Identifiers
    4.1.7.1  Declaring Arrays
    4.1.7.2  Array Initalizers
 4.2  Language Directives
  4.2.1  Include Files and the #include Directive.
  4.2.2  The #declare and #local Directives
    4.2.2.1  Declaring identifiers
    4.2.2.2  #declare vs. #local
    4.2.2.3  Identifier Name Collisions
    4.2.2.4  Destroying Identifiers with #undef
  4.2.3  File I/O Directives
    4.2.3.1  The #fopen Directive
    4.2.3.2  The #fclose Directive
    4.2.3.3  The #read Directive
    4.2.3.4  The #write Directive
  4.2.4  The #default Directive
  4.2.5  The #version Directive
  4.2.6  Conditional Directives
    4.2.6.1  The #if...#else...#end Directives
    4.2.6.2  The #ifdef and #ifndef Directives
    4.2.6.3  The #switch, #case, #range and #break Directives
    4.2.6.4  The #while...#end Directive
  4.2.7  User Message Directives
    4.2.7.1  Text Message Streams
    4.2.7.2  Text Formatting
  4.2.8  User Defined Macros
    4.2.8.1  The #macro Directive
    4.2.8.2  Invoking Macros
    4.2.8.3  Are POV-Ray Macros a Function or a Macro?
    4.2.8.4  Returning a Value Like a Function
    4.2.8.5  Returning Values Via Parameters
 4.3  POV-Ray Coordinate System
  4.3.1  Transformations
    4.3.1.1  Translate
    4.3.1.2  Scale
    4.3.1.3  Rotate
    4.3.1.4  Matrix Keyword
  4.3.2  Transformation Order
  4.3.3  Transform Identifiers
  4.3.4  Transforming Textures and Objects
 4.4  Camera
  4.4.1  Placing the Camera
    4.4.1.1  Location and Look_At
    4.4.1.2  The Sky Vector
    4.4.1.3  Angle
    4.4.1.4  The Direction Vector
    4.4.1.5  Up and Right Vectors
     4.4.1.5.1  Aspect Ratio
     4.4.1.5.2  Handedness
    4.4.1.6  Transforming the Camera
  4.4.2  Types of Projection
  4.4.3  Focal Blur
  4.4.4  Camera Ray Perturbation
  4.4.5  Camera Identifiers
 4.5  Objects
  4.5.1  Finite Solid Primitives
    4.5.1.1  Blob
    4.5.1.2  Box
    4.5.1.3  Cone
    4.5.1.4  Cylinder
    4.5.1.5  Height Field
    4.5.1.6  Julia Fractal
    4.5.1.7  Lathe
    4.5.1.8  Prism
    4.5.1.9  Sphere
    4.5.1.10  Superquadric Ellipsoid
    4.5.1.11  Surface of Revolution
    4.5.1.12  Text
    4.5.1.13  Torus
  4.5.2  Finite Patch Primitives
    4.5.2.1  Bicubic Patch
    4.5.2.2  Disc
    4.5.2.3  Mesh
    4.5.2.4  Polygon
    4.5.2.5  Triangle and Smooth Triangle
  4.5.3  Infinite Solid Primitives
    4.5.3.1  Plane
    4.5.3.2  Poly, Cubic and Quartic
    4.5.3.3  Quadric
  4.5.4  Constructive Solid Geometry
    4.5.4.1  Inside and Outside
    4.5.4.2  Union
    4.5.4.3  Intersection
    4.5.4.4  Difference
    4.5.4.5  Merge
  4.5.5  Light Sources
    4.5.5.1  Point Lights
    4.5.5.2  Spotlights
    4.5.5.3  Cylindrical Lights
    4.5.5.4  Area Lights
    4.5.5.5  Shadowless Lights
    4.5.5.6  Looks_like
    4.5.5.7  Light Fading
    4.5.5.8  Atmospheric Media Interaction
    4.5.5.9  Atmospheric Attenuation
  4.5.6  Object Modifiers
    4.5.6.1  Clipped_By
    4.5.6.2  Bounded_By
    4.5.6.3  Material
    4.5.6.4  Inverse
    4.5.6.5  Hollow
    4.5.6.6  No_Shadow
    4.5.6.7  Sturm
 4.6  Interior
  4.6.1  Why are Interior and Media Necessary?
  4.6.2  Empty and Solid Objects
  4.6.3  Refraction
  4.6.4  Attenuation
  4.6.5  Faked Caustics
  4.6.6  Object Media
 4.7  Textures
  4.7.1  Pigment
    4.7.1.1  Solid Color Pigments
    4.7.1.2  Color List Pigments
    4.7.1.3  Color Maps
    4.7.1.4  Pigment Maps and Pigment Lists
    4.7.1.5  Image Maps
     4.7.1.5.1  Specifying an Image Map
     4.7.1.5.2  The Filter and Transmit Bitmap Modifiers
     4.7.1.5.3  Using the Alpha Channel
    4.7.1.6  Quick Color
  4.7.2  Normal
    4.7.2.1  Slope Maps
    4.7.2.2  Normal Maps and Normal Lists
    4.7.2.3  Bump Maps
     4.7.2.3.1  Specifying a Bump Map
     4.7.2.3.2  Bump_Size
     4.7.2.3.3  Use_Index and Use_Color
  4.7.3  Finish
    4.7.3.1  Ambient
    4.7.3.2  Diffuse Reflection Items
     4.7.3.2.1  Diffuse
     4.7.3.2.2  Brilliance
     4.7.3.2.3  Crand Graininess
    4.7.3.3  Highlights
     4.7.3.3.1  Phong Highlights
     4.7.3.3.2  Specular Highlight
     4.7.3.3.3  Metallic Highlight Modifier
    4.7.3.4  Specular Reflection
    4.7.3.5  Iridescence
  4.7.4  Halo
  4.7.5  Patterned Textures
    4.7.5.1  Texture Maps
    4.7.5.2  Tiles
    4.7.5.3  Material Maps
     4.7.5.3.1  Specifying a Material Map
  4.7.6  Layered Textures
  4.7.7  Patterns
    4.7.7.1  Agate
    4.7.7.2  Average
    4.7.7.3  Boxed
    4.7.7.4  Bozo
    4.7.7.5  Brick
    4.7.7.6  Bumps
    4.7.7.7  Checker
    4.7.7.8  Crackle
    4.7.7.9  Cylindrical
    4.7.7.10  Density_File
    4.7.7.11  Dents
    4.7.7.12  Gradient
    4.7.7.13  Granite
    4.7.7.14  Hexagon
    4.7.7.15  Leopard
    4.7.7.16  Mandel
    4.7.7.17  Marble
    4.7.7.18  Onion
    4.7.7.19  Planar
    4.7.7.20  Quilted
    4.7.7.21  Radial
    4.7.7.22  Ripples
    4.7.7.23  Spherical
    4.7.7.24  Spiral1
    4.7.7.25  Spiral2
    4.7.7.26  Spotted
    4.7.7.27  Waves
    4.7.7.28  Wood
    4.7.7.29  Wrinkles
  4.7.8  Pattern Modifiers
    4.7.8.1  Transforming Patterns
    4.7.8.2  Frequency and Phase
    4.7.8.3  Waveforms
    4.7.8.4  Turbulence
    4.7.8.5  Octaves
    4.7.8.6  Lambda
    4.7.8.7  Omega
    4.7.8.8  Warps
     4.7.8.8.1  Black Hole Warp
     4.7.8.8.2  Repeat Warp
     4.7.8.8.3  Turbulence Warp
    4.7.8.9  Bitmap Modifiers
     4.7.8.9.1  The once Option
     4.7.8.9.2  The map_type Option
     4.7.8.9.3  The interpolate Option
 4.8  Media
  4.8.1  Media Types
    4.8.1.1  Absorption
    4.8.1.2  Emission
    4.8.1.3  Scattering
  4.8.2  Sampling Parameters
  4.8.3  Density
    4.8.3.1  General Density Modifiers
    4.8.3.2  Density with color_map
    4.8.3.3  Density Maps and Density Lists
    4.8.3.4  Multiple Density vs. Multiple Media
 4.9  Atmospheric Effects
  4.9.1  Atmospheric Media
  4.9.2  Background
  4.9.3  Fog
  4.9.4  Sky Sphere
  4.9.5  Rainbow
 4.10  Global Settings
  4.10.1  ADC_Bailout
  4.10.2  Ambient Light
  4.10.3  Assumed_Gamma
    4.10.3.1  Monitor Gamma
    4.10.3.2  Image File Gamma
    4.10.3.3  Scene File Gamma
  4.10.4  HF_Gray_16
  4.10.5  Irid_Wavelength
  4.10.6  Max_Trace_Level
  4.10.7  Max_Intersections
  4.10.8  Number_Of_Waves
  4.10.9  Radiosity
    4.10.9.1  How Radiosity Works
    4.10.9.2  Adjusting Radiosity
     4.10.9.2.1  brightness
     4.10.9.2.2  count
     4.10.9.2.3  distance_maximum
     4.10.9.2.4  error_bound
     4.10.9.2.5  gray_threshold
     4.10.9.2.6  low_error_factor
     4.10.9.2.7  minimum_reuse
     4.10.9.2.8  nearest_count
     4.10.9.2.9  recursion_limit
    4.10.9.3  Tips on Radiosity

5  APPENDICES
 5.1  Copyright, Legal Information and License -- POVLEGAL.DOC
  5.1.1  General License Agreement -- POVLEGAL.DOC
  5.1.2  Usage Provisions
  5.1.3  General Rules For All Distribution
  5.1.4  Definition Of "Full Package"
  5.1.5  Conditions For CD-ROM or Shareware/Freeware
           Distribution
  5.1.6  Conditions For On-Line Services And Bbs's Including
           Internet
  5.1.7  Online Or Remote Execution Of POV-Ray
  5.1.8  Permitted Modification And Custom Versions
  5.1.9  Conditions For Distribution Of Custom Versions
  5.1.10  Conditions For Commercial Bundling
  5.1.11  POV-Team Endorsement Prohibitions
  5.1.12  Retail Value Of This Software
  5.1.13  Other Provisions
  5.1.14  Revocation Of License
  5.1.15  Disclaimer
  5.1.16  Technical Support
 5.2  Authors
  5.2.1  Contacting the Authors
 5.3  What to do if you don't have POV-Ray
  5.3.1  Which Version of POV-Ray should you use?
    5.3.1.1  Microsoft Windows 95/98/NT
    5.3.1.2  MS-Dos & Windows 3.x
    5.3.1.3  Linux for Intel x86
    5.3.1.4  Apple Macintosh
    5.3.1.5  Amiga
    5.3.1.6  SunOS
    5.3.1.7  Generic Unix
    5.3.1.8  All Versions
  5.3.2  Where to Find POV-Ray Files
    5.3.2.1  World Wide Website www.povray.org
    5.3.2.2  Books, Magazines and CD-ROMs
 5.4  Compiling POV-Ray
  5.4.1  Directory Structure
  5.4.2  Configuring POV-Ray Source
  5.4.3  Conclusion
 5.5  Suggested Reading
 
 


1.0    Introduction
This document details the use of the Persistence of Vision (tm) Ray-
Tracer (POV-Ray (tm)). It is divided into five parts:

  1)This introduction which explains what POV-Ray is and what
     ray-tracing is. It gives a brief overview of how to create
     ray-traced images.
  2)A "Beginning Tutorial" which explains step by step how to
     use the different features of POV-Ray.
  3)A complete reference on "Scene Description Language" in
     which you describe the scene.
  4)A complete reference on "POV-Ray Options" which explains
     options (set either by command line switches or by INI file
     keywords) that tell POV-Ray how to render the scenes.
  5)And in our "APPENDICES" you will find some tips and hints,
     where to get the latest version and versions for other
     platforms, information on compiling custom versions of POV-
     Ray, suggested reading, contact addresses and legal
     information.
POV-Ray runs on MS-Dos, Windows 3.x, Windows for Workgroups 3.11,
Windows 95, Windows NT, Apple Macintosh 68k, Macintosh Power PC,
Amiga, Linux, Sun-OS, UNIX and other platforms.

We assume that if you are reading this document then you already
have POV-Ray installed and running.  However the POV-Team does
distribute this file by itself in various formats including
online on the internet.  If you don't have POV-Ray or aren't sure
you have the official version or the latest version, see appendix
"What to do if you don't have POV-Ray".

This document covers only the generic parts of the program which
are common to each version.  Each version has platform-specific
documentation not included here.  We recommend you finish reading
this introductory section then read the platform-specific
information before trying the tutorial here.

The platform-specific docs will show you how to render a sample
scene and will give you detailed description of the platform-
specific features.

The MS-Dos version documentation contains a plain text file
POVMSDOS.DOC which contains its specific docs.  It can be found
in the main directory where you installed POV-Ray such as
C:\POVRAY3.

The Windows version documentation is available on the POV-Ray
program's Help menu or press the F1 key while in the program.

The Mac platform documentation consists of a self-displaying
document called "POV-Ray MacOS Read Me" which contains
information specific to the Mac version of POV-Ray. It is best to
read this document first, to learn how to set up and start using
the Mac version of POV-Ray. This document is in the
"Documentation" folder in the main "POV-Ray 3" folder.

The Amiga version documentation is made up of Html documents,
stored in the same place of general POV-Ray docs; the 'root'
document is "POVRAY3:POV-Reference/AmigaPOV.html" when the
program is installed following the instruction given.  Amiga
specific documentation and POV-Ray general docs are available
pressing Help key in the POV-Gui program; this feature is
available in POV-Gui since version 2.1

The Linux version documentation contains a plain text file
povlinux.doc which contains its specific docs.  It can be found
in the main directory where you installed POV-Ray such as
/usr/povray3.

The SunOS version documentation contains a plain text file
povsunos.doc which contains its specific docs.  It can be found
in the main directory where you installed POV-Ray such as
/usr/povray3.

The generic Unix version documentation contains a plain text file
povunix.doc which contains its specific docs.  It can be found in
the main directory where you installed POV-Ray such as
/usr/povray3.


1.1  Program Description
The Persistence of Vision(tm) Ray-Tracer creates three-dimensional,
photo-realistic images using a rendering technique called ray-
tracing. It reads in a text file containing information
describing the objects and lighting in a scene and generates an
image of that scene from the view point of a camera also
described in the text file. Ray-tracing is not a fast process by
any means, but it produces very high quality images with
realistic reflections, shading, perspective and other effects.


1.2  What is Ray-Tracing?
Ray-tracing is a rendering technique that calculates an image of
a scene by simulating the way rays of light travel in the real
world.  However it does its job backwards.  In the real world,
rays of light are emitted from a light source and illuminate
objects.  The light reflects off of the objects or passes through
transparent objects.  This reflected light hits our eyes or
perhaps a camera lens.  Because the vast majority of rays never
hit an observer, it would take forever to trace a scene.

Ray-tracing programs like POV-Ray start with their simulated
camera and trace rays backwards out into the scene.  The user
specifies the location of the camera, light sources, and objects
as well as the surface texture properties of objects, their
interiors (if transparent) and any atmospheric media such as fog,
haze, or fire.

For every pixel in the final image one or more viewing rays are
shot from the camera, into the scene to see if it intersects with
any of the objects in the scene. These "viewing rays" originate
from the viewer, represented by the camera, and pass through the
viewing window (representing the final image).

Every time an object is hit, the color of the surface at that
point is calculated. For this purpose rays are sent backwards to
each light source to determine the amount of light coming from
the source. These "shadow rays" are tested to tell whether the
surface point lies in shadow or not. If the surface is reflective
or transparent new rays are set up and traced in order to
determine the contribution of the reflected and refracted light
to the final surface color.

Special features like inter-diffuse reflection (radiosity),
atmospheric effects and area lights make it necessary to shoot a
lot of additional rays into the scene for every pixel.


1.3  What is POV-Ray?
The Persistence of Vision (tm) Ray-Tracer was developed from
DKBTrace 2.12 (written by David K. Buck and Aaron A. Collins) by
a bunch of people, called the POV-Team (tm), in their spare time.
The headquarters of the POV-Team is on the internet at
http://www.povray.org (see "Where to Find POV-Ray Files" for more
details).

The POV-Ray (tm) package includes detailed instructions on using the
ray-tracer and creating scenes. Many stunning scenes are included
with POV-Ray so you can start creating images immediately when
you get the package. These scenes can be modified so you don't
have to start from scratch.

In addition to the pre-defined scenes, a large library of pre-
defined shapes and materials is provided.  You can include these
shapes and materials in your own scenes by just including the
library file name at the top of your scene file, and by using the
shape or material name in your scene.

Here are some highlights of POV-Ray's features:

  * Easy to use scene description language.
  * Large library of stunning example scene files.
  * Standard include files that pre-define many shapes, colors
  and textures.
  * Very high quality output image files (up to 48-bit color).
  * 15 and 24 bit color display on many computer platforms using
  appropriate hardware.
  * Create landscapes using smoothed height fields.
  * Many camera types, including perspective, panorama,
  orthographic, fisheye, etc.
  * Spotlights, cylindrical lights and area lights for
  sophisticated  lighting.
  * Phong and specular highlighting for more realistic-looking
  surfaces.
  * Inter-diffuse reflection (radiosity) for more realistic
  lighting.
  * Atmospheric effects like atmosphere, ground-fog and rainbow.
  * Particle media to model effects like clouds, dust, fire and
  steam.
  * Several image file output formats including Targa, PNG and
  PPM.
  * Basic shape primitives such as ... spheres, boxes, quadrics,
  cylinders, cones, triangles and planes.
  * Advanced shape primitives such as ... Torii (donuts), bezier
  patches, height fields (mountains), blobs, quartics, smooth
  triangles, text, fractals, superquadrics, surfaces of
  revolution, prisms, polygons, lathes and fractals.
  * Shapes can easily be combined to create new complex shapes
  using Constructive Solid Geometry (CSG). POV-Ray supports
  unions, merges, intersections and differences.
  * Objects are assigned materials called textures (a texture
  describes the coloring and surface properties of a shape) and
  interior properties such as index of refraction and particle
  media (formerly known as "halos").
  * Built-in color and normal patterns: Agate, Bozo, Bumps,
  Checker, Crackle, Dents, Granite, Gradient, Hexagon, Leopard,
  Mandel, Marble, Onion, Quilted, Ripples, Spotted, Spiral,
  Radial, Waves, Wood, Wrinkles and image file mapping.
  * Users can create their own textures or use pre-defined
  textures such as ... Brass, Chrome, Copper, Gold, Silver,
  Stone, Wood.
  * Combine textures using layering of semi-transparent textures
  or tiles of textures or material map files.
  * Display preview of image while rendering (not available on
  all platforms).
  * Halt and save a render part way through, and continue
  rendering the halted partial render later.

1.4  How Do I Begin?
POV-Ray scenes are described in a special text language called a
"scene description language".  You will type commands into a
plain text file and POV-Ray will read it to create the image.
The process of running POV-Ray is a little different on each
platform or operating system.  You should read the platform-
specific documentation as suggested earlier in this introduction.
It will tell you how to command POV-Ray to turn your text scene
description into an image.  You should try rendering several
sample images before attempting to create your own.

Once you know how to run POV-Ray on your computer and your
operating system, you can proceed with the tutorial which
follows.  The tutorial explains how to describe the scene using
the POV-Ray language.


1.5  Notation and Basic Assumptions
Throughout the tutorial and reference section of this document,
the following notation is used to mark keywords of the scene
description language, command line switches, INI file keywords
and file names.
     keyword       mono-spaced bold    POV-Ray keywords and
                                       punctuation
     +W640 +H480   mono-spaced bold    command-line switches
     C:\MYFILE.PO  mono-spaced         file names,
     V                                 directories, paths
     SYNTAX_ITEM   italics, all caps   required syntax item
     [SYNTAX_ITEM  italics, all caps,  optional syntax item
     ]             braces
     SYNTAX_ITEM.  italics, all caps,  one or more syntax
     ..            ellipsis            items
     [SYNTAX_ITEM  italics, all caps,  zero or more syntax
     ...]          braces, ellipsis    items
     Value_1       italics, mixed      a float value or
                   case                expression
     <Value_1>     italics, mixed      a vector value or
                   case, angle braces  expression
     [ ITEM ]      bold square braces  ITEM enclosed in
                                       required braces
     ITEM1   |     vertical bar        choice of ITEM1 or
     ITEM2                             ITEM2


In the plain ASCII version of the document there is no visible
difference between the different notations.

Note that POV-Ray is a command-line program on MS-Dos, Unix and
other text-based operating system and is menu-driven on Windows
and Macintosh platforms.  Some of these operating systems use
folders to store files while others use directories.  Some
separate the folders and sub-folders with a slash character (/),
back-slash character (\), or others.  We have tried to make this
documentation as generic as possible but sometimes we have to
refer to folders, files, options etc. and there's no way to
escape it. Here are some assumptions we make...

1) You installed POV-Ray in the "C:\POVRAY3" directory.  For MS-
Dos this is probably true but for Unix it might be
"/usr/povray3", or for Windows it might be "C:\Program Files\POV-
Ray for Windows", for Mac it might be "MyHD:Apps:POV-Ray 3:", or
you may have used some other drive or directory.  So if we tell
you that "Include files are stored in the \povray3\include
directory,"  we assume you can translate that to something like
"::POVRAY3:INCLUDE" or "C:\Program Files\POV-Ray for
Windows\include" or whatever is appropriate for your platform,
operating system and installation.

2) POV-Ray uses command-line switches and INI files to choose
options in all versions but Windows and Mac also use dialog boxes
or menu choices to set options.  We will describe options
assuming you are using switches or INI files when describing what
the options do. We have taken care to use the same terminology in
designing menus and dialogs as we use in describing switches or
INI keywords. See your version-specific documentation on menu and
dialogs.

3) Some of you are reading this using a help-reader, built-in
help, web-browser, formatted printout, or plain text file.  We
assume you know how to get around in which ever medium you're
using.  We'll say "See the chapter on "Setting POV-Ray Option" we
assume you can click, scroll, browse, flip pages or whatever to
get there.


1.6  What's New in POV-Ray 3.1?
Here is an overview of what is new in POV-Ray 3.1 since version
3.0.


1.6.1     Media Replaces Halo & Atmosphere
The keywords halo and atmosphere have been totally eliminated
with no backwards compatibility of any kind provided. They have
been replaced by a new feature called media.  At the scene level,
media acts as atmospheric media for fog, haze, dust, etc.  On
objects, media is not part of texture like halo was. Object media
is now part of a new feature called interior.  Media is not just
a rename for halo.  It is a new model with some similar features
of halo.  BECAUSE POV-Ray 3.1 DISCONTINUES SOME 3.0 FEATURES YOU
MAY WISH TO KEEP 3.0 TO RENDER OLDER SCENES.

Any pattern type (bozo, wood, dents, etc.) may be used as a
density function for media.

New patterns spherical, cylindrical, planar, and boxed added for
pigment, normal, texture, and density.

New wave types cubic_wave and poly_wave Float have been added.

New object modifier interior{...}.  Interior contains information
about the interior of the object which was formerly contained in
the finish and halo parts of a texture. Interior items are no
longer part of the texture.  Instead, they attach directly to the
objects. The finish items moved are ior, caustic, fade_power, and
fade_distance.  The refraction keyword is no longer necessary.
Any ior other than 1.0 turns on refraction.  These 5 finish
keywords which are now part of interior will still work in finish
but will generate warnings.  Some obscure texture_map statements
with varying ior will not work.

Added reflection_exponent Float to finish to give more realistic
reflection of very bright objects.


1.6.2     New #macro Feature
Add fully recursive and parameterized #macro directive.  Define
like this...

  #macro MyMacro (P1,P2,P3)   ...  #end
Invoke like this...

  MyMacro (5,x*5,MyTexture)
Note no '#' sign precedes invocation.  Macros can be invoked
almost anywhere. Parameters must be identifiers or any item that
can be declared, MyMacro(pigment{Green},MyObject) for example.

Added #local IDENTIFIER= STATEMENT as alternative to #declare to
create temporary local identifier in macros or include files.


1.6.3     Arrays Added
Added multi-dimension arrays

  #declare MyArray=array[20]
 or

  #local PrivateArray=array[30]
 or

  #declare Rows=5; #declare Cols=4;
  #declare Table=array[Rows][Cols]
Added optional initializer syntax for arrays.

 #declare MyArray=array[2][3]{{1,2,3},{4,5,6}}
Subscripts start at 0.  Anything that can be declared may be in
an array. Arrays are initialized as null.  You must later fill
each element with values.

Added float functions for arrays.  Given #declare MyArray =
array[4][5] then dimensions(MyArray) is 2 and
dimension_size(MyArray,2) is 5.


1.6.4     File I/O and other Directives
Added #fopen, #fclose, #read, and #write directives for user text
files.

Added #undef identifier directive.  Un-declares previously
declared identifier.  Works on locals or globals.

Added requirement that any directive which can end in a float or
expression must be terminated by a semi-colon.  Specifically this
means any #declare or #local of float, vector or color or the
#version directive.


1.6.5     Additional New Features
Added Bezier splines to lathe and prism. The spline is made of
segments having four points each. Thus there are always four
times the number of  segments in a prism or lathe. A four point
Bezier spline uses 3rd order Bernstein blending functions which
are sufficient for smooth curves.

Added float constant clock_delta returns time between frames.




2.0    Beginning Tutorial
The beginning tutorial explains step by step how to use POV-Ray's
scene description language to create own your scenes. The use of
almost every feature of POV-Ray's language is explained in
detail. We will learn basic things like placing cameras and light
sources. We will also learn how to create a large variety of
objects and how to assign different textures to them. The more
sophisticated features like radiosity, interior, media and
atmospheric effects will be explained in detail.


2.1  Our First Image
We will create the scene file for a simple picture. Since ray-
tracers thrive on spheres, that is what we will render first.


2.1.1     Understanding POV-Ray's Coordinate System
First, we have to tell POV-Ray where our camera is and where it
is looking. To do this, we use 3D coordinates. The usual
coordinate system for POV-Ray has the positive y-axis pointing
up, the positive x-axis pointing to the right, and the positive z-
axis pointing into the screen as follows:



 The left-handed coordinate system (the z-axis is pointing away)
                                
This kind of coordinate system is called a left-handed coordinate
system. If we use our left hand's fingers we can easily see why
it is called left-handed. We just point our thumb in the
direction of the positive x-axis (to the right), the index finger
in the direction of the positive y-axis (straight up) and the
middle finger in the positive z-axis direction (forward). We can
only do this with our left hand. If we had used our right hand we
would not have been able to point the middle finger in the
correct direction.

The left hand can also be used to determine rotation directions.
To do this we must perform the famous "Computer Graphics
Aerobics" exercise. We hold up our left hand and point our thumb
in the positive direction of the axis of rotation. Our fingers
will curl in the positive direction of rotation. Similarly if we
point our thumb in the negative direction of the axis our fingers
will curl in the negative direction of rotation.



"Computer Graphics Aerobics" to determine the rotation direction.
                                
In the above illustration, the left hand is curling around the x-
axis. The thumb points in the positive x direction and the
fingers curl over in the positive rotation direction.

If we want to use a right-handed system, as some CAD systems and
modelers do, the right vector in the camera specification needs
to be changed. See the detailed description in "Handedness". In a
right-handed system we use our right hand for the "Aerobics".

There is some controversy over whether POV-Ray's method of doing
a right-handed system is really proper. To avoid problems we
stick with the left-handed system which is not in dispute.


2.1.2     Adding Standard Include Files
Using our personal favorite text editor, we create a file called
demo.pov. Note some versions of POV-Ray come with their own built-
in text editor which may be easier to use. We then type in the
following text. The input is case sensitive, so we have to be
sure to get capital and lowercase letters correct.

  #include "colors.inc"    // The include files contain
  #include "stones.inc"    // pre-defined scene elements
The first include statement reads in definitions for various
useful colors. The second include statement reads in a collection
of stone textures.

POV-Ray comes with many standard include files.  Others of
interest are:

  #include "textures.inc"    // pre-defined scene elements
  #include "shapes.inc"
  #include "glass.inc"
  #include "metals.inc"
  #include "woods.inc"
They read pre-defined textures, shapes, glass, metal, and wood
textures. It is a good idea to have a look through them to see a
few of the many possible shapes and textures available.

We should only include files we really need in our scene. Some of
the include files coming with POV-Ray are quite large and we
should better save the parsing time and memory if we don't need
them. In the following examples we will only use the colors.inc,
and stones.inc include files.

We may have as many include files as needed in a scene file.
Include files may themselves contain include files, but we are
limited to declaring includes nested only ten levels deep.

Filenames specified in the include statements will be searched
for in the current directory first. If it fails to find your .Inc
files in the current directory, POV-Ray searches any "library
paths" that you have specified.  Library paths are options set by
the +L command-line switch or Library_Path option. See the
chapter "Setting POV-Ray Options" for more information on library
paths.

Because it is more useful to keep include files in a separate
directory, standard installation of POV-Ray place these files in
the \povray3\include directory.  If you get an error message
saying that POV-Ray cannot open "colors.inc" or other include
files, make sure that you specify the library path properly.


2.1.3     Adding a Camera
The camera statement describes where and how the camera sees the
scene. It gives x-, y- and z-coordinates to indicate the position
of the camera and what part of the scene it is pointing at.  We
describe the coordinates using a three-part vector. A vector is
specified by putting three numeric values between a pair of angle
brackets and separating the values with commas.

We add the following camera statement to the scene.

  camera {
    location <0, 2, -3>
    look_at  <0, 1,  2>
  }
Briefly, location <0,2,-3> places the camera up two units and
back three units from the center of the ray-tracing universe
which is at <0,0,0>. By default +z is into the screen and -z is
back out of the screen.

Also look_at <0,1,2> rotates the camera to point at the
coordinates <0,1,2>. A point 1 unit up from the origin and 2
units away from the origin.  This makes it 5 units in front of
and 1 unit lower than the camera. The look_at point should be the
center of attention of our image.


2.1.4     Describing an Object
Now that the camera is set up to record the scene, let's place a
yellow sphere into the scene. We add the following to our scene
file:

  sphere {
    <0, 1, 2>, 2
    texture {
      pigment { color Yellow }
    }
  }
The first vector specifies the center of the sphere. In this
example the x coordinate is zero so it is centered left and
right. It is also at y=1 or one unit up from the origin. The z
coordinate is 2 which is five units in front of the camera, which
is at z=-3. After the center vector is a comma followed by the
radius which in this case is two units. Since the radius is half
the width of a sphere, the sphere is four units wide.


2.1.5     Adding Texture to an Object
After we have defined the location and size of the sphere, we
need to describe the appearance of the surface. The texture
statement specifies these parameters. Texture blocks describe the
color, bumpiness and finish properties of an object. In this
example we will specify the color only. This is the minimum we
must do. All other texture options except color will use default
values.

The color we define is the way we want an object to look if fully
illuminated. If we were painting a picture of a sphere we would
use dark shades of a color to indicate the shadowed side and
bright shades on the illuminated side. However ray-tracing takes
care of that for you. We only need to pick the basic color
inherent in the object and POV-Ray brightens or darkens it
depending on the lighting in the scene. Because we are defining
the basic color the object actually has rather than how it looks
the parameter is called pigment.

Many types of color patterns are available for use in a pigment
statement. The keyword color specifies that the whole object is
to be one solid color rather than some pattern of colors. We can
use one of the color identifiers previously defined in the
standard include file colors.inc.

If no standard color is available for our needs, we may define
our own color by using the color keyword followed by red, green,
and blue keywords specifying the amount of red, green and blue to
be mixed. For example a nice shade of pink can be specified by:

  color red 1.0 green 0.8 blue 0.8
The values after each keyword should be in the range from 0.0 to
2.0. Any of the three components not specified will default to 0.
A shortcut notation may also be used. The following produces the
same shade of pink:

  color rgb <1.0, 0.8, 0.8>
Colors are explained in more detail in section "Specifying
Colors".


2.1.6     Defining a Light Source
One more detail is needed for our scene. We need a light source.
Until we create one, there is no light in this virtual world.
Thus we add the line

Thus we add the line

  light_source { <2, 4, -3> color White}
to the scene file to get our first complete POV-Ray scene file as
shown below.

  #include "colors.inc"
  background { color Cyan }
  camera {
    location <0, 2, -3>
    look_at  <0, 1,  2>
  }
  sphere {
    <0, 1, 2>, 2
    texture {
      pigment { color Yellow }
    }
  }
  light_source { <2, 4, -3> color White}
The vector in the light_source statement specifies the location
of the light as two units to our right, four units above the
origin and three units back from the origin. The light source is
an invisible tiny point that emits light.  It has no physical
shape, so no texture is needed.

That's it! We close the file and render a small picture of it
using whatever methods you used for your particular platform.  If
you specified a preview display it will appear on your screen.
If you specified an output file (the default is file output on),
then POV-Ray also created a file.  Note that if you do not have
high color or true color display hardware then the preview image
may look poor but the full detail is written to the image file
regardless of the type of display.

The scene we just traced isn't quite state of the art but we will
have to start with the basics before we soon get to much more
fascinating features and scenes.


2.2  Simple Shapes
So far we have just used the sphere shape. There are many other
types of shapes that can be rendered by POV-Ray. The following
sections will describe how to use some of the more simple objects
as a replacement for the sphere used above.


2.2.1     Box Object
The box is one of the most common objects used. We try this
example in place of the sphere:

  box {
    <-1, 0,   -1>,  // Near lower left corner
    < 1, 0.5,  3>   // Far upper right corner
    texture {
      T_Stone25     // Pre-defined from stones.inc
      scale 4       // Scale by the same amount in all
                    // directions
    }
    rotate y*20     // Equivalent to "rotate <0,20,0>"
  }
In the example we can see that a box is defined by specifying the
3D coordinates of its opposite corners. The first vector is
generally  the minimum x-, y- and z-coordinates and the 2nd
vector should be the maximum x-, y- and z-values however any two
opposite corners may be used. Box objects can only be defined
parallel to the axes of the world coordinate system. We can later
rotate them to any angle. Note that we can perform simple math on
values and vectors. In the rotate parameter we multiplied the
vector identifier y by 20. This is the same as <0,1,0>*20 or
<0,20,0>.


2.2.2     Cone Object
Here's another example showing how to use a cone:

  cone {
    <0, 1, 0>, 0.3    // Center and radius of one end
    <1, 2, 3>, 1.0    // Center and radius of other end
    texture { T_Stone25 scale 4 }
  }
The cone shape is defined by the center and radius of each end.
In this example one end is at location <0,1,0> and has a radius
of 0.3 while the other end is centered at <1,2,3> with a radius
of 1. If we want the cone to come to a sharp point we must use
radius=0. The solid end caps are parallel to each other and
perpendicular to the cone axis. If we want an open cone with no
end caps we have to add the keyword open after the 2nd radius
like this:

  cone {
    <0, 1, 0>, 0.3    // Center and radius of one end
    <1, 2, 3>, 1.0    // Center and radius of other end
    open              // Removes end caps
    texture { T_Stone25 scale 4 }
  }

2.2.3     Cylinder Object
We may also define a cylinder like this:

  cylinder {
    <0, 1, 0>,     // Center of one end
    <1, 2, 3>,     // Center of other end
    0.5            // Radius
    open           // Remove end caps
    texture { T_Stone25 scale 4 }
  }

2.2.4     Plane Object
Let's try out a computer graphics standard "The Checkered Floor".
We add the following object to the first version of the demo.pov
file, the one including the sphere.

  plane { <0, 1, 0>, -1
    pigment {
      checker color Red, color Blue
    }
  }
The object defined here is an infinite plane. The vector <0,1,0>
is the surface normal of the plane (i.e. if we were standing on
the surface, the normal points straight up). The number afterward
is the distance that the plane is displaced along the normal from
the origin -- in this case, the floor is placed at y=-1 so that
the sphere at y=1, radius=2, is resting on it.

We note that even though there is no texture statement there is
an implied texture here. We might find that continually typing
statements that are nested like texture {pigment} can get to be
tiresome so POV-Ray let's us leave out the texture statement
under many circumstances. In general we only need the texture
block surrounding a texture identifier (like the T_Stone25
example above), or when creating layered textures (which are
covered later).

This pigment uses the checker color pattern and specifies that
the two colors red and blue should be used.

Because the vectors <1,0,0>, <0,1,0> and <0,0,1> are used
frequently, POV-Ray has three built-in vector identifiers x, y
and z respectively that can be used as a shorthand. Thus the
plane could be defined as:

  plane { y, -1
    pigment { ... }
  }
Note that we do not use angle brackets around vector identifiers.

Looking at the floor, we notice that the ball casts a shadow on
the floor. Shadows are calculated very accurately by the ray-
tracer, which creates precise, sharp shadows. In the real world,
penumbral or "soft" shadows are often seen. Later we will learn
how to use extended light sources to soften the shadows.


2.3  CSG Objects
Constructive Solid Geometry, or CSG, is a powerful tool to
combine primitive objects to create more complex objects as shown
in the following sections.


2.3.1     What is CSG?
CSG stands for Constructive Solid Geometry. POV-Ray allows us to
construct complex solids by combining primitive shapes in four
different ways. In the union statement, two or more shapes are
added together. With the intersection statement, two or more
shapes are combined to make a new shape that consists of the area
common to both shapes. The difference statement, an initial shape
has all subsequent shapes subtracted from it. And last not least
merge, which is like a union where the surfaces inside the union
are removed (useful in transparent CSG objects). We will deal
with each of these in detail in the next few sections.

CSG objects can be extremely complex. They can be deeply nested.
In other words there can be unions of differences or
intersections of merges or differences of intersections or even
unions of intersections of differences of merges... ad infinitum.
CSG objects are (almost always) finite objects and thus respond
to auto-bounding and can be transformed like any other POV
primitive shape.


2.3.2     CSG Union
Let's try making a simple union. Create a file called csgdemo.pov
and edit it as follows:

  #include "colors.inc"
  camera {
    location <0, 1, -10>
    look_at 0
    angle 36
  }
  light_source { <500, 500, -1000> White }
  plane { y, -1.5
    pigment { checker Green White }
  }
Let's add two spheres each translated 0.5 units along the x-axis
in each direction. We color one blue and the other red.

  sphere { <0, 0, 0>, 1
    pigment { Blue }
    translate -0.5*x
  }
  sphere { <0, 0, 0>, 1
    pigment { Red }
    translate 0.5*x
  }
We trace this file and note the results. Now we place a union
block around the two spheres. This will create a single CSG union
out of the two objects.

  union{
    sphere { <0, 0, 0>, 1
      pigment { Blue }
      translate -0.5*x
    }
    sphere { <0, 0, 0>, 1
      pigment { Red }
      translate 0.5*x
    }
  }
We trace the file again. The union will appear no different from
what each sphere looked like on its own, but now we can give the
entire union a single texture and transform it as a whole. Let's
do that now.

  union{
    sphere { <0, 0, 0>, 1
      translate -0.5*x
    }
    sphere { <0, 0, 0>, 1
      translate 0.5*x
    }
    pigment { Red }
    scale <1, .25, 1>
    rotate <30, 0, 45>
  }
We trace the file again. As we can see, the object has changed
dramatically. We experiment with different values of scale and
rotate and try some different textures.

There are many advantages of assigning only one texture to a CSG
object instead of assigning the texture to each individual
component. First, it is much easier to use one texture if our CSG
object has a lot of components because changing the objects
appearance involves changing only one single texture. Second, the
file parses faster because the texture has to be parsed only
once. This may be a great factor when doing large scenes or
animations. Third, using only one texture saves memory because
the texture is only stored once and referenced by all components
of the CSG object. Assigning the texture to all n components
means that it is stored n times.


2.3.3     CSG Intersection
Now let's use these same spheres to illustrate the next kind of
CSG object, the intersection. We change the word union to
intersection and delete the scale and rotate statements:

  intersection {
    sphere { <0, 0, 0>, 1
      translate -0.5*x
    }
    sphere { <0, 0, 0>, 1
      translate 0.5*x
    }
    pigment { Red }
  }
We trace the file and will see a lens-shaped object instead of
the two spheres. This is because an intersection consists of the
area shared by both shapes, in this case the lens-shaped area
where the two spheres overlap. We like this lens-shaped object so
we will use it to demonstrate differences.


2.3.4     CSG Difference
We rotate the lens-shaped intersection about the y-axis so that
the broad side is facing the camera.

  intersection{
    sphere { <0, 0, 0>, 1
      translate -0.5*x
    }
    sphere { <0, 0, 0>, 1
      translate 0.5*x
    }
    pigment { Red }
    rotate 90*y
  }
Let's create a cylinder and stick it right in the middle of the
lens.

  cylinder { <0, 0, -1> <0, 0, 1>, .35
    pigment { Blue }
  }
We render the scene to see the position of the cylinder. We will
place a difference block around both the lens-shaped intersection
and the cylinder like this:

  difference {
    intersection {
      sphere { <0, 0, 0>, 1
        translate -0.5*x
      }
      sphere { <0, 0, 0>, 1
        translate 0.5*x
      }
      pigment { Red }
      rotate 90*y
    }
    cylinder { <0, 0, -1> <0, 0, 1>, .35
      pigment { Blue }
    }
  }
We render the file again and see the lens-shaped intersection
with a neat hole in the middle of it where the cylinder was. The
cylinder has been subtracted from the intersection. Note that the
pigment of the cylinder causes the surface of the hole to be
colored blue. If we eliminate this pigment the surface of the
hole will be red.

OK, let's get a little wilder now. Let's declare our perforated
lens object to give it a name. Let's also eliminate all textures
in the declared object because we will want them to be in the
final union instead.

  #declare Lens_With_Hole = difference {
    intersection {
      sphere { <0, 0, 0>, 1
        translate -0.5*x
      }
      sphere { <0, 0, 0>, 1
        translate 0.5*x
      }
      rotate 90*y
    }
    cylinder { <0, 0, -1> <0, 0, 1>, .35 }
  }
Let's use a union to build a complex shape composed of copies of
this object.

  union {
    object { Lens_With_Hole translate <-.65, .65, 0> }
    object { Lens_With_Hole translate <.65, .65, 0> }
    object { Lens_With_Hole translate <-.65, -.65, 0> }
    object { Lens_With_Hole translate <.65, -.65, 0> }
    pigment { Red }
  }
We render the scene. An interesting object to be sure. But let's
try something more. Let's make it a partially-transparent object
by adding some filter to the pigment block.

  union {
    object { Lens_With_Hole translate <-.65, .65, 0> }
    object { Lens_With_Hole translate <.65, .65, 0> }
    object { Lens_With_Hole translate <-.65, -.65, 0> }
    object { Lens_With_Hole translate <.65, -.65, 0> }
    pigment { Red filter .5 }
  }
We render the file again. This looks pretty good... only... we
can see parts of each of the lens objects inside the union! This
is not good.


2.3.5     CSG Merge
This brings us to the fourth kind of CSG object, the merge.
Merges are the same as unions, but the geometry of the objects in
the CSG that is inside the merge is not traced. This should
eliminate the problem with our object. Let's try it.

  merge {
    object { Lens_With_Hole translate <-.65, .65, 0> }
    object { Lens_With_Hole translate <.65, .65, 0> }
    object { Lens_With_Hole translate <-.65, -.65, 0> }
    object { Lens_With_Hole translate <.65, -.65, 0> }
    pigment { Red filter .5 }
  }
Sure enough, it does!


2.3.6     CSG Pitfalls
There is a severe pitfall in the CSG code that we have to be
aware of.


2.3.6.1   Coincidence Surfaces
POV-Ray uses inside/outside tests to determine the points at
which a ray intersects a CSG object. A problem arises when the
surfaces of two different shapes coincide because there is no way
(due to numerical problems) to tell whether a point on the
coincident surface belongs to one shape or the other.

Look at the following example where a cylinder is used to cut a
hole in a larger box.

  difference {
    box { -1, 1 pigment { Red } }
    cylinder { -z, z, 0.5 pigment { Green } }
  }
Note that the vectors -1 and 1 in the box definition expand to <-
1,-1,-1> and <1,1,1> respectively.

If we trace this object we see red speckles where the hole is
supposed to be. This is caused by the coincident surfaces of the
cylinder and the box. One time the cylinder's surface is hit
first by a viewing ray, resulting in the correct rendering of the
hole, and another time the box is hit first, leading to a wrong
result where the hole vanishes and red speckles appear.

This problem can be avoided by increasing the size of the
cylinder to get rid of the coincidence surfaces. This is done by:

  difference {
    box { -1, 1 pigment { Red } }
    cylinder { -1.001*z, 1.001*z, 0.5 pigment { Green } }
  }
In general we have to make the subtracted object a little bit
larger in a CSG difference. We just have to look for coincident
surfaces and increase the subtracted object appropriately to get
rid of those surfaces.

The same problem occurs in CSG intersections and is also avoided
by scaling some of the involved objects.


2.4  Advanced Shapes
After we have gained some experience with the simpler shapes
available in POV-Ray it is time to go on to the more advanced,
thrilling shapes.

We should be aware that the shapes described below are not
trivial to understand. We needn't be worried though if we do not
know how to use them or how they work. We just try the examples
and play with the features described in the reference chapter.
There is nothing better than learning by doing.

You may wish to skip to the chapter "Simple Texture Options"
before proceeding with these advanced shapes.


2.4.1     Bicubic Patch Object
Bicubic or Bezier patches are useful surface representations
because they allow an easy definition of surfaces using only a
few control points. The control points serve to determine the
shape of the patch. Instead of defining the vertices of
triangles, we simply give the coordinates of the control points.
A single patch has 16 control points, one at each corner, and the
rest positioned to divide the patch into smaller sections. For
ray-tracing (or rendering) the patches are approximated using
triangles.

Bezier patches are almost always created using a third party
modeler so for this tutorial, we will use moray (any other
modeler that supports Bezier patches and POV-Ray can also be
used).  We will use moray only to create the patch itself, not
the other elements of the scene.

Note that moray is not included with POV-Ray.  It is a separate
shareware program that currently only runs on MS-Dos and Win95/NT
but this tutorial assumes you are using the MS-Dos version.  If
you do not have moray or are not on MS-Dos, you can still render
the sample scene described below, even though you cannot see how
moray created it. Simply type in the bicubic_patch declaration
listed below.

Bezier patches are actually very useful and, with a little
practice, some pretty amazing things can be created with them.
For our first tutorial, let's make a sort of a teepee/tent shape
using a single sheet patch.

First, we start moray and, from the main edit screen, we click on
"CREATE". We Name our object Teepee. The "CREATE BEZIER PATCH"
dialogue box will appear. We have to make sure that "SHEET" is
depressed. We click on "OK, CREATE". At the bottom of the main
edit screen, we click on "EXTENDED EDIT".

We hold the cursor over the "TOP" view and right click to make
the pop-up menu appear. We click on "MAXIMIZE". We [ALT]-drag to
zoom in a little. We click on "MARK ALL", and under the
transformation mode box, "UFRM SCL". We drag the mouse to scale
the patch until it is approximately four units wide. We click on
"TRANSLATE", and move the patch so that its center is over the
origin. We right click "MINIMIZE" and "UNMARK ALL".

We [SHIFT]-drag a box around the lower right control point to
mark it. We [ALT]-zoom into the "FRONT" view so that we can see
the patch better.  In the "FRONT" view, we "TRANSLATE" that point
10 units along the negative z-axis (we note that in MORAY z is
up). We "UNMARK ALL". We repeat this procedure for each of the
other three corner points. We make sure we remember to "UNMARK
ALL" once each point has been translated. We should have a shape
that looks as though it is standing on four pointed legs. We
"UNMARK ALL".

Working once again in the "TOP" view, we [SHIFT]-drag a box
around the four center control points to mark them. We right-
click over the "TOP" view and "MAXIMIZE". We click on "UFRM SCL"
and drag the mouse to scale the four points close together. We
[ALT]-drag to zoom closer and get them as close together as we
can. We [ALT]-drag to zoom out, right click and "MINIMIZE".

In the "FRONT" view, we "TRANSLATE" the marked points 10 units
along the positive z-axis. We "UNMARK ALL". The resulting shape
is quite interesting, was simple to model, and could not be
produced using CSG primitives. Now let's use it in a scene.

We click on "DONE" to return to the main edit screen. We note
that u_steps and v_steps are both set to 3 and flatness is set to
0.01. We leave them alone for now. We click on "FILES" and then
"SAVE SEL" (save selection). We name our new file teepee1.mdl. We
press [F3] and open teepee1.mdl. There is no need to save the
original file. When teepee1 is open, we create a quick "dummy"
texture (moray will not allow us to export data without a
texture). We use white with default finish and name it TeePeeTex.
We apply it to the object, save the file and press [CTRL-F9].
moray will create two files: teepee1.inc and teepee1.pov.

We exit moray and copy teepee1.inc and teepee1.pov into our
working directory where we are doing these tutorials.  We create
a new file called bezdemo.pov and edit it as follows:

  #include "colors.inc"
  camera {
    location <0, .1, -60>
    look_at 0
    angle 40
  }
  background { color Gray25 }  //to make the patch easier to see
  light_source { <300, 300, -700> White }
  plane { y, -12
    texture {
      pigment {
        checker
        color Green
        color Yellow
      }
    }
  }
Using a text editor, we create and declare a simple texture for
our teepee object:

  #declare TeePeeTex = texture {
    pigment {
      color rgb <1, 1, 1,>
    }
    finish {
      ambient .2
      diffuse .6
    }
  }
We paste in the bezier patch data from teepee1.pov (the
additional object keywords added by moray were removed):

  bicubic_patch {
    type 1 flatness 0.0100 u_steps 3 v_steps 3,
    <-5.174134, 5.528420, -13.211995>,
    <-1.769023, 5.528420, 0.000000>,
    <1.636088, 5.528420, 0.000000>,
    <5.041199, 5.528420, -13.003932>,
    <-5.174134, 1.862827, 0.000000>,
    <0.038471, 0.031270, 18.101474>,
    <0.036657, 0.031270, 18.101474>,
    <5.041199, 1.862827, 0.000000>,
    <-5.174134, -1.802766, 0.000000>,
    <0.038471, 0.028792, 18.101474>,
    <0.036657, 0.028792, 18.101474>,
    <5.041199, -1.802766, 0.000000>,
    <-5.174134, -5.468359, -13.070366>,
    <-1.769023, -5.468359, 0.000000>,
    <1.636088, -5.468359, 0.000000>,
    <4.974128, -5.468359, -12.801446>
    texture {
      TeePeeTex
    }
    rotate -90*x  // to orient the object to LHC
    rotate 25*y   // to see the four "legs" better
  }
We add the above rotations so that the patch is oriented to POV-
Ray's left-handed coordinate system (remember the patch was made
in moray in a right handed coordinate system), so we can see all
four legs. Rendering this at 200x150 -a we see pretty much what
we expect, a white teepee over a green and yellow checkered
plane. Let's take a little closer look. We render it again, this
time at 320x200.

Now we see that something is amiss. There appears to be sharp
angling, almost like facing, especially near the top. This is
indeed a kind of facing and is due to the u_steps and v_steps
parameters. Let's change these from 3 to 4 and see what happens.

That's much better, but it took a little longer to render. This
is an unavoidable tradeoff. If we want even finer detail, we must
use a u_steps and v_steps value of 5 and set flatness to 0. But
we must expect to use lots of memory and an even longer tracing
time.

Well, we can't just leave this scene without adding a few items
just for interest. We declare the patch object and scatter a few
of them around the scene:

  #declare TeePee = bicubic_patch {
    type 1 flatness 0.0100 u_steps 3 v_steps 3,
    <-5.174134, 5.528420, -13.211995>,
    <-1.769023, 5.528420, 0.000000>,
    <1.636088, 5.528420, 0.000000>,
    <5.041199, 5.528420, -13.003932>,
    <-5.174134, 1.862827, 0.000000>,
    <0.038471, 0.031270, 18.101474>,
    <0.036657, 0.031270, 18.101474>,
    <5.041199, 1.862827, 0.000000>,
    <-5.174134, -1.802766, 0.000000>,
    <0.038471, 0.028792, 18.101474>,
    <0.036657, 0.028792, 18.101474>,
    <5.041199, -1.802766, 0.000000>,
    <-5.174134, -5.468359, -13.070366>,
    <-1.769023, -5.468359, 0.000000>,
    <1.636088, -5.468359, 0.000000>,
    <4.974128, -5.468359, -12.801446>
    texture {
      TeePeeTex
     }
     rotate -90*x // to orient the object to LHC
     rotate 25*y  // to see the four "legs" better
  }
  object { TeePee }
  object { TeePee translate <8, 0, 8> }
  object { TeePee translate <-9, 0, 9> }
  object { TeePee translate <18, 0, 24> }
  object { TeePee translate <-18, 0, 24> }
That looks good. Let's do something about that boring gray
background. We delete the background declaration and replace it
with:

  plane { y, 500
    texture {
      pigment { SkyBlue }
      finish { ambient 1 diffuse 0}
     }
     texture {
       pigment {
         bozo
         turbulence .5
         color_map {
           [0 White]
           [1 White filter 1]
         }
       }
       finish { ambient 1 diffuse 0 }
       scale <1000, 250, 250>
       rotate <5, 45, 0>
    }
  }
This adds a pleasing cirrus-cloud filled sky. Now, let's change
the checkered plane to rippled sand dunes:

  plane {y,-12
    texture {
      pigment {
        color <.85, .5, .15>
      }
      finish {
        ambient .25
        diffuse .6
        crand .5
      }
      normal {
        ripples .35
        turbulence .25
        frequency 5
      }
      scale 10
      translate 50*x
    }
  }
We render this. Not bad! Let's just add one more element.  Let's
place a golden egg under each of the teepees. And since this is a
bezier patch tutorial, let's make the eggs out of bezier patches.

We return to moray and create another bezier patch. We name it
Egg1 and select "CYLINDRICAL 2 - PATCH" from the "CREATE BEZIER
PATCH" dialogue box. We click on "EXTENDED EDIT". We "MARK ALL"
and rotate the patch so that the cylinder lays on its side. We
"UNMARK ALL". In the "FRONT" view, we [SHIFT]-drag a box around
the four points on the right end to mark them. In the "SIDE"
view, we right click and "MAXIMIZE".  We [ALT]-drag to zoom in a
little closer. We "UFRM SCL" the points together as close as
possible. We zoom in closer to get them nice and tight. We zoom
out, right click and "MINIMIZE".

We click on "TRANSLATE" and drag the points to the left so that
they are aligned on the z-axis with the next group of four
points. This should create a blunt end to the patch. We repeat
this procedure for the other end. We "UNMARK ALL".

In the "FRONT" view, the control grid should be a rectangle now
and the patch should be an ellipsoid. We [SHIFT]-drag a box
around the upper right corner of the control grid to mark those
points. We then [SHIFT]-drag a box around the lower right corner
to mark those points as well. In the "SIDE" view, we "UFRM SCL"
the points apart a little to make that end of the egg a little
wider than the other. We "UNMARK ALL".

The egg may need a little proportional adjustment. We should be
able to "MARK ALL" and "LOCAL SCL" in the three views until we
get it to look like an egg. When we are satisfied that it does,
we "UNMARK ALL" and click on done. Learning from our teepee
object, we now go ahead and change u_steps and v_steps to 4.

We create a dummy texture, white with default finish, name it
EggTex and apply it to the egg. From the FILES menu, we "SAVE
SEL" to filename egg1.mdl. We load this file and export ([CTRL
F9]). We exit moray and copy the files egg1.inc and egg1.pov into
our working directory.

Back in bezdemo.pov, we create a nice, shiny gold texture:

  #declare EggTex = texture {
    pigment { BrightGold }
    finish {
      ambient .1
      diffuse .4
      specular 1
      roughness 0.001
      reflection .5
      metallic
    }
  }
And while we're at it, let's dandy up our TeePeeTex texture:

  #declare TeePeeTex = texture {
    pigment { Silver }
    finish {
      ambient .1
      diffuse .4
      specular 1
      roughness 0.001
      reflection .5
      metallic
    }
  }
Now we paste in our egg patch data and declare our egg:

  #declare Egg = union { // Egg1
    bicubic_patch {
      type 1 flatness 0.0100 u_steps 4 v_steps 4,
      <2.023314, 0.000000, 4.355987>,
      <2.023314, -0.000726, 4.355987>,
      <2.023312, -0.000726, 4.356867>,
      <2.023312, 0.000000, 4.356867>,
      <2.032037, 0.000000, 2.734598>,
      <2.032037, -1.758562, 2.734598>,
      <2.027431, -1.758562, 6.141971>,
      <2.027431, 0.000000, 6.141971>,
      <-1.045672, 0.000000, 3.281572>,
      <-1.045672, -1.758562, 3.281572>,
      <-1.050279, -1.758562, 5.414183>,
      <-1.050279, 0.000000, 5.414183>,
      <-1.044333, 0.000000, 4.341816>,
      <-1.044333, -0.002947, 4.341816>,
      <-1.044341, -0.002947, 4.345389>,
      <-1.044341, 0.000000, 4.345389>
    }
    bicubic_patch {
      type 1 flatness 0.0100 u_steps 4 v_steps 4,
      <2.023312, 0.000000, 4.356867>,
      <2.023312, 0.000726, 4.356867>,
      <2.023314, 0.000726, 4.355987>,
      <2.023314, 0.000000, 4.355987>,
      <2.027431, 0.000000, 6.141971>,
      <2.027431, 1.758562, 6.141971>,
      <2.032037, 1.758562, 2.734598>,
      <2.032037, 0.000000, 2.734598>,
      <-1.050279, 0.000000, 5.414183>,
      <-1.050279, 1.758562, 5.414183>,
      <-1.045672, 1.758562, 3.281572>,
      <-1.045672, 0.000000, 3.281572>,
      <-1.044341, 0.000000, 4.345389>,
      <-1.044341, 0.002947, 4.345389>,
      <-1.044333, 0.002947, 4.341816>,
      <-1.044333, 0.000000, 4.341816>
    }
    texture { EggTex }
    translate <0.5, 0, -5>  // centers the egg around the origin
    translate -9.8*y        // places the egg on the ground
  }
We now place a copy of the egg under each teepee. This should
require only the x- and z-coordinates of each teepee to be
changed:

  object { Egg }
  object { Egg translate <8, 0, 8> }
  object { Egg translate <-9, 0, 9> }
  object { Egg translate <18, 0, 24> }
  object { Egg translate <-18, 0, 24> }
                                
                                
           Scene build with different Bezier patches.
                                
We render this at low resolution such as 320x240. Everything
looks good so we run it again at 640x480.  Now we see that there
is still some facing near the top of the teepees and on the eggs
as well. The only solution is to raise u_steps and v_steps from 4
to 5 and set flatness to 0 for all our bezier objects. We make
the changes and render it again at 640x480.  The facets are gone.


2.4.2     Blob Object
Blobs are described as spheres and cylinders covered with "goo"
which stretches to smoothly join them (see section "Blob"). Ideal
for modeling atoms and molecules, blobs are also powerful tools
for creating many smooth flowing "organic" shapes.

A slightly more mathematical way of describing a blob would be to
say that it is one object made up of two or more component
pieces. Each piece is really an invisible field of force which
starts out at a particular strength and falls off smoothly to
zero at a given radius. Where ever these components overlap in
space, their field strength gets added together (and yes, we can
have negative strength which gets subtracted out of the total as
well). We could have just one component in a blob, but except for
seeing what it looks like there is little point, since the real
beauty of blobs is the way the components interact with one
another.

Let us take a simple example blob to start. Now, in fact there
are a couple different types of components but we will look at
them a little later. For the sake of a simple first example, let
us just talk about spherical components. Here is a sample POV-Ray
code showing a basic camera, light, and a simple two component
blob (this scene is called blobdem1.pov):

  #include "colors.inc"
  background{White}
  camera {
    angle 15
    location <0,2,-10>
    look_at <0,0,0>
  }
  light_source { <10, 20, -10> color White }
  blob {
    threshold .65
    sphere { <.5,0,0>, .8, 1 pigment {Blue} }
    sphere { <-.5,0,0>,.8, 1 pigment {Pink} }
    finish { phong 1 }
  }
                                
                                
                    A simple, two-part blob.
                                
The threshold is simply the overall strength value at which the
blob becomes visible. Any points within the blob where the
strength matches the threshold exactly form the surface of the
blob shape. Those less than the threshold are outside and those
greater than are inside the blob.

We note that the spherical component looks a lot like a simple
sphere object. We have the sphere keyword, the vector
representing the location of the center of the sphere and the
float representing the radius of the sphere. But what is that
last float value? That is the individual strength of that
component. In a spherical component, that is how strong the
component's field is at the center of the sphere. It will fall
off in a linear progression until it reaches exactly zero at the
radius of the sphere.

Before we render this test image, we note that we have given each
component a different pigment. POV-Ray allows blob components to
be given separate textures. We have done this here to make it
clearer which parts of the blob are which. We can also texture
the whole blob as one, like the finish statement at the end,
which applies to all components since it appears at the end,
outside of all the components. We render the scene and get a
basic kissing spheres type blob.

The image we see shows the spheres on either side, but they are
smoothly joined by that bridge section in the center. This bridge
represents where the two fields overlap, and therefore stay above
the threshold for longer than elsewhere in the blob. If that is
not totally clear, we add the following two objects to our scene
and re-render (see file blobdem2.pov). We note that these are
meant to be entered as separate sphere objects, not more
components in the blob.

  sphere { <.5,0,0>, .8
    pigment { Yellow transmit .75 }
  }
  sphere { <-.5,0,0>, .8
    pigment { Green transmit .75 }
  }
                                
                                
             The spherical components made visible.
                                
Now the secrets of the kissing spheres are laid bare. These semi-
transparent spheres show where the components of the blob
actually are. If we have not worked with blobs before, we might
be surprised to see that the spheres we just added extend way
farther out than the spheres that actually show up on the blobs.
That of course is because our spheres have been assigned a
starting strength of one, which gradually fades to zero as we
move away from the sphere's center. When the strength drops below
the threshold (in this case 0.65) the rest of the sphere becomes
part of the outside of the blob and therefore is not visible.

See the part where the two transparent spheres overlap? We note
that it exactly corresponds to the bridge between the two
spheres. That is the region where the two components are both
contributing to the overall strength of the blob at that point.
That is why the bridge appears: that region has a high enough
strength to stay over the threshold, due to the fact that the
combined strength of two spherical components is overlapping
there.


2.4.2.1   Component Types and Other New Features
The shape shown so far is interesting, but limited. POV-Ray has a
few extra tricks that extend its range of usefulness however. For
example, as we have seen, we can assign individual textures to
blob components, we can also apply individual transformations
(translate, rotate and scale) to stretch, twist, and squash
pieces of the blob as we require. And perhaps most interestingly,
the blob code has been extended to allow cylindrical components.

Before we move on to cylinders, it should perhaps be mentioned
that the old style of components used in previous versions of POV-
Ray still work. Back then, all components were spheres, so it was
not necessary to say sphere or cylinder. An old style component
had the form:

  component Strength, Radius, <Center>
This has the same effect as a spherical component, just as we
already saw above. This is only useful for backwards
compatibility. If we already have POV-Ray files with blobs from
earlier versions, this is when we would need to recognize these
components. We note that the old style components did not put
braces around the strength, radius and center, and of course, we
cannot independently transform or texture them.  Therefore if we
are modifying an older work into a new version, it may arguably
be of benefit to convert old style components into spherical
components anyway.

Now for something new and different: cylindrical components. It
could be argued that all we ever needed to do to make a roughly
cylindrical portion of a blob was string a line of spherical
components together along a straight line. Which is fine, if we
like having extra to type, and also assuming that the cylinder
was oriented along an axis.  If not, we would have to work out
the mathematical position of each component to keep it is a
straight line. But no more! Cylindrical components have arrived.

We replace the blob in our last example with the following and re-
render. We can get rid of the transparent spheres too, by the
way.

  blob {
    threshold .65
    cylinder { <-.75,-.75,0>, <.75,.75,0>, .5, 1 }
    pigment { Blue }
    finish { phong 1 }
  }
We only have one component so that we can see the basic shape of
the cylindrical component. It is not quite a true cylinder - more
of a sausage shape, being a cylinder capped by two hem-spheres.
We think of it as if it were an array of spherical components all
closely strung along a straight line.

As for the component declaration itself: simple, logical, exactly
as we would expect it to look (assuming we have been awake so
far): it looks pretty much like the declaration of a cylinder
object, with vectors specifying the two endpoints and a float
giving the radius of the cylinder. The last float, of course, is
the strength of the component. Just as with spherical components,
the strength will determine the nature and degree of this
component's interaction with its fellow components. In fact, next
let us give this fellow something to interact with, shall we?


2.4.2.2   Complex Blob Constructs and Negative Strength
Beginning a new POV-Ray file called blobdem3.pov, we enter this
somewhat more complex example:

  #include "colors.inc"
  background{White}
  camera {
    angle 20
    location<0,2,-10>
    look_at<0,0,0>
  }
  light_source { <10, 20, -10> color White }
  blob {
    threshold .65
    sphere { <-.23,-.32,0>,.43, 1 scale <1.95,1.05,.8> }   //palm
    sphere { <+.12,-.41,0>,.43, 1 scale <1.95,1.075,.8> }  //palm
    sphere { <-.23,-.63,0>, .45, .75 scale <1.78, 1.3,1> }
//midhand
    sphere { <+.19,-.63,0>, .45, .75 scale <1.78, 1.3,1> }
//midhand
    sphere { <-.22,-.73,0>, .45, .85 scale <1.4, 1.25,1> } //heel
    sphere { <+.19,-.73,0>, .45, .85 scale <1.4, 1.25,1> } //heel
    cylinder { <-.65,-.28,0>, <-.65,.28,-.05>, .26, 1 }
//lower pinky
    cylinder { <-.65,.28,-.05>, <-.65, .68,-.2>, .26, 1 }
//upper pinky
    cylinder { <-.3,-.28,0>, <-.3,.44,-.05>, .26, 1 }
//lower ring
    cylinder { <-.3,.44,-.05>, <-.3, .9,-.2>, .26, 1 }
//upper ring
    cylinder { <.05,-.28,0>, <.05, .49,-.05>, .26, 1 }
//lower middle
    cylinder { <.05,.49,-.05>, <.05, .95,-.2>, .26, 1 }
//upper middle
    cylinder { <.4,-.4,0>, <.4, .512, -.05>, .26, 1 }
//lower index
    cylinder { <.4,.512,-.05>, <.4, .85, -.2>, .26, 1 }
//upper index
    cylinder { <.41, -.95,0>, <.85, -.68, -.05>, .25, 1 }
//lower thumb
    cylinder { <.85,-.68,-.05>, <1.2, -.4, -.2>, .25, 1 }
//upper thumb
    pigment { Flesh }
  }
                                
                                
                     A hand made with blobs.
                                
As we can guess from the comments, we are building a hand here.
After we render this image, we can see there are a few problems
with it. The palm and heel of the hand would look more realistic
if we used a couple dozen smaller components rather than the half
dozen larger ones we have used, and each finger should have three
segments instead of two, but for the sake of a simplified
demonstration, we can overlook these points. But there is one
thing we really need to address here: This poor fellow appears to
have horrible painful swelling of the joints!

A review of what we know of blobs will quickly reveal what went
wrong. The joints are places where the blob components overlap,
therefore the combined strength of both components at that point
causes the surface to extend further out, since it stays over the
threshold longer. To fix this, what we need are components
corresponding to the overlap region which have a negative
strength to counteract part of the combined field strength. We
add the following components to our blob (see file blobdem4.pov).

  sphere { <-.65,.28,-.05>, .26, -1 } //counteract pinky knuckle
bulge
  sphere { <-.65,-.28,0>, .26, -1 }   //counteract pinky palm
bulge
  sphere { <-.3,.44,-.05>, .26, -1 }  //counteract ring knuckle
bulge
  sphere { <-.3,-.28,0>, .26, -1 }    //counteract ring palm
bulge
  sphere { <.05,.49,-.05>, .26, -1 }  //counteract middle knuckle
bulge
  sphere { <.05,-.28,0>, .26, -1 }    //counteract middle palm
bulge
  sphere { <.4,.512,-.05>, .26, -1 }  //counteract index knuckle
bulge
  sphere { <.4,-.4,0>, .26, -1 }      //counteract index palm
bulge
  sphere { <.85,-.68,-.05>, .25, -1 } //counteract thumb knuckle
bulge
  sphere { <.41,-.7,0>, .25, -.89 }   //counteract thumb heel
bulge
                                
                                
              The hand without the swollen joints.
                                
Much better! The negative strength of the spherical components
counteracts approximately half of the field strength at the
points where to components overlap, so the ugly, unrealistic (and
painful looking) bulging is cut out making our hand considerably
improved. While we could probably make a yet more realistic hand
with a couple dozen additional components, what we get this time
is a considerable improvement. Any by now, we have enough basic
knowledge of blob mechanics to make a wide array of smooth,
flowing organic shapes!


2.4.3     Height Field Object
A height_field is an object that has a surface that is determined
by the color value or palette index number of an image designed
for that purpose. With height fields, realistic mountains and
other types of terrain can easily be made. First, we need an
image from which to create the height field. It just so happens
that POV-Ray is ideal for creating such an image.

We make a new file called image.pov and edit it to contain the
following:

  #include "colors.inc"
  global_settings {
    assumed_gamma 2.2
    hf_gray_16
  }
The hf_gray_16 keyword causes the output to be in a special 16
bit grayscale that is perfect for generating height fields. The
normal 8 bit output will lead to less smooth surfaces.

Now we create a camera positioned so that it points directly down
the z-axis at the origin.

  camera {
    location <0, 0, -10>
    look_at 0
  }
We then create a plane positioned like a wall at z=0. This plane
will completely fill the screen. It will be colored with white
and gray wrinkles.

  plane { z, 10
    pigment {
      wrinkles
      color_map {
       [0 0.3*White]
       [1 White]
      }
    }
  }
Finally, create a light source.

  light_source { <0, 20, -100> color White }
We render this scene at 640x480 +A0.1 +FT. We will get an image
that will produce an excellent height field. We create a new file
called hfdemo.pov and edit it as follows:

  #include "colors.inc"
We add a camera that is two units above the origin and ten units
back ...

  camera{
    location <0, 2, -10>
    look_at 0
    angle 30
  }
... and a light source.

  light_source{ <1000,1000,-1000> White }
Now we add the height field. In the following syntax, a Targa
image file is specified, the height field is smoothed, it is
given a simple white pigment, it is translated to center it
around the origin and it is scaled so that it resembles mountains
and fills the screen.

  height_field {
    tga "image.tga"
    smooth
    pigment { White }
    translate <-.5, -.5, -.5>
    scale <17, 1.75, 17>
  }
We save the file and render it at 320x240 -A. Later, when we are
satisfied that the height field is the way we want it, we render
it at a higher resolution with anti-aliasing.

                                
                                
         A height field created completely with POV-Ray.
                                
Wow! The Himalayas have come to our computer screen!


2.4.4     Lathe Object
In the real world, lathe refers to a process of making patterned
rounded shapes by spinning the source material in place and
carving pieces out as it turns. The results can be elaborate,
smoothly rounded, elegant looking artifacts such as table legs,
pottery, etc. In POV-Ray, a lathe object is used for creating
much the same kind of items, although we are referring to the
object itself rather than the means of production.

Here is some source for a really basic lathe (called
lathdem1.pov).

  #include "colors.inc"
  background{White}
  camera {
    angle 10
    location <1, 9, -50>
    look_at <0, 2, 0>
  }
  light_source {
    <20, 20, -20> color White
  }
  lathe {
    linear_spline
    6,
    <0,0>, <1,1>, <3,2>, <2,3>, <2,4>, <0,4>
    pigment { Blue }
    finish {
      ambient .3
      phong .75
    }
  }
                                
                                
                     A simple lathe object.
                                
We render this, and what we see is a fairly simply type of lathe,
which looks like a child's top. Let's take a look at how this
code produced the effect.

First, a set of six points are declared which the raytracer
connects with lines. We note that there are only two components
in the vectors which describe these points. The lines that are
drawn are assumed to be in the x-y-plane, therefore it is as if
all the z-components were assumed to be zero. The use of a two-
dimensional vector is mandatory (Attempting to use a 3D vector
would trigger an error... with one exception, which we will
explore later in the discussion of splines).

Once the lines are determined, the ray-tracer rotates this line
around the y-axis, and we can imagine a trail being left through
space as it goes, with the surface of that trail being the
surface of our object.

The specified points are connected with straight lines because we
used the linear_spline keyword. There are other types of splines
available with the lathe, which will result in smooth curving
lines, and even rounded curving points of transition, but we will
get back to that in a moment.

First, we would like to digress a moment to talk about the
difference between a lathe and a surface of revolution object
(SOR). The SOR object, described in a separate tutorial, may seem
terribly similar to the lathe at first glance. It too declares a
series of points and connects them with curving lines and then
rotates them around the y-axis. The lathe has certain advantages,
such as different kinds of splines, linear, quadratic and cubic,
and one more thing:

The simpler mathematics used by a SOR doesn't allow the curve to
double back over the same y-coordinates, thus, if using a SOR,
any sudden twist which cuts back down over the same heights that
the curve previously covered will trigger an error. For example,
suppose we wanted a lathe to arc up from <0,0> to <2,2>, then to
dip back down to <4,0>. Rotated around the y-axis, this would
produce something like a gelatin mold - a rounded semi torus,
hollow in the middle. But with the SOR, as soon as the curve
doubled back on itself in the y-direction, it would become an
illegal declaration.

Still, the SOR has one powerful strong point: because it uses
simpler order mathematics, it generally tends to render faster
than an equivalent lathe. So in the end, its a matter of: we use
a SOR if its limitations will allow, but when we need a more
flexible shape, we go with the lathe instead.


2.4.4.1   Understanding The Concept of Splines
It would be helpful, in order to understand splines, if we had a
sort of Spline Workshop where we could practice manipulating
types and points of splines and see what the effects were like.
So let's make one! Now that we know how to create a basic lathe,
it will be easy (see file lathdem2.pov):

  #include "colors.inc"
  camera {
    orthographic
    up <0, 5, 0>
    right <5, 0, 0>
    location <2.5, 2.5, -100>
    look_at <2.5, 2.5, 0>
  }
  /* set the control points to be used */
  #declare Red_Point    = <1.00, 0.00, 0>;
  #declare Orange_Point = <1.75, 1.00, 0>;
  #declare Yellow_Point = <2.50, 2.00, 0>;
  #declare Green_Point  = <2.00, 3.00, 0>;
  #declare Blue_Point   = <1.50, 4.00, 0>;
  /* make the control points visible */
  cylinder { Red_Point, Red_Point - 20*z, .1
    pigment { Red }
    finish { ambient 1 }
  }
  cylinder { Orange_Point, Orange_Point - 20*z, .1
    pigment { Orange }
    finish { ambient 1 }
  }
  cylinder { Yellow_Point, Yellow_Point - 20*z, .1
    pigment { Yellow }
    finish { ambient 1 }
  }
  cylinder { Green_Point, Green_Point - 20*z, .1
    pigment { Green }
    finish { ambient 1 }
  }
  cylinder { Blue_Point, Blue_Point- 20*z, .1
    pigment { Blue }
    finish { ambient 1 }
  }
  /* something to make the curve show up */
  lathe {
    linear_spline
    5,
    Red_Point,
    Orange_Point,
    Yellow_Point,
    Green_Point,
    Blue_Point
    pigment { White }
    finish { ambient 1 }
  }
                                
                                
                   A simple "Spline Workshop".
                                
Now, we take a deep breath. We know that all looks a bit weird,
but with some simple explanations, we can easily see what all
this does.

First, we are using the orthographic camera. If we haven't read
up on that yet, a quick summary is: it renders the scene flat,
eliminating perspective distortion so that in a side view, the
objects look like they were drawn on a piece of graph paper (like
in the side view of a modeler or CAD package). There are several
uses for this practical new type of camera, but here it is
allowing us to see our lathe and cylinders edge on, so that what
we see is almost like a cross section of the curve which makes
the lathe, rather than the lathe itself. To further that effect,
we eliminated shadowing with the ambient 1 finish, which of
course also eliminates the need for lighting. We have also
positioned this particular side view so that <0,0> appears at the
lower left of our scene.

Next, we declared a set of points. We note that we used 3D
vectors for these points rather than the 2D vectors we expect in
a lathe. That's the exception we mentioned earlier. When we
declare a 3D point, then use it in a lathe, the lathe only uses
the first two components of the vector, and whatever is in the
third component is simply ignored. This is handy here, since it
makes this example possible.

Next we do two things with the declared points. First we use them
to place small diameter cylinders at the locations of the points
with the circular caps facing the camera. Then we re-use those
same vectors to determine the lathe. Since trying to declare a 2D
vector can have some odd results, and isn't really what our
cylinder declarations need anyway, we can take advantage of the
lathe's tendency to ignore the third component by just setting
the z-coordinate in these 3D vectors to zero.

The end result is: when we render this code, we see a white lathe
against a black background showing us how the curve we've
declared looks, and the circular ends of the cylinders show us
where along the x-y-plane our control points are. In this case,
it's very simple. The linear spline has been used so our curve is
just straight lines zig-zagging between the points. We change the
declarations of Red_Point and Blue_Point to read as follows (see
file lathdem3.pov).

  #declare Red_Point  = <2.00, 0.00, 0>;
  #declare Blue_Point = <0.00, 4.00, 0>;
                                
                                
                Moving some points of the spline.
                                
We re-render and, as we can see, all that happens is that the
straight line segments just move to accommodate the new position
of the red and blue points. Linear splines are so simple, we
could manipulate them in our sleep, no?

Let's try something different. First, we change the points to the
following (see file lathdem4.pov).

  #declare Red_Point    = <1.00, 0.00, 0>;
  #declare Orange_Point = <2.00, 1.00, 0>;
  #declare Yellow_Point = <3.50, 2.00, 0>;
  #declare Green_Point  = <2.00, 3.00, 0>;
  #declare Blue_Point   = <1.50, 4.00, 0>;
                                
                                
                    A quadratic spline lathe.
                                
We then go down to the lathe declaration and change linear_spline
to quadratic_spline. We re-render and what do we have?  Well,
there's a couple of things worthy of note this time. First, we
will see that instead of straight lines we have smooth arcs
connecting the points. These arcs are made from quadratic curves,
so our lathe looks much more interesting this time. Also,
Red_Point is no longer connected to the curve. What happened?

Well, while any two points can determine a straight line, it
takes three to determine a quadratic curve. POV-Ray looks not
only to the two points to be connected, but to the point
immediately preceding them to determine the formula of the
quadratic curve that will be used to connect them. The problem
comes in at the beginning of the curve. Beyond the first point in
the curve there is no previous point. So we need to declare one.
Therefore, when using a quadratic spline, we must remember that
the first point we specify is only there so that POV-Ray can
determine what curve to connect the first two points with. It
will not show up as part of the actual curve.

There's just one more thing about this lathe example. Even though
our curve is now put together with smooth curving lines, the
transitions between those lines is... well, kind of choppy, no?
This curve looks like the lines between each individual point
have been terribly mismatched. Depending on what we are trying to
make, this could be acceptable, or, we might long for a more
smoothly curving shape. Fortunately, if the latter is true, we
have another option.

The quadratic spline takes longer to render than a linear spline.
The math is more complex. Still longer needs the cubic spline,
yet, for a really smoothed out shape, this is the only way to go.
We go back into our example, and simply replace quadratic_spline
with cubic_spline (see file lathdem5.pov). We render one more
time, and take a look at what we have.

                                
                                
                      A cubic spline lathe.
                                
While a quadratic spline takes three points to determine the
curve, a cubic needs four. So, as we might expect, Blue_Point has
now dropped out of the curve, just as Red_Point did, as the first
and last points of our curve are now only control points for
shaping the curves between the remaining points. But look at the
transition from Orange_Point to Yellow_Point and then back to
Green_Point. Now, rather than looking mismatched, our curve
segments look like one smoothly joined curve.

The concept of splines is a handy and necessary one, which will
be seen again in the prism and polygon objects. But with a little
tinkering we can quickly get a feel for working with them.


2.4.5     Mesh Object
Mesh objects are very useful because they allow us to create
objects containing hundreds or thousands of triangles. Compared
to a simple union of triangles the mesh object stores the
triangles more efficiently. Copies of mesh objects need only a
little additional memory because the triangles are stored only
once.

Almost every object can be approximated using triangles but we
may need a lot of triangles to create more complex shapes. Thus
we will only create a very simple mesh example. This example will
show a very useful feature of the triangles meshes though: a
different texture can be assigned to each triangle in the mesh.

Now let's begin. We will create a simple box with differently
colored sides. We create an empty file called meshdemo.pov and
add the following lines.

  camera {
    location <20, 20, -50>
    look_at <0, 5, 0>
  }
  light_source { <50, 50, -50> color rgb<1, 1, 1> }
  #declare Red = texture {
    pigment { color rgb<0.8, 0.2, 0.2> }
    finish { ambient 0.2 diffuse 0.5 }
  }
  #declare Green = texture {
    pigment { color rgb<0.2, 0.8, 0.2> }
    finish { ambient 0.2 diffuse 0.5 }
  }
  #declare Blue = texture {
    pigment { color rgb<0.2, 0.2, 0.8> }
    finish { ambient 0.2 diffuse 0.5 }
  }
We must declare all textures we want to use inside the mesh
before the mesh is created. Textures cannot be specified inside
the mesh due to the poor memory performance that would result.

Now we add the mesh object. Three sides of the box will use
individual textures while the other will use the global mesh
texture.

  mesh {
    /* top side */
    triangle { <-10, 10, -10>, <10, 10, -10>, <10, 10, 10>
      texture { Red }
    }
    triangle { <-10, 10, -10>, <-10, 10, 10>, <10, 10, 10>
      texture { Red }
    }
    /* bottom side */
    triangle { <-10, -10, -10>, <10, -10, -10>, <10, -10, 10> }
    triangle { <-10, -10, -10>, <-10, -10, 10>, <10, -10, 10> }
    /* left side */
    triangle { <-10, -10, -10>, <-10, -10, 10>, <-10, 10, 10> }
    triangle { <-10, -10, -10>, <-10, 10, -10>, <-10, 10, 10> }
    /* right side */
    triangle { <10, -10, -10>, <10, -10, 10>, <10, 10, 10>
      texture { Green }
    }
    triangle { <10, -10, -10>, <10, 10, -10>, <10, 10, 10>
      texture { Green }
    }
    /* front side */
    triangle { <-10, -10, -10>, <10, -10, -10>, <-10, 10, -10>
      texture { Blue }
    }
    triangle { <-10, 10, -10>, <10, 10, -10>, <10, -10, -10>
      texture { Blue }
    }
    /* back side */
    triangle { <-10, -10, 10>, <10, -10, 10>, <-10, 10, 10> }
    triangle { <-10, 10, 10>, <10, 10, 10>, <10, -10, 10> }
    texture {
      pigment { color rgb<0.9, 0.9, 0.9> }
      finish { ambient 0.2 diffuse 0.7 }
    }
  }
Tracing the scene at 320x240 we will see that the top, right and
front side of the box have different textures. Though this is not
a very impressive example it shows what we can do with mesh
objects. More complex examples, also using smooth triangles, can
be found under the scene directory as chesmsh.pov and
robotmsh.pov.


2.4.6     Polygon Object
The polygon object can be used to create any planar, n-sided
shapes like squares, rectangles, pentagons, hexagons, octagons,
etc.

A polygon is defined by a number of points that describe its
shape. Since polygons have to be closed the first point has to be
repeated at the end of the point sequence.

In the following example we will create the word "POV" using just
one polygon statement.

We start with thinking about the points we need to describe the
desired shape. We want the letters to lie in the x-y-plane with
the letter O being at the center. The letters extend from y=0 to
y=1. Thus we get the following points for each letter (the z
coordinate is automatically set to zero).

Letter P (outer polygon):
    <-0.8, 0.0>, <-0.8, 1.0>,
    <-0.3, 1.0>, <-0.3, 0.5>,
    <-0.7, 0.5>, <-0.7, 0.0>
Letter P (inner polygon):
    <-0.7, 0.6>, <-0.7, 0.9>,
    <-0.4, 0.9>, <-0.4, 0.6>
Letter O (outer polygon):
    <-0.25, 0.0>, <-0.25, 1.0>,
    < 0.25, 1.0>, < 0.25, 0.0>
Letter O (inner polygon):
    <-0.15, 0.1>, <-0.15, 0.9>,
    < 0.15, 0.9>, < 0.15, 0.1>
Letter V:
    <0.45, 0.0>, <0.30, 1.0>,
    <0.40, 1.0>, <0.55, 0.1>,
    <0.70, 1.0>, <0.80, 1.0>,
    <0.65, 0.0>
Both letters P and O have a hole while the letter V consists of
only one polygon. We'll start with the letter V because it is
easier to define than the other two letters.

We create a new file called polygdem.pov and add the following
text.

  camera {
    orthographic
    location <0, 0, -10>
    right 1.3 * 4/3 * x
    up 1.3 * y
    look_at <0, 0.5, 0>
  }
  light_source { <25, 25, -100> color rgb 1 }
  polygon {
    8,
    <0.45, 0.0>, <0.30, 1.0>, // Letter "V"
    <0.40, 1.0>, <0.55, 0.1>,
    <0.70, 1.0>, <0.80, 1.0>,
    <0.65, 0.0>,
    <0.45, 0.0>
    pigment { color rgb <1, 0, 0> }
  }
As noted above the polygon has to be closed by appending the
first point to the point sequence. A closed polygon is always
defined by a sequence of points that ends when a point is the
same as the first point.

After we have created the letter V we'll continue with the letter
P. Since it has a hole we have to find a way of cutting this hole
into the basic shape. This is quite easy. We just define the
outer shape of the letter P, which is a closed polygon, and add
the sequence of points that describes the hole, which is also a
closed polygon. That's all we have to do. There'll be a hole
where both polygons overlap.

In general we will get holes whenever an even number of sub-
polygons inside a single polygon statement overlap. A sub-polygon
is defined by a closed sequence of points.

The letter P consists of two sub-polygons, one for the outer
shape and one for the hole. Since the hole polygon overlaps the
outer shape polygon we'll get a hole.

After we have understood how multiple sub-polygons in a single
polygon statement work, it is quite easy to add the missing O
letter.

Finally, we get the complete word POV.

  polygon {
    30,
    <-0.8, 0.0>, <-0.8, 1.0>,    // Letter "P"
    <-0.3, 1.0>, <-0.3, 0.5>,    // outer shape
    <-0.7, 0.5>, <-0.7, 0.0>,
    <-0.8, 0.0>,
    <-0.7, 0.6>, <-0.7, 0.9>,    // hole
    <-0.4, 0.9>, <-0.4, 0.6>,
    <-0.7, 0.6>
    <-0.25, 0.0>, <-0.25, 1.0>,  // Letter "O"
    < 0.25, 1.0>, < 0.25, 0.0>,  // outer shape
    <-0.25, 0.0>,
    <-0.15, 0.1>, <-0.15, 0.9>,  // hole
    < 0.15, 0.9>, < 0.15, 0.1>,
    <-0.15, 0.1>,
    <0.45, 0.0>, <0.30, 1.0>,    // Letter "V"
    <0.40, 1.0>, <0.55, 0.1>,
    <0.70, 1.0>, <0.80, 1.0>,
    <0.65, 0.0>,
    <0.45, 0.0>
    pigment { color rgb <1, 0, 0> }
  }
                                
                                
         The word "POV" made with one polygon statement.
                                

2.4.7     Prism Object
The prism is essentially a polygon or closed curve which is swept
along a linear path. We can imagine the shape so swept leaving a
trail in space, and the surface of that trail is the surface of
our prism. The curve or polygon making up a prism's face can be a
composite of any number of sub-shapes, can use any kind of three
different splines, and can either keep a constant width as it is
swept, or slowly tapering off to a fine point on one end. But
before this gets too confusing, let's start one step at a time
with the simplest form of prism. We enter and render the
following POV code (see file prismdm1.pov).

  #include "colors.inc"
  background{White}
  camera {
    angle 20
    location <2, 10, -30>
    look_at <0, 1, 0>
  }
  light_source { <20, 20, -20> color White }
  prism {
    linear_sweep
    linear_spline
    0, // sweep the following shape from here ...
    1, // ... up through here
    7, // the number of points making up the shape ...
    <3,5>, <-3,5>, <-5,0>, <-3,-5>, <3, -5>, <5,0>, <3,5>
    pigment { Green }
  }
                                
                                
                    A hexagonal prism shape.
                                
This produces a hexagonal polygon, which is then swept from y=0
through y=1. In other words, we now have an extruded hexagon. One
point to note is that although this is a six sided figure, we
have used a total of seven points. That is because the polygon is
supposed to be a closed shape, which we do here by making the
final point the same as the first. Technically, with linear
polygons, if we didn't do this, POV-Ray would automatically join
the two ends with a line to force it to close, although a warning
would be issued. However, this only works with linear splines, so
we mustn't get too casual about those warning messages!


2.4.7.1   Teaching An Old Spline New Tricks
If we followed the section on splines covered under the lathe
tutorial (see section "Understanding The Concept of Splines"), we
know that there are two additional kinds of splines besides
linear: the quadratic and the cubic spline. Sure enough, we can
use these with prisms to make a more free form, smoothly curving
type of prism.

There is just one catch, and we should read this section
carefully to keep from tearing our hair out over mysterious "too
few points in prism" messages which keep our prism from
rendering. We can probably guess where this is heading: how to
close a non-linear spline. Unlike the linear spline, which simply
draws a line between the last and first points if we forget to
make the last point equal to the first, quadratic and cubic
splines are a little more fussy.

First of all, we remember that quadratic splines determine the
equation of the curve which connects any two points based on
those two points and the previous point, so the first point in
any quadratic spline is just control point and won't actually be
part of the curve.  What this means is: when we make our shape
out of a quadratic spline, we must match the second point to the
last, since the first point is not on the curve - it's just a
control point needed for computational purposes.

Likewise, cubic splines need both the first and last points to be
control points, therefore, to close a shape made with a cubic
spline, we must match the second point to the second from last
point. If we don't match the correct points on a quadratic or
cubic shape, that's when we will get the "too few points in
prism" error. POV-Ray is still waiting for us to close the shape,
and when it runs out of points without seeing the closure, an
error is issued.

Confused? Okay, how about an example? We replace the prism in our
last bit of code with this one (see file prismdm2.pov).

  prism {
    cubic_spline
    0, // sweep the following shape from here ...
    1, // ... up through here
    6, // the number of points making up the shape ...
    < 3, -5>, // point#1 (control point... not on curve)
    < 3,  5>, // point#2  ... THIS POINT ...
    <-5,  0>, // point#3
    < 3, -5>, // point#4
    < 3,  5>, // point#5 ... MUST MATCH THIS POINT
    <-5,  0>  // point#6 (control point... not on curve)
    pigment { Green }
  }
                                
                                
                A cubic, triangular prism shape.
                                
This simple prism produces what looks like an extruded triangle
with its corners sanded smoothly off. Points two, three and four
are the corners of the triangle and point five closes the shape
by returning to the location of point two. As for points one and
six, they are our control points, and aren't part of the shape -
they're just there to help compute what curves to use between the
other points.


2.4.7.2   Smooth Transitions
Now a handy thing to note is that we have made point one equal
point four, and also point six equals point three. Yes, this is
important. Although this prism would still be legally closed if
the control points were not what we've made them, the curve
transitions between points would not be as smooth. We change
points one and six to <4,6> and <0,7> respectively and re-render
to see how the back edge of the shape is altered (see file
prismdm3.pov).

To put this more generally, if we want a smooth closure on a
cubic spline, we make the first control point equal to the third
from last point, and the last control point equal to the third
point. On a quadratic spline, the trick is similar, but since
only the first point is a control point, make that equal to the
second from last point.


2.4.7.3   Multiple Sub-Shapes
Just as with the polygon object (see section "Polygon Object")
the prism is very flexible, and allows us to make one prism out
of several sub-prisms. To do this, all we need to do is keep
listing points after we have already closed the first shape. The
second shape can be simply an add on going off in another
direction from the first, but one of the more interesting
features is that if any even number of sub-shapes overlap, that
region where they overlap behaves as though it has been cut away
from both sub-shapes. Let's look at another example. Once again,
same basic code as before for camera, light and so forth, but we
substitute this complex prism (see file prismdm4.pov).

  prism {
    linear_sweep
    cubic_spline
    0,  // sweep the following shape from here ...
    1,  // ... up through here
    18, // the number of points making up the shape ...
    <3,-5>, <3,5>, <-5,0>, <3, -5>, <3,5>, <-5,0>, // sub-shape
#1
    <2,-4>, <2,4>, <-4,0>, <2,-4>, <2,4>, <-4,0>,  // sub-shape
#2
    <1,-3>, <1,3>, <-3,0>, <1, -3>, <1,3>, <-3,0>  // sub-shape
#3
    pigment { Green }
  }
                                
                                
        Using sub-shapes to create a more complex shape.
                                
For readability purposes, we have started a new line every time
we moved on to a new sub-shape, but the ray-tracer of course
tells where each shape ends based on whether the shape has been
closed (as described earlier). We render this new prism, and look
what we've got. It's the same familiar shape, but it now looks
like a smaller version of the shape has been carved out of the
center, then the carved piece was sanded down even smaller and
set back in the hole.

Simply, the outer rim is where only sub-shape one exists, then
the carved out part is where sub-shapes one and two overlap. In
the extreme center, the object reappears because sub-shapes one,
two, and three overlap, returning us to an odd number of
overlapping pieces. Using this technique we could make any number
of extremely complex prism shapes!


2.4.7.4   Conic Sweeps And The Tapering Effect
In our original prism, the keyword linear_sweep is actually
optional. This is the default sweep assumed for a prism if no
type of sweep is specified. But there is another, extremely
useful kind of sweep: the conic sweep. The basic idea is like the
original prism, except that while we are sweeping the shape from
the first height through the second height, we are constantly
expanding it from a single point until, at the second height, the
shape has expanded to the original points we made it from. To
give a small idea of what such effects are good for, we replace
our existing prism with this (see file prismdm4.pov):

  prism {
    conic_sweep
    linear_spline
    0, // height 1
    1, // height 2
    5, // the number of points making up the shape...
    <4,4>,<-4,4>,<-4,-4>,<4,-4>,<4,4>
    rotate <180, 0, 0>
    translate <0, 1, 0>
    scale <1, 4, 1>
    pigment { gradient y scale .2 }
  }
                                
                                
            Creating a pyramid using conic sweeping.
                                
The gradient pigment was selected to give some definition to our
object without having to fix the lights and the camera angle
right at this moment, but when we render it, we what we've
created? A horizontally striped pyramid! By now we can recognize
the linear spline connecting the four points of a square, and the
familiar final point which is there to close the spline.

Notice all the transformations in the object declaration. That's
going to take a little explanation. The rotate and translate are
easy. Normally, a conic sweep starts full sized at the top, and
tapers to a point at y=0, but of course that would be upside down
if we're making a pyramid. So we flip the shape around the x-axis
to put it right side up, then since we actually orbited around
the point, we translate back up to put it in the same position it
was in when we started.

The scale is to put the proportions right for this example. The
base is eight units by eight units, but the height (from y=1 to
y=0) is only one unit, so we've stretched it out a little. At
this point, we're probably thinking, "why not just sweep up from
y=0 to y=4 and avoid this whole scaling thing?"

That is a very important gotcha! with conic sweeps. To see what's
wrong with that, let's try and put it into practice (see file
prismdm5.pov). We must make sure to remove the scale statement,
and then replace the line which reads

  1, // height 2
with

  4, // height 2
This sets the second height at y=4, so let's re-render and see if
the effect is the same.

                                
                                
  Choosing a second height larger than one for the conic sweep.
                                
Whoa! Our height is correct, but our pyramid's base is now huge!
What went wrong here? Simple. The base, as we described it with
the points we used actually occurs at y=1 no matter what we set
the second height for. But if we do set the second height higher
than one, once the sweep passes y=1, it keeps expanding outward
along the same lines as it followed to our original base, making
the actual base bigger and bigger as it goes.

To avoid losing control of a conic sweep prism, it is usually
best to let the second height stay at y=1, and use a scale
statement to adjust the height from its unit size. This way we
can always be sure the base's corners remain where we think they
are.

That leads to one more interesting thing about conic sweeps. What
if we for some reason don't want them to taper all the way to a
point? What if instead of a complete pyramid, we want more of a
ziggurat step? Easily done. After putting the second height back
to one, and replacing our scale statement, we change the line
which reads

  0, // height 1
to

  0.251, // height 1
                                
                                
        Increasing the first height for the conic sweep.
                                
When we re-render, we see that the sweep stops short of going all
the way to its point, giving us a pyramid without a cap. Exactly
how much of the cap is cut off depends on how close the first
height is to the second height.


2.4.8     Superquadric Ellipsoid Object
Sometimes we want to make an object that does not have perfectly
sharp edges like a box does. Then, the superquadric ellipsoid
shape made by the superellipsoid is a useful object. It is
described by the simple syntax:

    superellipsoid { <Value_E, Value_N >}
Where Value_E and Value_N are float values greater than zero and
less than or equal to one. Let's make a superellipsoid and
experiment with the values of Value_E and Value_N to see what
kind of shapes we can make.

We create a file called supellps.pov and edit it as follows:

  #include "colors.inc"
  camera {
    location <10, 5, -20>
    look_at 0
    angle 15
  }
  background { color rgb <.5, .5, .5> }
  light_source { <10, 50, -100> White }
The addition of a gray background makes it a little easier to see
our object. We now type:

  superellipsoid { <.25, .25>
    pigment { Red }
  }
We save the file and trace it at 200x150 -A to see the shape. It
will look like a box, but the edges will be rounded off. Now
let's experiment with different values of Value_E and Value_N.
For the next trace, try <1, 0.2>. The shape now looks like a
cylinder, but the top edges are rounded. Now try <0.1, 1>. This
shape is an odd one! We don't know exactly what to call it, but
it is interesting. Finally, lets try <1, 1>. Well, this is more
familiar... a sphere!

There are a couple of facts about superellipsoids we should know.
First, we should not use a value of 0 for either Value_E nor
Value_N. This will cause POV-Ray to incorrectly make a black box
instead of our desired shape. Second, very small values of
Value_E and Value_N may yield strange results so they should be
avoided. Finally, the Sturmian root solver will not work with
superellipsoids.

Superellipsoids are finite objects so they respond to auto-
bounding and can be used in CSG.

Now let's use the superellipsoid to make something that would be
useful in a scene. We will make a tiled floor and place a couple
of superellipsoid objects hovering over it. We can start with the
file we have already made.

We rename it to tiles.pov and edit it so that it reads as
follows:

  #include "colors.inc"
  #include "textures.inc"
  camera {
    location <10, 5, -20>
    look_at 0
    angle 15
  }
  background { color rgb <.5, .5, .5> }
  light_source{ <10, 50, -100> White }
Note that we have added #include "textures.inc" so we can use pre-
defined textures. Now we want to define the superellipsoid which
will be our tile.

  #declare Tile = superellipsoid { <0.5, 0.1>
    scale <1, .05, 1>
  }
Superellipsoids are roughly 2*2*2 units unless we scale them
otherwise. If we wish to lay a bunch of our tiles side by side,
they will have to be offset from each other so they don't
overlap. We should select an offset value that is slightly more
than 2 so that we have some space between the tiles to fill with
grout. So we now add this:

  #declare Offset = 2.1;
We now want to lay down a row of tiles. Each tile will be offset
from the original by an ever-increasing amount in both the +z and
-z directions. We refer to our offset and multiply by the tile's
rank to determine the position of each tile in the row. We also
union these tiles into a single object called Row like this:

  #declare Row = union {
    object { Tile }
    object { Tile translate z*Offset }
    object { Tile translate z*Offset*2 }
    object { Tile translate z*Offset*3 }
    object { Tile translate z*Offset*4 }
    object { Tile translate z*Offset*5 }
    object { Tile translate z*Offset*6 }
    object { Tile translate z*Offset*7 }
    object { Tile translate z*Offset*8 }
    object { Tile translate z*Offset*9 }
    object { Tile translate z*Offset*10 }
    object { Tile translate -z*Offset }
    object { Tile translate -z*Offset*2 }
    object { Tile translate -z*Offset*3 }
    object { Tile translate -z*Offset*4 }
    object { Tile translate -z*Offset*5 }
    object { Tile translate -z*Offset*6 }
  }
This gives us a single row of 17 tiles, more than enough to fill
the screen. Now we must make copies of the Row and translate
them, again by the offset value, in both the +x and -x directions
in ever increasing amounts in the same manner.

  object { Row }
  object { Row translate x*Offset }
  object { Row translate x*Offset*2 }
  object { Row translate x*Offset*3 }
  object { Row translate x*Offset*4 }
  object { Row translate x*Offset*5 }
  object { Row translate x*Offset*6 }
  object { Row translate x*Offset*7 }
  object { Row translate -x*Offset }
  object { Row translate -x*Offset*2 }
  object { Row translate -x*Offset*3 }
  object { Row translate -x*Offset*4 }
  object { Row translate -x*Offset*5 }
  object { Row translate -x*Offset*6 }
  object { Row translate -x*Offset*7 }
Finally, our tiles are complete. But we need a texture for them.
To do this we union all of the Rows together and apply a White
Marble pigment and a somewhat shiny reflective surface to it:

  union{
    object { Row }
    object { Row translate x*Offset }
    object { Row translate x*Offset*2 }
    object { Row translate x*Offset*3 }
    object { Row translate x*Offset*4 }
    object { Row translate x*Offset*5 }
    object { Row translate x*Offset*6 }
    object { Row translate x*Offset*7 }
    object { Row translate -x*Offset }
    object { Row translate -x*Offset*2 }
    object { Row translate -x*Offset*3 }
    object { Row translate -x*Offset*4 }
    object { Row translate -x*Offset*5 }
    object { Row translate -x*Offset*6 }
    object { Row translate -x*Offset*7 }
    pigment { White_Marble }
    finish { phong 1 phong_size 50 reflection .35 }
  }
We now need to add the grout. This can simply be a white plane.
We have stepped up the ambient here a little so it looks whiter.

  plane { y, 0  //this is the grout
    pigment { color White }
    finish { ambient .4 diffuse .7 }
  }
To complete our scene, let's add five different superellipsoids,
each a different color, so that they hover over our tiles and are
reflected in them.

  superellipsoid {
    <0.1, 1>
    pigment { Red }
    translate <5, 3, 0>
    scale .45
  }
  superellipsoid {
    <1, 0.25>
    pigment { Blue }
    translate <-5, 3, 0>
    scale .45
  }
  superellipsoid {
    <0.2, 0.6>
    pigment { Green }
    translate <0, 3, 5>
    scale .45
  }
  superellipsoid {
    <0.25, 0.25>
    pigment { Yellow }
    translate <0, 3, -5>
    scale .45
  }
  superellipsoid {
    <1, 1>
    pigment { Pink }
    translate y*3
    scale .45
  }
                                
                                
       Some superellipsoids hovering above a tiled floor.
                                
We trace the scene at 320x200 -A to see the result. If we are
happy with that, we do a final trace at 640x480 +A0.2.


2.4.9     Surface of Revolution Object
Bottles, vases and glasses make nice objects in ray-traced
scenes. We want to create a golden cup using the surface of
revolution object (SOR object).

We first start by thinking about the shape of the final object.
It is quite difficult to come up with a set of points that
describe a given curve without the help of a modeling program
supporting POV-Ray's surface of revolution object. If such a
program is available we should take advantage of it.

                                
                                
           The point configuration of our cup object.
                                
We will use the point configuration shown in the figure above.
There are eight points describing the curve that will be rotated
about the y-axis to get our cup. The curve was calculated using
the method described in the reference section (see "Surface of
Revolution").

Now it is time to come up with a scene that uses the above SOR
object. We edit a file called sordemo.pov and enter the following
text.

  #include "colors.inc"
  #include "golds.inc"
  global_settings { assumed_gamma 2.2 }
  camera {
    location <10, 15, -20>
    look_at <0, 5, 0>
    angle 45
  }
  background { color rgb<0.2, 0.4, 0.8>  }
  light_source { <100, 100, -100> color rgb 1 }
  plane { y, 0
    pigment { checker color Red, color Green scale 10 }
  }
  sor {
    8,
    <0.0,  -0.5>,
    <3.0,   0.0>,
    <1.0,   0.2>,
    <0.5,   0.4>,
    <0.5,   4.0>,
    <1.0,   5.0>,
    <3.0,  10.0>,
    <4.0,  11.0>
    texture { T_Gold_1B }
  }
The scene contains our cup object resting on a checkered plane.
Tracing this scene results in the image below.

                                
                                
                 A surface of revolution object.
                                
The surface of revolution is described by starting with the
number of points followed by the points with ascending heights.
Each point determines the radius of the curve for a given height.
E. g. the first point tells POV-Ray that at height -0.5 the
radius is 0. We should take care that each point has a larger
height than its predecessor. If this is not the case the program
will abort with an error message.


2.4.10    Text Object
Creating text objects using POV-Ray always used to mean that the
letters had to be built either from CSG, a painstaking process or
by using a black and white image of the letters as a height
field, a method that was only somewhat satisfactory. Now, for POV-
Ray 3.0, a new primitive has been introduced that can use any
TrueType font to create text objects. These objects can be used
in CSG, transformed and textured just like any other POV
primitive.

For this tutorial, we will make two uses of the text object.
First, let's just make some block letters sitting on a checkered
plane. Any TTF font should do, but for this tutorial, we will use
the timrom.ttf or cyrvetic.ttf which come bundled with POV-Ray.
We create a file called textdemo.pov and edit it as follows:

  #include "colors.inc"
  camera {
    location <0, 1, -10>
    look_at 0
    angle 35
  }
  light_source { <500,500,-1000> White }
  plane { y,0
    pigment { checker Green White }
  }
Now let's add the text object. We will use the font timrom.ttf
and we will create the string "POV-RAY 3.0". For now, we will
just make the letters red. The syntax is very simple. The first
string in quotes is the font name, the second one is the string
to be rendered. The two floats are the thickness and offset
values. The thickness float determines how thick the block
letters will be. Values of .5 to 2 are usually best for this. The
offset value will add to the kerning distance of the letters. We
will leave this a 0 for now.

  text { ttf "timrom.ttf" "POV-RAY 3.0" 1, 0
    pigment { Red }
  }
Rendering this at 200x150 -A, we notice that the letters are off
to the right of the screen. This is because they are placed so
that the lower left front corner of the first letter is at the
origin. To center the string we need to translate it -x some
distance. But how far? In the docs we see that the letters are
all 0.5 to 0.75 units high. If we assume that each one takes
about 0.5 units of space on the x-axis, this means that the
string is about 6 units long (12 characters and spaces). Let's
translate the string 3 units along the negative x-axis.

  text { ttf "timrom.ttf" "POV-RAY 3.0" 1, 0
    pigment { Red }
    translate -3*x
  }
That's better. Now let's play around with some of the parameters
of the text object. First, let's raise the thickness float to
something outlandish... say 25!

  text { ttf "timrom.ttf" "POV-RAY 3.0" 25, 0
    pigment { Red }
    translate -2.25*x
  }
Actually, that's kind of cool. Now let's return the thickness
value to 1 and try a different offset value. Change the offset
float from 0 to 0.1 and render it again.

Wait a minute?! The letters go wandering off up at an angle! That
is not what the docs describe! It almost looks as if the offset
value applies in both the x- and y-axis instead of just the x
axis like we intended. Could it be that a vector is called for
here instead of a float? Let's try it. We replace 0.1 with 0.1*x
and render it again.

That works! The letters are still in a straight line along the x-
axis, just a little further apart. Let's verify this and try to
offset just in the y-axis. We replace 0.1*x with 0.1*y. Again,
this works as expected with the letters going up to the right at
an angle with no additional distance added along the x-axis. Now
let's try the z-axis. We replace 0.1*y with 0.1*z. Rendering this
yields a disappointment. No offset occurs! The offset value can
only be applied in the x- and y-directions.

Let's finish our scene by giving a fancier texture to the block
letters, using that cool large thickness value, and adding a
slight y-offset. For fun, we will throw in a sky sphere, dandy up
our plane a bit, and use a little more interesting camera
viewpoint (we render the following scene at 640x480 +A0.2):

  #include "colors.inc"
  camera {
    location <-5,.15,-2>
    look_at <.3,.2,1>
    angle 35
  }
  light_source { <500,500,-1000> White }
  plane { y,0
    texture {
      pigment { SeaGreen }
      finish { reflection .35 specular 1 }
      normal { ripples .35 turbulence .5 scale .25 }
    }
  }
  text { ttf "timrom.ttf" "POV-RAY 3.0" 25, 0.1*y
    pigment { BrightGold }
    finish { reflection .25 specular 1 }
    translate -3*x
  }
  #include "skies.inc"
  sky_sphere { S_Cloud5 }
Let's try using text in a CSG object. We will attempt to create
an inlay in a stone block using a text object. We create a new
file called textcsg.pov and edit it as follows:

  #include "colors.inc"
  #include "stones.inc"
  background { color rgb 1 }
  camera {
    location <-3, 5, -15>
    look_at 0
    angle 25
  }
  light_source { <500,500,-1000> White }
Now let's create the block. We want it to be about eight units
across because our text string "POV-RAY 3.0" is about six units
long. We also want it about four units high and about one unit
deep. But we need to avoid a potential coincident surface with
the text object so we will make the first z-coordinate 0.1
instead of 0. Finally, we will give this block a nice stone
texture.

  box { <-3.5, -1, 0.1>, <3.5, 1, 1>
    texture { T_Stone10 }
  }
Next, we want to make the text object. We can use the same object
we used in the first tutorial except we will use slightly
different thickness and offset values.

  text { ttf "timrom.ttf" "POV-RAY 3.0" 0.15, 0
    pigment { BrightGold }
    finish { reflection .25 specular 1 }
    translate -3*x
  }
We remember that the text object is placed by default so that its
front surface lies directly on the x-y-plane. If the front of the
box begins at z=0.1 and thickness is set at 0.15, the depth of
the inlay will be 0.05 units. We place a difference block around
the two objects.

  difference {
    box { <-3.5, -1, 0.1>, <3.5, 1, 1>
      texture { T_Stone10 }
    }
    text { ttf "timrom.ttf" "POV-RAY 3.0" 0.15, 0
      pigment { BrightGold }
      finish { reflection .25 specular 1 }
      translate -3*x
    }
  }
                                
                                
                     Text carved from stone.
                                
We render this at 200x150 -A. We can see the inlay clearly and
that it is indeed a bright gold color. We re-render at 640x480
+A0.2 to see the results more clearly, but be forewarned... this
trace will take a little time.


2.4.11    Torus Object
A torus can be thought of as a donut or an inner-tube. It is a
shape that is vastly useful in many kinds of CSG so POV-Ray has
adopted this 4th order quartic polynomial as a primitive shape.
The syntax for a torus is so simple that it makes it a very easy
shape to work with once we learn what the two float values mean.
Instead of a lecture on the subject, let's create one and do some
experiments with it.

We create a file called tordemo.pov and edit it as follows:

  #include "colors.inc"
  camera {
    location <0, .1, -25>
    look_at 0
    angle 30
  }
  background { color Gray50 } // to make the torus easy to see
  light_source{ <300, 300, -1000> White }
  torus { 4, 1        // major and minor radius
    rotate -90*x      // so we can see it from the top
    pigment { Green }
  }
We trace the scene. Well, it's a donut alright. Let's try
changing the major and minor radius values and see what happens.
We change them as follows:

  torus { 5, .25      // major and minor radius
That looks more like a hula-hoop! Let's try this:

  torus { 3.5, 2.5    // major and minor radius
Whoa! A donut with a serious weight problem!

With such a simple syntax, there isn't much else we can do to a
torus besides change its texture... or is there? Let's see...

Torii are very useful objects in CSG. Let's try a little
experiment. We make a difference of a torus and a box:

  difference {
    torus { 4, 1
      rotate x*-90  // so we can see it from the top
    }
    box { <-5, -5, -1>, <5, 0, 1> }
    pigment { Green }
  }
Interesting... a half-torus. Now we add another one flipped the
other way. Only, let's declare the original half-torus and the
necessary transformations so we can use them again:

  #declare Half_Torus = difference {
    torus { 4, 1
      rotate -90*x  // so we can see it from the top
    }
    box { <-5, -5, -1>, <5, 0, 1> }
    pigment { Green }
  }
  #declare Flip_It_Over = 180*x;
  #declare Torus_Translate = 8;  // twice the major radius
Now we create a union of two Half_Torus objects:

  union {
    object { Half_Torus }
    object { Half_Torus
      rotate Flip_It_Over
      translate Torus_Translate*x
    }
  }
This makes an S-shaped object, but we can't see the whole thing
from our present camera. Let's add a few more links, three in
each direction, move the object along the +z-direction and rotate
it about the +y-axis so we can see more of it. We also notice
that there appears to be a small gap where the half Torii meet.
This is due to the fact that we are viewing this scene from
directly on the x-z-plane. We will change the camera's y-
coordinate from 0 to 0.1 to eliminate this.

  union {
    object { Half_Torus }
    object { Half_Torus
      rotate Flip_It_Over
      translate x*Torus_Translate
    }
    object { Half_Torus
      translate x*Torus_Translate*2
    }
    object { Half_Torus
      rotate Flip_It_Over
      translate x*Torus_Translate*3
    }
    object { Half_Torus
      rotate Flip_It_Over
      translate -x*Torus_Translate
    }
    object { Half_Torus
      translate -x*Torus_Translate*2
    }
    object { Half_Torus
      rotate Flip_It_Over
      translate -x*Torus_Translate*3
    }
    object { Half_Torus
      translate -x*Torus_Translate*4
    }
    rotate y*45
    translate z*20
  }
Rendering this we see a cool, undulating, snake-like something-or-
other. Neato. But we want to model something useful, something
that we might see in real life. How about a chain?

Thinking about it for a moment, we realize that a single link of
a chain can be easily modeled using two half tori and two
cylinders. We create a new file. We can use the same camera,
background, light source and declared objects and transformations
as we used in tordemo.pov:

  #include "colors.inc"
  camera {
    location <0, .1, -25>
    look_at 0
    angle 30
  }
  background { color Gray50 }
  light_source{ <300, 300, -1000> White }
  #declare Half_Torus = difference {
    torus { 4,1
      sturm
      rotate x*-90  // so we can see it from the top
    }
    box { <-5, -5, -1>, <5, 0, 1> }
    pigment { Green }
  }
  #declare Flip_It_Over = x*180;
  #declare Torus_Translate = 8;
Now, we make a complete torus of two half tori:

  union {
    object { Half_Torus }
    object { Half_Torus rotate Flip_It_Over }
  }
This may seem like a wasteful way to make a complete torus, but
we are really going to move each half apart to make room for the
cylinders. First, we add the declared cylinder before the union:

  #declare Chain_Segment = cylinder { <0, 4, 0>, <0, -4, 0>, 1
    pigment { Green }
  }
We then add two Chain_Segments to the union and translate them so
that they line up with the minor radius of the torus on each
side:

  union {
    object { Half_Torus }
    object { Half_Torus rotate Flip_It_Over }
    object { Chain_Segment translate  x*Torus_Translate/2 }
    object { Chain_Segment translate -x*Torus_Translate/2 }
  }
Now we translate the two half tori +y and -y so that the clipped
ends meet the ends of the cylinders. This distance is equal to
half of the previously declared Torus_Translate:

  union {
    object { Half_Torus
      translate y*Torus_Translate/2
    }
    object { Half_Torus
      rotate Flip_It_Over
      translate -y*Torus_Translate/2
    }
    object { Chain_Segment
      translate x*Torus_Translate/2
    }
    object { Chain_Segment
      translate -x*Torus_Translate/2
    }
  }
We render this and viola! A single link of a chain. But we aren't
done yet! Whoever heard of a green chain? We would rather use a
nice metallic color instead. First, we remove any pigment blocks
in the declared torsos and cylinders. Then we add the following
before the union:

  #declare Chain_Gold = texture {
    pigment { BrightGold }
    finish {
      ambient .1
      diffuse .4
      reflection .25
      specular 1
      metallic
    }
  }
We then add the texture to the union and declare the union as a
single link:

  #declare Link = union {
    object { Half_Torus
      translate y*Torus_Translate/2
    }
    object { Half_Torus
      rotate Flip_It_Over
      translate -y*Torus_Translate/2
    }
    object { Chain_Segment
      translate x*Torus_Translate/2
    }
    object { Chain_Segment
      translate -x*Torus_Translate/2
    }
    texture { Chain_Gold }
  }
Now we make a union of two links. The second one will have to be
translated +y so that its inner wall just meets the inner wall of
the other link, just like the links of a chain. This distance
turns out to be double the previously declared Torus_Translate
minus 2 (twice the minor radius). This can be described by the
expression:

  Torus_Translate*2-2*y
We declare this expression as follows:

  #declare Link_Translate = Torus_Translate*2-2*y;
In the object block, we will use this declared value so that we
can multiply it to create other links. Now, we rotate the second
link 90*y so that it is perpendicular to the first, just like
links of a chain. Finally, we scale the union by 1/4 so that we
can see the whole thing:

  union {
    object { Link }
    object { Link translate y*Link_Translate rotate y*90 }
    scale .25
  }
We render this and we will see a very realistic pair of links. If
we want to make an entire chain, we must declare the above union
and then create another union of this declared object. We must be
sure to remove the scaling from the declared object:

  #declare Link_Pair =
  union {
    object { Link }
    object { Link translate y*Link_Translate rotate y*90 }
  }
Now we declare our chain:

  #declare Chain = union {
    object { Link_Pair}
    object { Link_Pair translate  y*Link_Translate*2 }
    object { Link_Pair translate  y*Link_Translate*4 }
    object { Link_Pair translate  y*Link_Translate*6 }
    object { Link_Pair translate -y*Link_Translate*2 }
    object { Link_Pair translate -y*Link_Translate*4 }
    object { Link_Pair translate -y*Link_Translate*6 }
  }
And finally we create our chain with a couple of transformations
to make it easier to see. These include scaling it down by a
factor of 1/10, and rotating it so that we can clearly see each
link:

  object { Chain scale .1 rotate <0, 45, -45> }
                                
                                
         The torus object can be used to create chains.
                                
We render this and we should see a very realistic gold chain
stretched diagonally across the screen.


2.5  The Light Source
In any ray-traced scene, the light needed to illuminate our
objects and their surfaces must come from a light source. There
are many kinds of light sources available in POV-Ray and careful
use of the correct kind can yield very impressive results. Let's
take a moment to explore some of the different kinds of light
sources and their various parameters.


2.5.1     The Pointlight Source
Pointlights are exactly what the name indicates. A pointlight has
no size, is invisible and illuminates everything in the scene
equally no matter how far away from the light source it may be
(this behavior can be changed). This is the simplest and most
basic light source. There are only two important parameters,
location and color. Let's design a simple scene and place a
pointlight source in it.

We create a new file and name it litedemo.pov. We edit it as
follows:

  #include "colors.inc"
  #include "textures.inc"
  camera {
    location  <-4, 3, -9>
    look_at   <0, 0, 0>
    angle 48
  }
We add the following simple objects:

  plane { y, -1
    texture {
      pigment {
        checker
        color rgb<0.5, 0, 0>
        color rgb<0, 0.5, 0.5>
      }
      finish {
        diffuse 0.4
        ambient 0.2
        phong 1
        phong_size 100
        reflection 0.25
      }
    }
  }
  torus { 1.5, 0.5
    texture { Brown_Agate }
    rotate <90, 160, 0>
    translate  <-1, 1, 3>
  }
  box { <-1, -1, -1>, <1, 1, 1>
    texture { DMFLightOak }
    translate  <2, 0, 2.3>
  }
  cone { <0,1,0>, 0, <0,0,0>, 1
    texture { PinkAlabaster }
    scale <1, 3, 1>
    translate  <-2, -1, -1>
  }
  sphere { <0,0,0>,1
    texture { Sapphire_Agate }
    translate  <1.5, 0, -2>
  }
Now we add a pointlight:

  light_source {
    <2, 10, -3>
    color White
  }
We render this at 200x150 -A and see that the objects are clearly
visible with sharp shadows. The sides of curved objects nearest
the light source are brightest in color with the areas that are
facing away from the light source being darkest. We also note
that the checkered plane is illuminated evenly all the way to the
horizon. This allows us to see the plane, but it is not very
realistic.


2.5.2     The Spotlight Source
Spotlights are a very useful type of light source. They can be
used to add highlights and illuminate features much as a
photographer uses spots to do the same thing. To create a
spotlight simply add the spotlight keyword to a regular point
light.  There are a few more parameters with spotlights than with
pointlights. These are radius, falloff, tightness and point_at.
The radius parameter is the angle of the fully illuminated cone.
The falloff parameter is the angle of the umbra cone where the
light falls off to darkness. The tightness is a parameter that
determines the rate of the light falloff. The point_at parameter
is just what it says, the location where the spotlight is
pointing to. Let's change the light in our scene as follows:

  light_source {
    <0, 10, -3>
    color White
    spotlight
    radius 15
    falloff 20
    tightness 10
    point_at <0, 0, 0>
  }
We render this at 200x150 -A and see that only the objects are
illuminated. The rest of the plane and the outer portions of the
objects are now unlit. There is a broad falloff area but the
shadows are still razor sharp. Let's try fiddling with some of
these parameters to see what they do. We change the falloff value
to 16 (it must always be larger than the radius value) and render
again.  Now the falloff is very narrow and the objects are either
brightly lit or in total darkness. Now we change falloff back to
20 and change the tightness value to 100 (higher is tighter) and
render again. The spotlight appears to have gotten much smaller
but what has really happened is that the falloff has become so
steep that the radius actually appears smaller.

We decide that a tightness value of 10 (the default) and a
falloff value of 18 are best for this spotlight and we now want
to put a few spots around the scene for effect. Let's place a
slightly narrower blue and a red one in addition to the white one
we already have:

  light_source {
    <10, 10, -1>
    color Red
    spotlight
    radius 12
    falloff 14
    tightness 10
    point_at <2, 0, 0>
  }
  light_source {
    <-12, 10, -1>
    color Blue
    spotlight
    radius 12
    falloff 14
    tightness 10
    point_at <-2, 0, 0>
  }
Rendering this we see that the scene now has a wonderfully
mysterious air to it. The three spotlights all converge on the
objects making them blue on one side and red on the other with
enough white in the middle to provide a balance.


2.5.3     The Cylindrical Light Source
Spotlights are cone shaped, meaning that their effect will change
with distance. The farther away from the spotlight an object is,
the larger the apparent radius will be. But we may want the
radius and falloff to be a particular size no matter how far away
the spotlight is. For this reason, cylindrical light sources are
needed. A cylindrical light source is just like a spotlight,
except that the radius and falloff regions are the same no matter
how far from the light source our object is. The shape is
therefore a cylinder rather than a cone. We can specify a
cylindrical light source by replacing the spotlight keyword with
the cylinder keyword. We try this now with our scene by replacing
all three spotlights with cylinder lights and rendering again. We
see that the scene is much dimmer. This is because the
cylindrical constraints do not let the light spread out like in a
spotlight. Larger radius and falloff values are needed to do the
job. We try a radius of 20 and a falloff of 30 for all three
lights. That's the ticket!


2.5.4     The Area Light Source
So far all of our light sources have one thing in common. They
produce sharp shadows. This is because the actual light source is
a point that is infinitely small. Objects are either in direct
sight of the light, in which case they are fully illuminated, or
they are not, in which case they are fully shaded. In real life,
this kind of stark light and shadow situation exists only in
outer space where the direct light of the sun pierces the total
blackness of space. But here on Earth, light bends around
objects, bounces off objects, and usually the source has some
dimension, meaning that it can be partially hidden from sight
(shadows are not sharp anymore). They have what is known as an
umbra, or an area of fuzziness where there is neither total light
or shade. In order to simulate these soft shadows, a ray-tracer
must give its light sources dimension. POV-Ray accomplishes this
with a feature known as an area light.

Area lights have dimension in two axis'. These are specified by
the first two vectors in the area light syntax. We must also
specify how many lights are to be in the array. More will give us
cleaner soft shadows but will take longer to render. Usually a
3*3 or a 5*5 array will suffice. We also have the option of
specifying an adaptive value. The adaptive keyword tells the ray-
tracer that it can adapt to the situation and send only the
needed rays to determine the value of the pixel. If adaptive is
not used, a separate ray will be sent for every light in the area
light.  This can really slow things down. The higher the adaptive
value the cleaner the umbra will be but the longer the trace will
take.  Usually an adaptive value of 1 is sufficient. Finally, we
probably should use the jitter keyword.  This tells the ray-
tracer to slightly move the position of each light in the area
light so that the shadows appear truly soft instead of giving us
an umbra consisting of closely banded shadows.

OK, let's try one. We comment out the cylinder lights and add the
following:

  light_source {
    <2, 10, -3>
    color White
    area_light <5, 0, 0>, <0, 0, 5>, 5, 5
    adaptive 1
    jitter
  }
This is a white area light centered at <2,10,-3>. It is 5 units
(along the x-axis) by 5 units (along the z-axis) in size and has
25 (5*5) lights in it. We have specified adaptive 1 and jitter.
We render this at 200x150 -A.

Right away we notice two things. The trace takes quite a bit
longer than it did with a point or a spotlight and the shadows
are no longer sharp! They all have nice soft umbrae around them.
Wait, it gets better.

Spotlights and cylinder lights can be area lights too! Remember
those sharp shadows from the spotlights in our scene? It would
not make much sense to use a 5*5 array for a spotlight, but a
smaller array might do a good job of giving us just the right
amount of umbra for a spotlight.  Let's try it. We comment out
the area light and change the cylinder lights so that they read
as follows:

  light_source {
    <2, 10, -3>
    color White
    spotlight
    radius 15
    falloff 18
    tightness 10
    area_light <1, 0, 0>, <0, 0, 1>, 2, 2
    adaptive 1
    jitter
    point_at <0, 0, 0>
  }
  light_source {
    <10, 10, -1>
    color Red
    spotlight
    radius 12
    falloff 14
    tightness 10
    area_light <1, 0, 0>, <0, 0, 1>, 2, 2
    adaptive 1
    jitter
    point_at <2, 0, 0>
  }
  light_source {
    <-12, 10, -1>
    color Blue
    spotlight
    radius 12
    falloff 14
    tightness 10
    area_light <1, 0, 0>, <0, 0, 1>, 2, 2
    adaptive 1
    jitter
    point_at <-2, 0, 0>
  }
We now have three area-spotlights, one unit square consisting of
an array of four (2*2) lights, three different colors, all
shining on our scene. We render this at 200x150 -A. It appears to
work perfectly. All our shadows have small, tight umbrae, just
the sort we would expect to find on an object under a real
spotlight.


2.5.5     The Ambient Light Source
The ambient light source is used to simulate the effect of inter-
diffuse reflection. If there wasn't inter-diffuse reflection all
areas not directly lit by a light source would be completely
dark. POV-Ray uses the ambient keyword to determine how much
light coming from the ambient light source is reflected by a
surface.

By default the ambient light source, which emits its light
everywhere and in all directions, is pure white (rgb <1,1,1>).
Changing its color can be used to create interesting effects.
First of all the overall light level of the scene can be adjusted
easily. Instead of changing all ambient values in every finish
only the ambient light source is modified. By assigning different
colors we can create nice effects like a moody reddish ambient
lighting. For more details about the ambient light source see
"Ambient Light".

Below is an example of a red ambient light source.

  global_settings { ambient_light rgb<1, 0, 0> }

2.5.6     Light Source Specials

2.5.6.1   Using Shadowless Lights
Light sources can be assigned the shadowless keyword and no
shadows will be cast due to its presence in a scene. Sometimes,
scenes are difficult to illuminate properly using the lights we
have chosen to illuminate our objects.  It is impractical and
unrealistic to apply a higher ambient value to the texture of
every object in the scene. So instead, we would place a couple of
fill lights around the scene. Fill lights are simply dimmer
lights with the shadowless keyword that act to boost the
illumination of other areas of the scene that may not be lit
well.  Let's try using one in our scene.

Remember the three colored area spotlights? We go back and un-
comment them and comment out any other lights we have made. Now
we add the following:

  light_source {
    <0, 20, 0>
    color Gray50
    shadowless
  }
This is a fairly dim light 20 units over the center of the scene.
It will give a dim illumination to all objects including the
plane in the background. We render it and see.


2.5.6.2   Assigning an Object to a Light Source
Light sources are invisible. They are just a location where the
light appears to be coming from. They have no true size or shape.
If we want our light source to be a visible shape, we can use the
looks_like keyword. We can specify that our light source can look
like any object we choose. When we use looks_like, then no_shadow
is applied to the object automatically. This is done so that the
object will not block any illumination from the light source.  If
we want some blocking to occur (as in a lampshade), it is better
to simply use a union to do the same thing. Let's add such an
object to our scene. Here is a light bulb we have made just for
this purpose:

  #declare Lightbulb = union {
    merge {
      sphere { <0,0,0>,1 }
      cylinder { <0,0,1>, <0,0,0>, 1
        scale <0.35, 0.35, 1.0>
        translate  0.5*z
      }
      texture {
        pigment {color rgb <1, 1, 1>}
        finish {ambient .8 diffuse .6}
      }
    }
    cylinder { <0,0,1>, <0,0,0>, 1
      scale <0.4, 0.4, 0.5>
      texture { Brass_Texture }
      translate  1.5*z
    }
    rotate -90*x
    scale .5
  }
Now we add the light source:

  light_source {
    <0, 2, 0>
    color White
    looks_like { Lightbulb }
  }
Rendering this we see that a fairly believable light bulb now
illuminates the scene. However, if we do not specify a high
ambient value, the light bulb is not lit by the light source. On
the plus side, all of the shadows fall away from the light bulb,
just as they would in a real situation. The shadows are sharp, so
let's make our bulb an area light:

  light_source {
    <0, 2, 0>
    color White
    area_light <1, 0, 0>, <0, 1, 0>, 2, 2
    adaptive 1
    jitter
    looks_like { Lightbulb }
  }
We note that we have placed this area light in the x-y-plane
instead of the x-z-plane. We also note that the actual appearance
of the light bulb is not affected in any way by the light source.
The bulb must be illuminated by some other light source or by, as
in this case, a high ambient value.


2.5.6.3   Using Light Fading
If it is realism we want, it is not realistic for the plane to be
evenly illuminated off into the distance. In real life, light
gets scattered as it travels so it diminishes its ability to
illuminate objects the farther it gets from its source. To
simulate this, POV-Ray allows us to use two keywords:
fade_distance, which specifies the distance at which full
illumination is achieved, and fade_power, an exponential value
which determines the actual rate of attenuation. Let's apply
these keywords to our fill light.

First, we make the fill light a little brighter by changing
Gray50 to Gray75. Now we change that fill light as follows:

  light_source {
    <0, 20, 0>
    color Gray75
    fade_distance 5
    fade_power 1
    shadowless
  }
This means that the full value of the fill light will be achieved
at a distance of 5 units away from the light source. The fade
power of 1 means that the falloff will be linear (the light falls
of at a constant rate). We render this to see the result.

That definitely worked!  Now let's try a fade power of 2 and a
fade distance of 10. Again, this works well. The falloff is much
faster with a fade power of 2 so we had to raise the fade
distance to 10.


2.6  Simple Texture Options
The pictures rendered so far where somewhat boring regarding the
appearance of the objects. Let's add some fancy features to the
texture.


2.6.1     Surface Finishes
One of the main features of a ray-tracer is its ability to do
interesting things with surface finishes such as highlights and
reflection. Let's add a nice little Phong highlight (shiny spot)
to a sphere. To do this we need to add a finish keyword followed
by a parameter. We change the definition of the sphere to this:

  sphere { <0, 1, 2>, 2
    texture {
      pigment { color Yellow } // Yellow is pre-defined in
COLORS.INC
      finish { phong 1 }
    }
  }
We render the scene. The phong keyword adds a highlight the same
color of the light shining on the object. It adds a lot of
credibility to the picture and makes the object look smooth and
shiny. Lower values of phong will make the highlight less bright
(values should be between 0 and 1).


2.6.2     Adding Bumpiness
The highlight we have added illustrates how much of our
perception depends on the reflective properties of an object. Ray-
tracing can exploit this by playing tricks on our perception to
make us see complex details that aren't really there.

Suppose we wanted a very bumpy surface on the object. It would be
very difficult to mathematically model lots of bumps. We can
however simulate the way bumps look by altering the way light
reflects off of the surface. Reflection calculations depend on a
vector called a surface normal. This is a vector which points
away from the surface and is perpendicular to it. By artificially
modifying (or perturbing) this normal vector we can simulate
bumps. We change the scene to read as follows and render it:

  sphere { <0, 1, 2>, 2
    texture {
      pigment { color Yellow }
      normal { bumps 0.4 scale 0.2 }
      finish { phong 1}
    }
  }
This tells POV-Ray to use the bumps pattern to modify the surface
normal. The value 0.4 controls the apparent depth of the bumps.
Usually the bumps are about 1 unit wide which doesn't work very
well with a sphere of radius 2. The scale makes the bumps 1/5th
as wide but does not affect their depth.


2.6.3     Creating Color Patterns
We can do more than assigning a solid color to an object. We can
create complex patterns in the pigment block like in this
example:

  sphere { <0, 1, 2>, 2
    texture {
      pigment {
        wood
        color_map {
          [0.0 color DarkTan]
          [0.9 color DarkBrown]
          [1.0 color VeryDarkBrown]
        }
        turbulence 0.05
        scale <0.2, 0.3, 1>
      }
      finish { phong 1 }
    }
  }
The keyword wood specifies a pigment pattern of concentric rings
like rings in wood. The color_map keyword specifies that the
color of the wood should blend from DarkTan to DarkBrown over the
first 90% of the vein and from DarkBrown to VeryDarkBrown over
the remaining 10%. The turbulence keyword slightly stirs up the
pattern so the veins aren't perfect circles and the scale keyword
adjusts the size of the pattern.

Most patterns are set up by default to give us one feature across
a sphere of radius 1.0. A feature is very roughly defined as a
color transition. For example, a wood texture would have one band
on a sphere of radius 1.0. In this example we scale the pattern
using the scale keyword followed by a vector. In this case we
scaled 0.2 in the x direction, 0.3 in the y direction and the z
direction is scaled by 1, which leaves it unchanged. Scale values
larger than one will stretch an element. Scale values smaller
than one will squish an element. A scale value of one will leave
an element unchanged.


2.6.4     Pre-defined Textures
POV-Ray has some very sophisticated textures pre-defined in the
standard include files glass.inc, metals.inc, stones.inc and
woods.inc. Some are entire textures with pigment, normal and/or
finish parameters already defined. Some are just pigments or just
finishes.  We change the definition of our sphere to the
following and then re-render it:

  sphere { <0, 1, 2>, 2
    texture {
      pigment {
        DMFWood4       // pre-defined in textures.inc
        scale 4        // scale by the same amount in all
                       // directions
      }
      finish { Shiny } // pre-defined in finish.inc
    }
  }
The pigment identifier DMFWood4 has already been scaled down
quite small when it was defined. For this example we want to
scale the pattern larger. Because we want to scale it uniformly
we can put a single value after the scale keyword rather than a
vector of x, y, z scale factors.

We look through the file textures.inc to see what pigments and
finishes are defined and try them out. We just insert the name of
the new pigment where DMFWood4 is now or try a different finish
in place of Shiny and re-render our file.

Here is an example of using a complete texture identifier rather
than just the pieces.

  sphere { <0, 1, 2>, 2
    texture { PinkAlabaster }
  }

2.7  Advanced Texture Options
The extremely powerful texturing ability is one thing that really
sets POV-Ray apart from other raytracers. So far we have not
really tried anything too complex but by now we should be
comfortable enough with the program's syntax to try some of the
more advanced texture options.

Obviously, we cannot try them all. It would take a tutorial a lot
more pages to use every texturing option available in POV-Ray.
For this limited tutorial, we will content ourselves to just
trying a few of them to give an idea of how textures are created.
With a little practice, we will soon be creating beautiful
textures of our own.

Note that early versions of POV-Ray made a distinction between
pigment and normal patterns, i. e. patterns that could be used
inside a normal or pigment statement. With POV-Ray 3.0 this
restriction was removed so that all patterns listed in section
"Patterns" can be used as a pigment or normal pattern.


2.7.1     Pigments
Every surface must have a color. In POV-Ray this color is called
a pigment. It does not have to be a single color. It can be a
color pattern, a color list or even an image map. Pigments can
also be layered one on top of the next so long as the uppermost
layers are at least partially transparent so the ones beneath can
show through. Let's play around with some of these kinds of
pigments.

We create a file called texdemo.pov and edit it as follows:

  #include "colors.inc"
  camera {
    location <1, 1, -7>
    look_at 0
    angle 36
  }
  light_source { <1000, 1000, -1000> White }
  plane { y, -1.5
    pigment { checker Green, White }
  }
  sphere { <0,0,0>, 1
    pigment { Red }
  }
Giving this file a quick test render at 200x150 -A we see that it
is a simple red sphere against a green and white checkered plane.
We will be using the sphere for our textures.


2.7.1.1   Using Color List Pigments
Before we begin we should note that we have already made one kind
of pigment, the color list pigment. In the previous example we
have used a checkered pattern on our plane. There are two other
kinds of color list pigments, brick and hexagon. Let's quickly
try each of these. First, we change the plane's pigment as
follows:

  pigment { hexagon Green, White, Yellow }
Rendering this we see a three-color hexagonal pattern. Note that
this pattern requires three colors. Now we change the pigment
to...

  pigment { brick Gray75, Red rotate -90*x scale .25 }
Looking at the resulting image we see that the plane now has a
brick pattern. We note that we had to rotate the pattern to make
it appear correctly on the flat plane. This pattern normally is
meant to be used on vertical surfaces. We also had to scale the
pattern down a bit so we could see it more easily. We can play
around with these color list pigments, change the colors, etc.
until we get a floor that we like.


2.7.1.2   Using Pigment and Patterns
Let's begin texturing our sphere by using a pattern and a color
map consisting of three colors. We replace the pigment block with
the following.

  pigment {
    gradient x
    color_map {
      [0.00 color Red]
      [0.33 color Blue]
      [0.66 color Yellow]
      [1.00 color Red]
    }
  }
Rendering this we see that the gradient pattern gives us an
interesting pattern of vertical stripes. We change the gradient
direction to y. The stripes are horizontal now. We change the
gradient direction to z. The stripes are now more like concentric
rings. This is because the gradient direction is directly away
from the camera. We change the direction back to x and add the
following to the pigment block.

  pigment {
    gradient x
    color_map {
      [0.00 color Red]
      [0.33 color Blue]
      [0.66 color Yellow]
      [1.00 color Red]
    }
    rotate -45*z          // <- add this line
  }
The vertical bars are now slanted at a 45 degree angle. All
patterns can be rotated, scaled and translated in this manner.
Let's now try some different types of patterns. One at a time, we
substitute the following keywords for gradient x and render to
see the result: bozo, marble, agate, granite, leopard, spotted
and wood (if we like we can test all patterns listed in section
"Patterns").

Rendering these we see that each results in a slightly different
pattern. But to get really good results each type of pattern
requires the use of some pattern modifiers.


2.7.1.3   Using Pattern Modifiers
Let's take a look at some pattern modifiers. First, we change the
pattern type to bozo. Then we add the following change.

  pigment {
    bozo
    frequency 3            // <- add this line
    color_map {
      [0.00 color Red]
      [0.33 color Blue]
      [0.66 color Yellow]
      [1.00 color Red]
    }
    rotate -45*z
  }
The frequency modifier determines the number of times the color
map repeats itself per unit of size. This change makes the bozo
pattern we saw earlier have many more bands in it. Now we change
the pattern type to marble. When we rendered this earlier, we saw
a banded pattern similar to gradient y that really did not look
much like marble at all. This is because marble really is a kind
of gradient and it needs another pattern modifier to look like
marble. This modifier is called turbulence. We change the line
frequency 3 to turbulence 1 and render again. That's better! Now
let's put frequency 3 back in right after the turbulence and take
another look. Even more interesting!

But wait, it gets better! Turbulence itself has some modifiers of
its own. We can adjust the turbulence several ways. First, the
float that follows the turbulence keyword can be any value with
higher values giving us more turbulence. Second, we can use the
keywords omega, lambda and octaves to change the turbulence
parameters. Let's try this now:

  pigment {
    marble
    turbulence 0.5
    lambda 1.5
    omega 0.8
    octaves 5
    frequency 3
    color_map {
      [0.00 color Red]
      [0.33 color Blue]
      [0.66 color Yellow]
      [1.00 color Red]
    }
    rotate 45*z
  }
Rendering this we see that the turbulence has changed and the
pattern looks different. We play around with the numerical values
of turbulence, lambda, omega and octaves to see what they do.


2.7.1.4   Using Transparent Pigments and Layered Textures
Pigments are described by numerical values that give the rgb
value of the color to be used (like color rgb<1,0,0> giving us a
red color). But this syntax will give us more than just the rgb
values. We can specify filtering transparency by changing it as
follows: color rgbf<1,0,0,1>. The f stands for filter, POV-Ray's
word for filtered transparency. A value of one means that the
color is completely transparent, but still filters the light
according to what the pigment is. In this case, the color will be
a transparent red, like red cellophane.

There is another kind of transparency in POV-Ray. It is called
transmittance or non-filtering transparency (the keyword is
transmit). It is different from filter in that it does not filter
the light according to the pigment color. It instead allows all
the light to pass through unchanged. It can be specified like
this: rgbt <1,0,0,1>.

Let's use some transparent pigments to create another kind of
texture, the layered texture. Returning to our previous example,
declare the following texture.

  #declare LandArea = texture {
      pigment {
        agate
        turbulence 1
        lambda 1.5
        omega .8
        octaves 8
        color_map {
          [0.00 color rgb <.5, .25, .15>]
          [0.33 color rgb <.1, .5, .4>]
          [0.86 color rgb <.6, .3, .1>]
          [1.00 color rgb <.5, .25, .15>]
        }
      }
    }
This texture will be the land area. Now let's make the oceans by
declaring the following.

  #declare OceanArea = texture {
      pigment {
        bozo
        turbulence .5
        lambda 2
        color_map {
          [0.00, 0.33 color rgb <0, 0, 1>
                      color rgb <0, 0, 1>]
          [0.33, 0.66 color rgbf <1, 1, 1, 1>
                      color rgbf <1, 1, 1, 1>]
          [0.66, 1.00 color rgb <0, 0, 1>
                      color rgb <0, 0, 1>]
        }
      }
    }
Note how the ocean is the opaque blue area and the land is the
clear area which will allow the underlying texture to show
through.

Now, let's declare one more texture to simulate an atmosphere
with swirling clouds.

  #declare CloudArea = texture {
    pigment {
      agate
      turbulence 1
      lambda 2
      frequency 2
      color_map {
        [0.0 color rgbf <1, 1, 1, 1>]
        [0.5 color rgbf <1, 1, 1, .35>]
        [1.0 color rgbf <1, 1, 1, 1>]
      }
    }
  }
Now apply all of these to our sphere.

  sphere { <0,0,0>, 1
    texture { LandArea }
    texture { OceanArea }
    texture { CloudArea }
  }
We render this and have a pretty good rendition of a little
planetoid. But it could be better. We don't particularly like the
appearance of the clouds. There is a way they could be done that
would be much more realistic.


2.7.1.5   Using Pigment Maps
Pigments may be blended together in the same way as the colors in
a color map using the same pattern keywords and a pigment_map.
Let's just give it a try.

We add the following declarations, making sure they appear before
the other declarations in the file.

  #declare Clouds1 = pigment {
      bozo
      turbulence 1
      color_map {
        [0.0 color White filter 1]
        [0.5 color White]
        [1.0 color White filter 1]
      }
    }
  #declare Clouds2 = pigment {
    agate
    turbulence 1
    color_map {
      [0.0 color White filter 1]
      [0.5 color White]
      [1.0 color White filter 1]
      }
    }
  #declare Clouds3 = pigment {
    marble
    turbulence 1
    color_map {
      [0.0 color White filter 1]
      [0.5 color White]
      [1.0 color White filter 1]
    }
  }
  #declare Clouds4 = pigment {
    granite
    turbulence 1
    color_map {
      [0.0 color White filter 1]
      [0.5 color White]
      [1.0 color White filter 1]
    }
  }
Now we use these declared pigments in our cloud layer on our
planetoid. We replace the declared cloud layer with.

  #declare CloudArea = texture {
    pigment {
      gradient y
      pigment_map {
        [0.00 Clouds1]
        [0.25 Clouds2]
        [0.50 Clouds3]
        [0.75 Clouds4]
        [1.00 Clouds1]
      }
    }
  }
We render this and see a remarkable pattern that looks very much
like weather patterns on the planet earth. They are separated
into bands, simulating the different weather types found at
different latitudes.


2.7.2     Normals
Objects in POV-Ray have very smooth surfaces. This is not very
realistic so there are several ways to disturb the smoothness of
an object by perturbing the surface normal. The surface normal is
the vector that is perpendicular to the angle of the surface. By
changing this normal the surface can be made to appear bumpy,
wrinkled or any of the many patterns available. Let's try a
couple of them.


2.7.2.1   Using Basic Normal Modifiers
We comment out the planetoid sphere for now and, at the bottom of
the file, create a new sphere with a simple, single color
texture.

  sphere { <0,0,0>, 1
    pigment { Gray75 }
    normal { bumps 1 scale .2 }
  }
Here we have added a normal block in addition to the pigment
block (note that these do not have to be included in a texture
block unless they need to be transformed together or need to be
part of a layered texture). We render this to see what it looks
like. Now, one at a time, we substitute for the keyword bumps the
following keywords: dents, wrinkles, ripples and waves (we can
also use any of the patterns listed in "Patterns"). We render
each to see what they look like. We play around with the float
value that follows the keyword. We also experiment with the scale
value.

For added interest, we change the plane texture to a single color
with a normal as follows.

  plane { y, -1.5
    pigment { color rgb <.65, .45, .35> }
    normal { dents .75 scale .25 }
  }

2.7.2.2   Blending Normals
Normals can be layered similar to pigments but the results can be
unexpected. Let's try that now by editing the sphere as follows.

  sphere { <0,0,0>, 1
    pigment { Gray75 }
      normal { radial frequency 10 }
      normal { gradient y scale .2 }
  }
As we can see, the resulting pattern is neither a radial nor a
gradient. It is instead the result of first calculating a radial
pattern and then calculating a gradient pattern. The results are
simply additive. This can be difficult to control so POV-Ray
gives the user other ways to blend normals.

One way is to use normal maps. A normal map works the same way as
the pigment map we used earlier. Let's change our sphere texture
as follows.

  sphere { <0,0,0>, 1
    pigment { Gray75 }
    normal {
      gradient y
      frequency 3
      turbulence .5
      normal_map {
        [0.00 granite]
        [0.25 spotted turbulence .35]
        [0.50 marble turbulence .5]
        [0.75 bozo turbulence .25]
        [1.00 granite]
      }
    }
  }
Rendering this we see that the sphere now has a very irregular
bumpy surface. The gradient pattern type separates the normals
into bands but they are turbulated, giving the surface a chaotic
appearance. But this give us an idea.

Suppose we use the same pattern for a normal map that we used to
create the oceans on our planetoid and applied it to the land
areas. Does it follow that if we use the same pattern and
modifiers on a sphere the same size that the shape of the pattern
would be the same? Wouldn't that make the land areas bumpy while
leaving the oceans smooth? Let's try it. First, let's render the
two spheres side-by-side so we can see if the pattern is indeed
the same. We un-comment the planetoid sphere and make the
following changes.

  sphere { <0,0,0>, 1
    texture { LandArea }
    texture { OceanArea }
    //texture { CloudArea }  // <-comment this out
    translate -x             // <- add this transformation
  }
Now we change the gray sphere as follows.

  sphere { <0,0,0>, 1
    pigment { Gray75 }
    normal {
      bozo
      turbulence .5
      lambda 2
      normal_map {
        [0.4 dents .15 scale .01]
        [0.6 agate turbulence 1]
        [1.0 dents .15 scale .01]
      }
    }
    translate x // <- add this transformation
  }
We render this to see if the pattern is the same. We see that
indeed it is. So let's comment out the gray sphere and add the
normal block it contains to the land area texture of our
planetoid. We remove the transformations so that the planetoid is
centered in the scene again.

  #declare LandArea = texture {
    pigment {
      agate
      turbulence 1
      lambda 1.5
      omega .8
      octaves 8
      color_map {
        [0.00 color rgb <.5, .25, .15>]
        [0.33 color rgb <.1, .5, .4>]
        [0.86 color rgb <.6, .3, .1>]
        [1.00 color rgb <.5, .25, .15>]
      }
    }
    normal {
      bozo
      turbulence .5
      lambda 2
      normal_map {
        [0.4 dents .15 scale .01]
        [0.6 agate turbulence 1]
        [1.0 dents .15 scale .01]
      }
    }
  }
Looking at the resulting image we see that indeed our idea works!
The land areas are bumpy while the oceans are smooth. We add the
cloud layer back in and our planetoid is complete.

There is much more that we did not cover here due to space
constraints. On our own, we should take the time to explore slope
maps, average and bump maps.


2.7.3     Finishes
The final part of a POV-Ray texture is the finish. It controls
the properties of the surface of an object. It can make it shiny
and reflective, or dull and flat. It can also specify what
happens to light that passes through transparent pigments, what
happens to light that is scattered by less-than-perfectly-smooth
surfaces and what happens to light that is reflected by surfaces
with thin-film interference properties. There are twelve
different properties available in POV-Ray to specify the finish
of a given object. These are controlled by the following
keywords: ambient, diffuse, brilliance, phong, specular,
metallic, reflection, crand and iridescence. Let's design a
couple of textures that make use of these parameters.


2.7.3.1   Using Ambient
Since objects in POV-Ray are illuminated by light sources, the
portions of those objects that are in shadow would be completely
black were it not for the first two finish properties, ambient
and diffuse. Ambient is used to simulate the light that is
scattered around the scene that does not come directly from a
light source. Diffuse determines how much of the light that is
seen comes directly from a light source. These two keywords work
together to control the simulation of ambient light. Let's use
our gray sphere to demonstrate this. Let's also change our plane
back to its original green and white checkered pattern.

  plane {y,-1.5
    pigment {checker Green, White}
  }
  sphere { <0,0,0>, 1
    pigment {Gray75}
    finish {
      ambient .2
      diffuse .6
  }
In the above example, the default values for ambient and diffuse
are used. We render this to see what the effect is and then make
the following change to the finish.

  ambient 0
  diffuse 0
The sphere is black because we have specified that none of the
light coming from any light source will be reflected by the
sphere. Let's change diffuse back to the default of 0.6.

Now we see the gray surface color where the light from the light
source falls directly on the sphere but the shaded side is still
absolutely black. Now let's change diffuse to 0.3 and ambient to
0.3.

The sphere now looks almost flat. This is because we have
specified a fairly high degree of ambient light and only a low
amount of the light coming from the light source is diffusely
reflected towards the camera. The default values of ambient and
diffuse are pretty good averages and a good starting point. In
most cases, an ambient value of 0.1 ... 0.2 is sufficient and a
diffuse value of 0.5 ... 0.7 will usually do the job. There are a
couple of exceptions. If we have a completely transparent surface
with high refractive and/or reflective values, low values of both
ambient and diffuse may be best. Here is an example:

sphere { <0,0,0>, 1
   pigment { White filter 1 }
   finish {
      ambient 0
      diffuse 0
      reflection .25
      specular 1
      roughness .001
   }
   interior{ior 1.33}
}
This is glass, obviously. Glass is a material that takes nearly
all of its appearance from its surroundings. Very little of the
surface is seen because it transmits or reflects practically all
of the light that shines on it. See glass.inc for some other
examples.

If we ever need an object to be completely illuminated
independently of the lighting situation in a given scene we can
do this artificially by specifying an ambient value of 1 and a
diffuse value of 0. This will eliminate all shading and simply
give the object its fullest and brightest color value at all
points. This is good for simulating objects that emit light like
light bulbs and for skies in scenes where the sky may not be
adequately lit by any other means.

Let's try this with our sphere now.

  sphere { <0,0,0>, 1
     pigment { White }
     finish {
        ambient 1
        diffuse 0
     }
  }
Rendering this we get a blinding white sphere with no visible
highlights or shaded parts. It would make a pretty good
streetlight.


2.7.3.2   Using Surface Highlights
In the glass example above, we noticed that there were bright
little hotspots on the surface. This gave the sphere a hard,
shiny appearance. POV-Ray gives us two ways to specify surface
specular highlights. The first is called Phong highlighting.
Usually, Phong highlights are described using two keywords: phong
and phong_size. The float that follows phong determines the
brightness of the highlight while the float following phong_size
determines its size. Let's try this.

  sphere { <0,0,0>, 1
    pigment { Gray50 }
    finish {
      ambient .2
      diffuse .6
      phong .75
      phong_size 25
    }
  }
Rendering this we see a fairly broad, soft highlight that gives
the sphere a kind of plastic appearance. Now let's change
phong_size to 150. This makes a much smaller highlight which
gives the sphere the appearance of being much harder and shinier.

There is another kind of highlight that is calculated by a
different means called specular highlighting. It is specified
using the keyword specular and operates in conjunction with
another keyword called roughness. These two keywords work
together in much the same way as phong and phong_size to create
highlights that alter the apparent shininess of the surface.
Let's try using specular in our sphere.

  sphere { <0,0,0>, 1
     pigment { Gray50 }
     finish {
        ambient .2
        diffuse .6
        specular .75
        roughness .1
    }
  }
Looking at the result we see a broad, soft highlight similar to
what we had when we used phong_size of 25. Change roughness to
.001 and render again. Now we see a small, tight highlight
similar to what we had when we used phong_size of 150. Generally
speaking, specular is slightly more accurate and therefore
slightly more realistic than phong but you should try both
methods when designing a texture. There are even times when both
phong and specular may be used on a finish.


2.7.3.3   Using Reflection and Metallic
There is another surface parameter that goes hand in hand with
highlights, reflection. Surfaces that are very shiny usually have
a degree of reflection to them. Let's take a look at an example.

  sphere { <0,0,0>, 1
     pigment { Gray50 }
     finish {
        ambient .2
        diffuse .6
        specular .75
        roughness .001
        reflection .5
     }
  }
We see that our sphere now reflects the green and white checkered
plane and the black background but the gray color of the sphere
seems out of place. This is another time when a lower diffuse
value is needed.  Generally, the higher reflection is the lower
diffuse should be. We lower the diffuse value to 0.3 and the
ambient value to 0.1 and render again. That is much better. Let's
make our sphere as shiny as a polished gold ball bearing.

  sphere { <0,0,0>, 1
     pigment { BrightGold }
     finish {
        ambient .1
        diffuse .1
        specular 1
        roughness .001
        reflection .75
     }
   }
That is very close but there is something wrong with the
highlight. To make the surface appear more like metal the keyword
metallic is used. We add it now to see the difference.

  sphere { <0,0,0>, 1
     pigment { BrightGold }
     finish {
        ambient .1
        diffuse .1
        specular 1
        roughness .001
        reflection .75
        metallic
     }
  }
We see that the highlight has taken on the color of the surface
rather than the light source. This gives the surface a more
metallic appearance.


2.7.3.4   Using Iridescence
Iridescence is what we see on the surface of an oil slick when
the sun shines on it. The rainbow effect is created by something
called thin-film interference (read section "Iridescence" for
details). For now let's just try using it. Iridescence is
specified by the irid statement and three values: amount,
thickness and turbulence. The amount is the contribution to the
overall surface color. Usually 0.1 to 0.5 is sufficient here. The
thickness affects the "busyness" of the effect. Keep this between
0.25 and 1 for best results. The turbulence is a little different
from pigment or normal turbulence. We cannot set octaves, lambda
or omega but we can specify an amount which will affect the
thickness in a slightly different way from the thickness value.
Values between 0.25 and 1 work best here too. Finally,
iridescence will respond to the surface normal since it depends
on the angle of incidence of the light rays striking the surface.
With all of this in mind, let's add some iridescence to our glass
sphere.

sphere { <0,0,0>, 1
     pigment { White filter 1 }
     finish {
        ambient .1
        diffuse .1
        reflection .2
        specular 1
        roughness .001
        irid {
          0.35
          thickness .5
          turbulence .5
        }
     }
     interior{
        ior 1.5
        fade_distance 5
        fade_power 1
        caustics 1
     }
}
We try to vary the values for amount, thickness and turbulence to
see what changes they make. We also try to add a normal block to
see what happens.


2.7.4     Working With Pigment Maps
Let's look at the pigment map. We must not confuse this with a
color map, as color maps can only take individual colors as
entries in the map, while pigment maps can use entire other
pigment patterns. To get a feel for these, let's begin by setting
up a basic plane with a simple pigment map. Now, in the following
example, we are going to declare each of the pigments we are
going to use before we actually use them. This isn't strictly
necessary (we could put an entire pigment description in each
entry of the map) but it just makes the whole thing more
readable.

  // simple Black on White checkboard... it's a classic
  #declare Pigment1 = pigment {
    checker color Black color White
    scale .1
  }
  // kind of a "psychedelic rings" effect
  #declare Pigment2 = pigment {
    wood
    color_map {
      [ 0.0 Red ]
      [ 0.3 Yellow ]
      [ 0.6 Green ]
      [ 1.0 Blue ]
    }
  }
  plane { -z, 0
    pigment {
      gradient x
      pigment_map {
        [ 0.0 Pigment1 ]
        [ 0.5 Pigment2 ]
        [ 1.0 Pigment1 ]
      }
    }
  }
Okay, what we have done here is very simple, and probably quite
recognizable if we have been working with color maps all along
anyway. All we have done is substituted a pigment map where a
color map would normally go, and as the entries in our map, we
have referenced our declared pigments. When we render this
example, we see a pattern which fades back and forth between the
classic checkerboard, and those colorful rings. Because we fade
from Pigment1 to Pigment2 and then back again, we see a clear
blending of the two patterns at the transition points. We could
just as easily get a sudden transition by amending the map to
read.

  pigment_map {
    [ 0.0 Pigment1 ]
    [ 0.5 Pigment1 ]
    [ 0.5 Pigment2 ]
    [ 1.0 Pigment2 ]
  }
Blending individual pigment patterns is just the beginning.


2.7.5     Working With Normal Maps
 For our next example, we replace the plane in the scene with
this one.

  plane { -z, 0
    pigment { White }
    normal {
      gradient x
      normal_map {
        [ 0.0 bumps 1 scale .1]
        [ 1.0 ripples 1 scale .1]
      }
    }
  }
First of all, we have chosen a solid white color to show off all
bumping to best effect. Secondly, we notice that our map blends
smoothly from all bumps at 0.0 to all ripples at 1.0, but because
this is a default gradient, it falls off abruptly back to bumps
at the beginning of the next cycle. We Render this and see just
enough sharp transitions to clearly see where one normal gives
over to another, yet also an example of how two normal patterns
look while they are smoothly blending into one another.

The syntax is the same as we would expect. We just changed the
type of map, moved it into the normal block and supplied
appropriate bump types. It is important to remember that as of
POV-Ray 3, all patterns that work with pigments work as normals
as well (and vice versa, of course) so we could just as easily
have blended from wood to granite, or any other pattern we like.
We experiment a bit and get a feel for what the different
patterns look like.

After seeing how interesting the various normals look blended, we
might like to see them completely blended all the way through
rather than this business of fading from one to the next. Well,
that is possible too, but we would be getting ahead of ourselves.
That is called the average function, and we will return to it a
little bit further down the page.


2.7.6     Working With Texture Maps
We know how to blend colors, pigment patterns, and normals, and
we are probably thinking what about finishes? What about whole
textures? Both of these can be kind of covered under one topic.
While there is no finish map per se, there are texture maps, and
we can easily adapt these to serve as finish maps, simply by
putting the same pigment and/or normal in each of the texture
entries of the map. Here is an example. We eliminate the declared
pigments we used before and the previous plane, and add the
following.

  #declare Texture1 = texture {
    pigment { Grey }
    finish { reflection 1 }
  }
  #declare Texture2 = texture {
    pigment { Grey }
    finish { reflection 0 }
  }
  cylinder { <-2, 5, -2>, <-2, -5, -2>, 1
    pigment { Blue }
  }
  plane { -z, 0
    rotate y * 30
    texture {
      gradient y
      texture_map {
        [ 0.0 Texture1 ]
        [ 0.4 Texture1 ]
        [ 0.6 Texture2 ]
        [ 1.0 Texture2 ]
      }
      scale 2
    }
  }
Now, what have we done here? The background plane alternates
vertically between two textures, identical except for their
finishes. When we render this, the cylinder has a reflection part
of the way down the plane, and then stops reflecting, then begins
and then stops again, in a gradient pattern down the surface of
the plane. With a little adaptation, this could be used with any
pattern, and in any number of creative ways, whether we just
wanted to give various parts of an object different finishes, as
we are doing here, or whole different textures altogether.

One might ask: if there is a texture map, why do we need pigment
and normal maps? Fair question. The answer: speed of calculation.
If we use a texture map, for every in-between point, POV-Ray must
make multiple calculations for each texture element, and then run
a weighted average to produce the correct value for that point.
Using just a pigment map (or just a normal map) decreases the
overall number of calculations, and our texture renders a bit
faster in the bargain. As a rule of thumb: we use pigment or
normal maps where we can and only fall back on texture maps if we
need the extra flexibility.


2.7.7     Working With List Textures
 If we have followed the corresponding tutorials on simple
pigments, we know that there are three patterns called color list
patterns, because rather than using a color map, these simple but
useful patterns take a list of colors immediately following the
pattern keyword. We're talking about checker, hexagon, and, new
to POV-Ray 3, the brick pattern.

Naturally they also work with whole pigments, normals, and entire
textures, just as the other patterns do above. The only
difference is that we list entries in the pattern (as we would do
with individual colors) rather than using a map of entries. Here
is an example. We strike the plane and any declared pigments we
had left over in our last example, and add the following to our
basic file.

  #declare Pigment1 = pigment {
    hexagon
    color Yellow color Green color Grey
    scale .1
  }
  #declare Pigment2 = pigment {
    checker
    color Red color Blue
    scale .1
  }
  #declare Pigment3 = pigment {
    brick
    color White color Black
    rotate -90*x
    scale .1
  }
  box { -5, 5
    pigment {
      hexagon
      pigment {Pigment1}
      pigment {Pigment2}
      pigment {Pigment3}
      rotate 90*x
    }
  }
We begin by declaring an example of each of the color list
patterns as individual pigments. Then we use the hexagon pattern
as a pigment list pattern, simply feeding it a list of pigments
rather than colors as we did above. There are two rotate
statements throughout this example, because bricks are aligned
along the z-direction, while hexagons align along the y-
direction, and we wanted everything to face toward the camera we
originally declared out in the -z-direction so we can really see
the patterns within patterns effect here.

Of course color list patterns used to be only for pigments, but
as of POV-Ray 3, everything that worked for pigments can now also
be adapted for normals or entire textures. A couple of quick
examples might look like

  normal {
    brick
    normal { granite .1 }
    normal { bumps 1 scale .1 }
  }
or...

  texture {
    checker
    texture { Gold_Metal }
    texture { Silver_Metal }
  }

2.7.8     What About Tiles?
In earlier versions of POV-Ray, there was a texture pattern
called tiles. By simply using a checker texture pattern (as we
just saw above), we can achieve the same thing as tiles used to
do, so it is now obsolete. It is still supported by POV-Ray 3 for
backwards compatibility with old scene files, but now is a good
time to get in the habit of using a checker pattern instead.


2.7.9     Average Function
Now things get interesting. Above, we began to see how pigments
and normals can fade from one to the other when we used them in
maps. But how about if we want a smooth blend of patterns all the
way through? That is where a new feature called average can come
in very handy. Average works with pigment, normal, and texture
maps, although the syntax is a little bit different, and when we
are not expecting it, the change can be confusing. Here is a
simple example. We use our standard includes, camera and light
source from above, and enter the following object.

  plane { -z, 0
    pigment { White }
    normal {
      average
      normal_map {
        [ gradient x ]
        [ gradient y ]
      }
    }
  }
What we have done here is pretty self explanatory as soon as we
render it. We have combined a vertical with a horizontal gradient
bump pattern, creating crisscrossing gradients. Actually, the
crisscrossing effect is a smooth blend of gradient x with
gradient y all the way across our plane. Now, what about that
syntax difference?

We see how our normal map has changed from earlier examples. The
floating point value to the left-hand side of each map entry has
been removed.  That value usually helps in procedurally mapping
each entry to the pattern we have selected, but average is a
smooth blend all the way through, not a pattern, so it cannot use
those values. In fact, including them may sometimes lead to
unexpected results, such as entries being lost or misrepresented
in some way. To ensure that we'll get the pattern blend we
anticipate, we leave off the floating point value.


2.7.10    Working With Layered Textures
With the multitudinous colors, patterns, and options for creating
complex textures in POV-Ray, we can easily become deeply
engrossed in mixing and tweaking just the right textures to apply
to our latest creations. But as we go, sooner or later there is
going to come that special texture. That texture that is sort of
like wood, only varnished, and with a kind of spotty yellow
streaking, and some vertical gray flecks, that looks like someone
started painting over it all, and then stopped, leaving part of
the wood visible through the paint.

Only... now what? How do we get all that into one texture? No
pattern can do that many things. Before we panic and say image
map there is at least one more option: layered textures.

With layered textures, we only need to specify a series of
textures, one after the other, all associated with the same
object. Each texture we list will be applied one on top of the
other, from bottom to top in the order they appear.

It is very important to note that we must have some degree of
transparency (filter or transmit) in the pigments of our upper
textures, or the ones below will get lost underneath. We won't
receive a warning or an error - technically it is legal to do
this: it just doesn't make sense. It is like spending hours
sketching an elaborate image on a bare wall, then slapping a
solid white coat of latex paint over it.

Let's design a very simple object with a layered texture, and
look at how it works. We create a file called LAYTEX.POV and add
the following lines.

  #include "colors.inc"
  #include "textures.inc"
  camera {
    location <0, 5, -30>
    look_at <0, 0, 0>
  }
  light_source { <-20, 30, -50> color White }
  plane { y, 0 pigment { checker color Green color Yellow  } }
  background { rgb <.7, .7, 1> }
  box { <-10, 0, -10>, <10, 10, 10>
    texture {
      Silver_Metal // a metal object ...
      normal {     // ... which has suffered a beating
        dents 2
        scale 1.5
      }
    } // (end of base texture)
    texture { // ... has some flecks of rust ...
      pigment {
        granite
        color_map {
          [0.0 rgb <.2, 0, 0> ]
          [0.2 color Brown ]
          [0.2 rgbt <1, 1, 1, 1> ]
          [1.0 rgbt <1, 1, 1, 1> ]
        }
        frequency 16
      }
    } // (end rust fleck texture)
    texture { // ... and some sooty black marks
      pigment {
        bozo
        color_map {
          [0.0 color Black ]
          [0.2 color rgbt <0, 0, 0, .5> ]
          [0.4 color rgbt <.5, .5, .5, .5> ]
          [0.5 color rgbt <1, 1, 1, 1> ]
          [1.0 color rgbt <1, 1, 1, 1> ]
        }
        scale 3
      }
    } // (end of sooty mark texture)
  } // (end of box declaration)
Whew. This gets complicated, so to make it easier to read, we
have included comments showing what we are doing and where
various parts of the declaration end (so we don't get lost in all
those closing brackets!). To begin, we created a simple box over
the classic checkerboard floor, and give the background sky a
pale blue color. Now for the fun part...

To begin with we made the box use the Silver_Metal texture as
declared in textures.inc (for bonus points, look up textures.inc
and see how this standard texture was originally created
sometime). To give it the start of its abused state, we added the
dents normal pattern, which creates the illusion of some denting
in the surface as if our mysterious metal box had been knocked
around quite a bit.

The flecks of rust are nothing but a fine grain granite pattern
fading from dark red to brown which then abruptly drops to fully
transparent for the majority of the color map. True, we could
probably come up with a more realistic pattern of rust using
pigment maps to cluster rusty spots, but pigment maps are a
subject for another tutorial section, so let's skip that just
now.

Lastly, we have added a third texture to the pot. The randomly
shifting bozo texture gradually fades from blackened centers to
semi-transparent medium gray, and then ultimately to fully
transparent for the latter half of its color map. This gives us a
look of sooty burn marks further marring the surface of the metal
box. The final result leaves our mysterious metal box looking
truly abused, using multiple texture patterns, one on top of the
other, to produce an effect that no single pattern could
generate!


2.7.10.1  Declaring Layered Textures
In the event we want to reuse a layered texture on several
objects in our scene, it is perfectly legal to declare a layered
texture. We won't repeat the whole texture from above, but the
general format would be something like this:

  #declare Abused_Metal =
    texture { /* insert your base texture here... */ }
    texture { /* and your rust flecks here... */ }
    texture { /* and of course, your sooty burn marks here */ }
POV-Ray has no problem spotting where the declaration ends,
because the textures follow one after the other with no objects
or directives in between. The layered texture to be declared will
be assumed to continue until it finds something other than
another texture, so any number of layers can be added in to a
declaration in this fashion.

One final word about layered textures: whatever layered texture
we create, whether declared or not, we must not leave off the
texture wrapper. In conventional single textures a common
shorthand is to have just a pigment, or just a pigment and
finish, or just a normal, or whatever, and leave them outside of
a texture statement. This shorthand does not extend to layered
textures. As far as POV-Ray is concerned we can layer entire
textures, but not individual pieces of textures. For example

  #declare Bad_Texture =
    texture { /* insert your base texture here... */ }
    pigment { Red filter .5 }
    normal { bumps 1 }
will not work. The pigment and the normal are just floating there
without being part of any particular texture. Inside an object,
with just a single texture, we can do this sort of thing, but
with layered textures, we would just generate an error whether
inside the object or in a declaration.


2.7.10.2  Another Layered Textures Example
To further explain how layered textures work another example is
described in detail. A tablecloth is created to be used in a
picnic scene. Since a simple red and white checkered cloth looks
entirely too new, too flat, and too much like a tiled floor,
layered textures are used to stain the cloth.

We're going to create a scene containing four boxes. The first
box has that plain red and white texture we started with in our
picnic scene, the second adds a layer meant to realistically fade
the cloth, the third adds some wine stains, and the final box
adds a few wrinkles (not another layer, but we must note when and
where adding changes to the surface normal have an effect in
layered textures).

We start by placing a camera, some lights, and the first box. At
this stage, the texture is plain tiling, not layered. See file
layered1.pov.

  #include "colors.inc"
  camera {
    location <0, 0, -6>
    look_at <0, 0, 0>
  }
  light_source { <-20, 30, -100> color White }
  light_source { <10, 30, -10> color White }
  light_source { <0, 30, 10> color White }
  #declare PLAIN_TEXTURE =
    // red/white check
    texture {
      pigment {
        checker
        color rgb<1.000, 0.000, 0.000>
        color rgb<1.000, 1.000, 1.000>
        scale <0.2500, 0.2500, 0.2500>
      }
    }
  // plain red/white check box
  box { <-1, -1, -1>, <1, 1, 1>
    texture {
      PLAIN_TEXTURE
    }
    translate  <-1.5, 1.2, 0>
  }
We render this scene. It is not particularly interesting, isn't
it? That is why we will use some layered textures to make it more
interesting.

First, we add a layer of two different, partially transparent
grays. We tile them as we had tiled the red and white colors, but
we add some turbulence to make the fading more realistic. We add
following box to the previous scene and re-render (see file
layered2.pov).

  #declare FADED_TEXTURE =
    // red/white check texture
    texture {
      pigment {
        checker
        color rgb<0.920, 0.000, 0.000>
        color rgb<1.000, 1.000, 1.000>
        scale <0.2500, 0.2500, 0.2500>
      }
    }
    // greys to fade red/white
    texture {
      pigment {
        checker
        color rgbf<0.632, 0.612, 0.688, 0.698>
        color rgbf<0.420, 0.459, 0.520, 0.953>
        turbulence 0.500
        scale <0.2500, 0.2500, 0.2500>
      }
    }
  // faded red/white check box
  box { <-1, -1, -1>, <1, 1, 1>
    texture {
      FADED_TEXTURE
    }
    translate  <1.5, 1.2, 0>
  }
Even though it is a subtle difference, the red and white checks
no longer look quite so new.

Since there is a bottle of wine in the picnic scene, we thought
it might be a nice touch to add a stain or two. While this effect
can almost be achieved by placing a flattened blob on the cloth,
what we really end up with is a spill effect, not a stain. Thus
it is time to add another layer.

Again, we add another box to the scene we already have scripted
and re-render (see file layered3.pov).

  #declare STAINED_TEXTURE =
    // red/white check
    texture {
      pigment {
        checker
        color rgb<0.920, 0.000, 0.000>
        color rgb<1.000, 1.000, 1.000>
        scale <0.2500, 0.2500, 0.2500>
      }
    }
    // greys to fade check
    texture {
      pigment {
        checker
        color rgbf<0.634, 0.612, 0.688, 0.698>
        color rgbf<0.421, 0.463, 0.518, 0.953>
        turbulence 0.500
        scale <0.2500, 0.2500, 0.2500>
      }
    }
    // wine stain
    texture {
      pigment {
        spotted
        color_map {
          [ 0.000  color rgb<0.483, 0.165, 0.165> ]
          [ 0.329  color rgbf<1.000, 1.000, 1.000, 1.000> ]
          [ 0.734  color rgbf<1.000, 1.000, 1.000, 1.000> ]
          [ 1.000  color rgb<0.483, 0.165, 0.165> ]
        }
        turbulence 0.500
        frequency 1.500
      }
    }
  // stained box
  box { <-1, -1, -1>, <1, 1, 1>
    texture {
      STAINED_TEXTURE
    }
    translate  <-1.5, -1.2, 0>
  }
Now there's a tablecloth texture with personality.

Another touch we want to add to the cloth are some wrinkles as if
the cloth had been rumpled. This is not another texture layer,
but when working with layered textures, we must keep in mind that
changes to the surface normal must be included in the uppermost
layer of the texture. Changes to lower layers have no effect on
the final product (no matter how transparent the upper layers
are).

We add this final box to the script and re-render (see file
layered4.pov)

  #declare WRINKLED_TEXTURE =
    // red and white check
    texture {
      pigment {
        checker
        color rgb<0.920, 0.000, 0.000>
        color rgb<1.000, 1.000, 1.000>
        scale <0.2500, 0.2500, 0.2500>
      }
    }
    // greys to "fade" checks
    texture {
      pigment {
        checker
        color rgbf<0.632, 0.612, 0.688, 0.698>
        color rgbf<0.420, 0.459, 0.520, 0.953>
        turbulence 0.500
        scale <0.2500, 0.2500, 0.2500>
      }
    }
    // the wine stains
    texture {
      pigment {
        spotted
        color_map {
          [ 0.000  color rgb<0.483, 0.165, 0.165> ]
          [ 0.329  color rgbf<1.000, 1.000, 1.000, 1.000> ]
          [ 0.734  color rgbf<1.000, 1.000, 1.000, 1.000> ]
          [ 1.000  color rgb<0.483, 0.165, 0.165> ]
        }
        turbulence 0.500
        frequency 1.500
      }
      normal {
        wrinkles 5.0000
      }
    }
  // wrinkled box
  box { <-1, -1, -1>, <1, 1, 1>
    texture {
      WRINKLED_TEXTURE
    }
    translate  <1.5, -1.2, 0>
  }
Well, this may not be the tablecloth we want at any picnic we're
attending, but if we compare the final box to the first, we see
just how much depth, dimension, and personality is possible just
by the use of creative texturing.

One final note: the comments concerning the surface normal do not
hold true for finishes. If a lower layer contains a specular
finish and an upper layer does not, any place where the upper
layer is transparent, the specular will show through.


2.7.11    When All Else Fails: Material Maps
We have some pretty powerful texturing tools at our disposal, but
what if we want a more free form arrangement of complex textures?
Well, just as image maps do for pigments, and bump maps do for
normals, whole textures can be mapped using a material map,
should the need arise.

Just as with image maps and bump maps, we need a source image in
bitmapped format which will be called by POV-Ray to serve as the
map of where the individual textures will go, but this time, we
need to specify what texture will be associated with which
palette index. To make such an image, we can use a paint program
which allows us to select colors by their palette index number
(the actual color is irrelevant, since it is only a map to tell
POV-Ray what texture will go at that location). Now, if we have
the complete package that comes with POV-Ray, we have in our
include files an image called povmap.gif which is a bitmapped
image that uses only the first four palette indices to create a
bordered square with the words "Persistence of Vision" in it.
This will do just fine as a sample map for the following example.
Using our same include files, the camera and light source, we
enter the following object.

  plane { -z, 0
    texture {
      material_map {
        gif "povmap.gif"
        interpolate 2
        once
        texture { PinkAlabaster }          // the inner border
        texture { pigment { DMFDarkOak } } // outer border
        texture { Gold_Metal }             // lettering
        texture { Chrome_Metal }           // the window panel
      }
      translate <-0.5, -0.5, 0>
      scale 5
    }
  }
The position of the light source and the lack of foreground
objects to be reflected do not show these textures off to their
best advantage. But at least we can see how the process works.
The textures have simply been placed according to the location of
pixels of a particular palette index. By using the once keyword
(to keep it from tiling), and translating and scaling our map to
match the camera we have been using, we get to see the whole
thing laid out for us.

Of course, that is just with palette mapped image formats, such
as GIF and certain flavors of PNG. Material maps can also use non-
paletted formats, such as the TGA files that POV-Ray itself
outputs. That leads to an interesting consequence: We can use POV-
Ray to produce source maps for POV-Ray! Before we wrap up with
some of the limitations of special textures, let's do one more
thing with material maps, to show how POV-Ray can make its own
source maps.

To begin with, if using an non-paletted image, POV-Ray looks at
the 8 bit red component of the pixel's color (which will be a
value from 0 to 255) to determine which texture from the list to
use. So to create a source map, we need to control very precisely
what the red value of a given pixel will be. We can do this by

  1.)  Using an rgb statement to choose our color such as rgb
  <N/255,0,0>, where "N" is the red value we want to assign that
  pigment, and then...
  2.)  Use no light sources and apply a finish of finish{ambient
  1} to all objects, to ensure that highlighting and shadowing
  will not interfere.
Confused? Alright, here is an example, which will generate a map
very much like povmap.gif which we used earlier, except in TGA
file format. We notice that we have given the pigments blue and
green components too. POV-Ray will ignore that in our final map,
so this is really for us humans, whose unaided eyes cannot tell
the difference between red variances of 0 to 4/255ths. Without
those blue and green variances, our map would look to our eyes
like a solid black screen. That may be a great way to send secret
messages using POV-Ray (plug it into a material map to decode)
but it is no use if we want to see what our source map looks like
to make sure we have what we expected to.

We render the following code, and name the resulting file
povmap.tga.

  camera {
    orthographic
    up <0, 5, 0>
    right <5, 0, 0>
    location <0, 0, -25>
    look_at <0, 0, 0>
  }
  plane { -z, 0
    pigment { rgb <1/255, 0, 0.5> }
    finish { ambient 1 }
  }
  box { <-2.3, -1.8, -0.2>, <2.3, 1.8, -0.2>
    pigment { rgb <0/255, 0, 1> }
    finish { ambient 1 }
  }
  box { <-1.95, -1.3, -0.4>, <1.95, 1.3, -0.3>
    pigment { rgb <2/255, 0.5, 0.5> }
    finish { ambient 1 }
  }
  text { ttf "crystal.ttf", "The vision", 0.1, 0
    scale <0.7, 1, 1>
    translate <-1.8, 0.25, -0.5>
    pigment { rgb <3/255, 1, 1> }
    finish { ambient 1 }
  }
  text { ttf "crystal.ttf", "Persists!", 0.1, 0
    scale <0.7, 1, 1>
    translate <-1.5, -1, -0.5>
    pigment { rgb <3/255, 1, 1> }
    finish { ambient 1 }
  }
All we have to do is modify our last material map example by
changing the material map from GIF to TGA and modifying the
filename. When we render using the new map, the result is
extremely similar to the palette mapped GIF we used before,
except that we didn't have to use an external paint program to
generate our source: POV-Ray did it all!


2.7.12    Limitations Of Special Textures
There are a couple limitations to all of the special textures we
have seen (from textures, pigment and normal maps through
material maps). First, if we have used the default directive to
set the default texture for all items in our scene, it will not
accept any of the special textures discussed here.  This is
really quite minor, since we can always declare such a texture
and apply it individually to all objects. It doesn't actually
prevent us from doing anything we couldn't otherwise do.

The other is more limiting, but as we will shortly see, can be
worked around quite easily. If we have worked with layered
textures, we have already seen how we can pile multiple texture
patterns on top of one another (as long as one texture has
transparency in it). This very useful technique has a problem
incorporating the special textures we have just seen as a layer.
But there is an answer!

For example, say we have a layered texture called Speckled_Metal,
which produces a silver metallic surface, and then puts tiny
specks of rust all over it. Then we decide, for a really rusty
look, we want to create patches of concentrated rust, randomly
over the surface. The obvious approach is to create a special
texture pattern, with transparency to use as the top layer. But
of course, as we have seen, we wouldn't be able to use that
texture pattern as a layer. We would just generate an error
message. The solution is to turn the problem inside out, and make
our layered texture part of the texture pattern instead, like
this

  // This part declares a pigment for use
  // in the rust patch texture pattern
  #declare Rusty = pigment {
    granite
    color_map {
      [ 0 rgb <0.2, 0, 0> ]
      [ 1 Brown ]
    }
    frequency 20
  }
  // And this part applies it
  // Notice that our original layered texture
  // "Speckled_Metal" is now part of the map
  #declare Rust_Patches = texture {
    bozo
    texture_map {
      [ 0.0  pigment {Rusty} ]
      [ 0.75 Speckled_Metal ]
      [ 1.0  Speckled_Metal ]
    }
  }
And the ultimate effect is the same as if we had layered the rust
patches on to the speckled metal anyway.

With the full array of patterns, pigments, normals, finishes,
layered and special textures, there is now practically nothing we
cannot create in the way of amazing textures. An almost infinite
number of new possibilities are just waiting to be created!


2.8  Using the Camera

2.8.1     Using Focal Blur
Let's construct a simple scene to illustrate the use of focal
blur. For this example we will use a pink sphere, a green box and
a blue cylinder with the sphere placed in the foreground, the box
in the center and the cylinder in the background. A checkered
floor for perspective and a couple of light sources will complete
the scene. We create a new file called focaldem.pov and enter the
following text

  #include "colors.inc"
  #include "shapes.inc"
  #include "textures.inc"
  sphere { <1, 0, -6>, 0.5
    finish {
      ambient 0.1
      diffuse 0.6
    }
    pigment { NeonPink }
  }
  box { <-1, -1, -1>, < 1,  1,  1>
    rotate <0, -20, 0>
    finish {
      ambient 0.1
      diffuse 0.6
    }
    pigment { Green }
  }
  cylinder { <-6, 6, 30>, <-6, -1, 30>, 3
    finish {
      ambient 0.1
      diffuse 0.6
    }
    pigment {NeonBlue}
  }
  plane { y, -1.0
    pigment {
      checker color Gray65 color Gray30
    }
  }
  light_source { <5, 30, -30> color White }
  light_source { <-5, 30, -30> color White }
Now we can proceed to place our focal blur camera to an
appropriate viewing position. Straight back from our three
objects will yield a nice view. Adjusting the focal point will
move the point of focus anywhere in the scene. We just add the
following lines to the file:

  camera {
    location <0.0, 1.0, -10.0>
    look_at  <0.0, 1.0,  0.0>
  //  focal_point <-6, 1, 30>    // blue cylinder in focus
  //  focal_point < 0, 1,  0>    // green box in focus
    focal_point < 1, 1, -6>    // pink sphere in focus
    aperture 0.4     // a nice compromise
  //  aperture 0.05    // almost everything is in focus
  //  aperture 1.5     // much blurring
  //  blur_samples 4       // fewer samples, faster to render
    blur_samples 20      // more samples, higher quality image
  }
The focal point is simply the point at which the focus of the
camera is at its sharpest. We position this point in our scene
and assign a value to the aperture to adjust how close or how far
away we want the focal blur to occur from the focused area.

The aperture setting can be considered an area of focus. Opening
up the aperture has the effect of making the area of focus
smaller while giving the aperture a smaller value makes the area
of focus larger. This is how we control where focal blur begins
to occur around the focal point.

The blur samples setting determines how many rays are used to
sample each pixel. Basically, the more rays that are used the
higher the quality of the resultant image, but consequently the
longer it takes to render. Each scene is different so we have to
experiment.  This tutorial has examples of 4 and 20 samples but
we can use more for high resolution images. We should not use
more samples than is necessary to achieve the desired quality -
more samples take more time to render. The confidence and
variance settings are covered in section "Focal Blur".

We experiment with the focal point, aperture, and blur sample
settings.  The scene has lines with other values that we can try
by commenting out the default line with double slash marks and un-
commenting the line we wish to try out. We make only one change
at a time to see the effect on the scene.

Two final points when tracing a scene using a focal blur camera.
We needn't specify anti-aliasing because the focal blur code uses
its one sampling method that automatically takes care of anti-
aliasing. Focal blur can only be used with the perspective
camera.


2.9  Using Atmospheric Effects
POV-Ray offers a variety of atmospheric effects, i. e. features
that affect the background of the scene or the air by which
everything is surrounded.

It is easy to assign a simple color or a complex color pattern to
a virtual sky sphere. You can create anything from a cloud free,
blue summer sky to a stormy, heavy clouded sky. Even starfields
can easily be created.

You can use different kinds of fog to create foggy scenes.
Multiple fog layers of different colors can add an eerie touch to
your scene.

A much more realistic effect can be created by using an
atmosphere, a constant fog that interacts with the light coming
from light sources. Beams of light become visible and objects
will cast shadows into the fog.

Last but not least you can add a rainbow to your scene.


2.9.1     The Background
The background feature is used to assign a color to all rays that
don't hit any object. This is done in the following way.

  camera {
    location <0, 0, -10>
    look_at <0, 0, 0>
  }
  background { color rgb <0.2, 0.2, 0.3> }
  sphere { 0, 1
    pigment { color rgb <0.8, 0.5, 0.2> }
  }
The background color will be visible if a sky sphere is used and
if some translucency remains after all sky sphere pigment layers
are processed.


2.9.2     The Sky Sphere
The sky_sphere can be used to easily create a cloud covered sky,
a nightly star sky or whatever sky you have in mind.

In the following examples we'll start with a very simple sky
sphere that will get more and more complex as we add new features
to it.


2.9.2.1   Creating a Sky with a Color Gradient
Beside the single color sky sphere that is covered with the
background feature the simplest sky sphere is a color gradient.

You may have noticed that the color of the sky varies with the
angle to the earth's surface normal. If you look straight up the
sky normally has a much deeper blue than it has at the horizon.

We want to model this effect using the sky sphere as shown in the
scene below (skysph1.pov).

  #include "colors.inc"
  camera {
    location <0, 1, -4>
    look_at <0, 2, 0>
    angle 80
  }
  light_source { <10, 10, -10> White }
  sphere { 2*y, 1
    pigment { color rgb <1, 1, 1> }
    finish { ambient 0.2 diffuse 0 reflection 0.6 }
  }
  sky_sphere {
    pigment {
      gradient y
      color_map {
        [0 color Red]
        [1 color Blue]
      }
      scale 2
      translate -1
    }
  }
The interesting part is the sky sphere statement. It contains a
pigment that describe the look of the sky sphere. We want to
create a color gradient along the viewing angle measured against
the earth's surface normal. Since the ray direction vector is
used to calculate the pigment colors we have to use the y-
gradient.

The scale and translate transformation are used to map the points
derived from the direction vector to the right range. Without
those transformations the pattern would be repeated twice on the
sky sphere. The scale statement is used to avoid the repetition
and the translate -1 statement moves the color at index zero to
the bottom of the sky sphere (that's the point of the sky sphere
you'll see if you look straight down).

After this transformation the color entry at position 0 will be
at the bottom of the sky sphere, i. e. below us, and the color at
position 1 will be at the top, i. e. above us.

The colors for all other positions are interpolated between those
two colors as you can see in the resulting image.

                                
                                
                  A simple gradient sky sphere.
                                
If you want to start one of the colors at a specific angle you'll
first have to convert the angle to a color map index. This is
done by using the formula

  color_map_index = (1 - cos(angle)) / 2
where the angle is measured against the negated earth's surface
normal. This is the surface normal pointing towards the center of
the earth. An angle of 0 degrees describes the point below us
while an angle of 180 degrees represents the zenith.

In POV-Ray you first have to convert the degree value to radian
values as it is shown in the following example.

  sky_sphere {
    pigment {
      gradient y
      color_map {
        [(1-cos(radians( 30)))/2 color Red]
        [(1-cos(radians(120)))/2 color Blue]
      }
      scale 2
      translate -1
    }
  }
This scene uses a color gradient that starts with a red color at
30 degrees and blends into the blue color at 120 degrees. Below
30 degrees everything is red while above 120 degrees all is blue.


2.9.2.2   Adding the Sun
In the following example we will create a sky with a red sun
surrounded by a red color halo that blends into the dark blue
night sky. We'll do this using only the sky sphere feature.

The sky sphere we use is shown below. A ground plane is also
added for greater realism (skysph2.pov).

  sky_sphere {
    pigment {
      gradient y
      color_map {
        [0.000 0.002 color rgb <1.0, 0.2, 0.0>
                     color rgb <1.0, 0.2, 0.0>]
        [0.002 0.200 color rgb <0.8, 0.1, 0.0>
                     color rgb <0.2, 0.2, 0.3>]
      }
      scale 2
      translate -1
    }
    rotate -135*x
  }
  plane { y, 0
    pigment { color Green }
    finish { ambient .3 diffuse .7 }
  }
The gradient pattern and the transformation inside the pigment
are the same as in the example in the previous section.

The color map consists of three colors. A bright, slightly
yellowish red that is used for the sun, a darker red for the halo
and a dark blue for the night sky. The sun's color covers only a
very small portion of the sky sphere because we don't want the
sun to become too big. The color is used at the color map values
0.000 and 0.002 to get a sharp contrast at value 0.002 (we don't
want the sun to blend into the sky). The darker red color used
for the halo blends into the dark blue sky color from value 0.002
to 0.200. All values above 0.200 will reveal the dark blue sky.

The rotate -135*x statement is used to rotate the sun and the
complete sky sphere to its final position. Without this rotation
the sun would be at 0 degrees, i.e. right below us.

                                
                                
               A red sun descends into the night.
                                
Looking at the resulting image you'll see what impressive effects
you can achieve with the sky sphere.


2.9.2.3   Adding Some Clouds
To further improve our image we want to add some clouds by adding
a second pigment. This new pigment uses the bozo pattern to
create some nice clouds. Since it lays on top of the other
pigment it needs some transparent colors in the color map (look
at entries 0.5 to 1.0).

  sky_sphere {
    pigment {
      gradient y
      color_map {
        [0.000 0.002 color rgb <1.0, 0.2, 0.0>
                     color rgb <1.0, 0.2, 0.0>]
        [0.002 0.200 color rgb <0.8, 0.1, 0.0>
                     color rgb <0.2, 0.2, 0.3>]
      }
      scale 2
      translate -1
    }
    pigment {
      bozo
      turbulence 0.65
      octaves 6
      omega 0.7
      lambda 2
      color_map {
          [0.0 0.1 color rgb <0.85, 0.85, 0.85>
                   color rgb <0.75, 0.75, 0.75>]
          [0.1 0.5 color rgb <0.75, 0.75, 0.75>
                   color rgbt <1, 1, 1, 1>]
          [0.5 1.0 color rgbt <1, 1, 1, 1>
                   color rgbt <1, 1, 1, 1>]
      }
      scale <0.2, 0.5, 0.2>
    }
    rotate -135*x
  }
                                
                                
                A cloudy sky with a setting sun.
                                
The sky sphere has one drawback as you might notice when looking
at the final image (skysph3.pov). The sun doesn't emit any light
and the clouds will not cast any shadows. If you want to have
clouds that cast shadows you'll have to use a real, large sphere
with an appropriate texture and a light source somewhere outside
the sphere.


2.9.3     The Fog
You can use the fog feature to add fog of two different types to
your scene: constant fog and ground fog. The constant fog has a
constant density everywhere while the ground fog's density
decreases as you move upwards.

The usage of both fog types will be described in the next
sections in detail.


2.9.3.1   A Constant Fog
The simplest fog type is the constant fog that has a constant
density in all locations. It is specified by a distance keyword
which actually describes the fog's density and a fog color.

The distance value determines the distance at which 36.8% of the
background are still visible (for a more detailed explanation of
how the fog is calculated read the reference section "Fog").

The fog color can be used to create anything from a pure white to
a red, blood-colored fog. You can also use a black fog to
simulate the effect of a limited range of vision.

The following example will show you how to add fog to a simple
scene (fog1.pov).

  #include "colors.inc"
  camera {
    location  <0, 20, -100>
  }
  background { color SkyBlue }
  plane { y, -10
    pigment {
      checker color Yellow color Green
      scale 20
    }
  }
  sphere { <0, 25, 0>, 40
    pigment { Red }
    finish { phong 1.0 phong_size 20 }
  }
  sphere { <-100, 150, 200>,  20
    pigment { Green }
    finish { phong 1.0 phong_size 20 }
  }
  sphere { <100, 25, 100>, 30
    pigment { Blue }
    finish { phong 1.0 phong_size 20 }
  }
  light_source { <100, 120, 40> color White}
  fog {
    distance 150
    color rgb<0.3, 0.5, 0.2>
  }
                                
                                
                         A foggy scene.
                                
According to their distance the spheres in this scene more or
less vanish in the greenish fog we used, as does the checkerboard
plane.


2.9.3.2   Setting a Minimum Translucency
If you want to make sure that the background does not completely
vanish in the fog you can set the transmittance channel of the
fog's color to the amount of background you always want to be
visible.

Using as transmittance value of 0.2 as in

  fog {
    distance 150
    color rgbt<0.3, 0.5, 0.2, 0.2>
  }
the fog's translucency never drops below 20% as you can see in
the resulting image (fog2.pov).

                                
                                
Adding a translucency threshold you make sure that the background
                        does not vanish.
                                

2.9.3.3   Creating a Filtering Fog
The greenish fog we have used so far doesn't filter the light
passing through it. All it does is to diminish the light's
intensity. We can change this by using a non-zero filter channel
in the fog's color (fog3.pov).

  fog {
    distance 150
    color rgbf<0.3, 0.5, 0.2, 1.0>
  }
The filter value determines the amount of light that is filtered
by the fog. In our example 100% of the light passing through the
fog will be filtered by the fog. If we had used a value of 0.7
only 70% of the light would have been filtered. The remaining 30%
would have passed unfiltered.

                                
                                
                        A filtering fog.
                                
You'll notice that the intensity of the objects in the fog is not
only diminished due to the fog's color but that the colors are
actually influenced by the fog. The red and especially the blue
sphere got a green hue.


2.9.3.4   Adding Some Turbulence to the Fog
In order to make our somewhat boring fog a little bit more
interesting we can add some turbulence, making it look like it
had a non-constant density (fog4.pov).

  fog {
    distance 150
    color rgbf<0.3, 0.5, 0.2, 1.0>
    turbulence 0.2
    turb_depth 0.3
  }
                                
                                
     Adding some turbulence makes the fog more interesting.
                                
The turbulence keyword is used to specify the amount of
turbulence used while the turb_depth value is used to move the
point at which the turbulence value is calculated along the
viewing ray. Values near zero move the point to the viewer while
values near one move it to the intersection point (the default
value is 0.5). This parameter can be used to avoid noise that may
appear in the fog due to the turbulence (this normally happens at
very far away intersection points, especially if no intersection
occurs, i. e. the background is hit). If this happens just lower
the turb_depth value until the noise vanishes.

You should keep in mind that the actual density of the fog does
not change. Only the distance-based attenuation value of the fog
is modified by the turbulence value at a point along the viewing
ray.


2.9.3.5   Using Ground Fog
The much more interesting and flexible fog type is the ground
fog, which is selected with the fog_type statement. It's
appearance is described with the fog_offset and fog_alt keywords.
The fog_offset specifies the height, i. e. y value, below which
the fog has a constant density of one. The fog_alt keyword
determines how fast the density of the fog will approach zero as
one moves along the y axis. At a height of fog_offset+fog_alt the
fog will have a density of 25%.

The following example (fog5.pov) uses a ground fog which has a
constant density below y=25 (the center of the red sphere) and
quickly falls off for increasing altitudes.

  fog {
    distance 150
    color rgbf<0.3, 0.5, 0.2, 1.0>
    fog_type 2
    fog_offset 25
    fog_alt 1
  }
                                
                                
    The ground fog only covers the lower parts of the world.'
                                

2.9.3.6   Using Multiple Layers of Fog
It is possible to use several layers of fog by using more than
one fog statement in your scene file. This is quite useful if you
want to get nice effects using turbulent ground fogs. You could
add up several, differently colored fogs to create an eerie scene
for example.

Just try the following example (fog6.pov).

  fog {
    distance 150
    color rgb<0.3, 0.5, 0.2>
    fog_type 2
    fog_offset 25
    fog_alt 1
    turbulence 0.1
    turb_depth 0.2
  }
  fog {
    distance 150
    color rgb<0.5, 0.1, 0.1>
    fog_type 2
    fog_offset 15
    fog_alt 4
    turbulence 0.2
    turb_depth 0.2
  }
  fog {
    distance 150
    color rgb<0.1, 0.1, 0.6>
    fog_type 2
    fog_offset 10
    fog_alt 2
  }
                                
                                
Quite nice results can be achieved using multiple layers of fog.
                                
You can combine constant density fogs, ground fogs, filtering
fogs, non-filtering fogs, fogs with a translucency threshold,
etc.


2.9.3.7   Fog and Hollow Objects
Whenever you use the fog feature and the camera is inside a non-
hollow object you won't get any fog effects. For a detailed
explanation why this happens see "Empty and Solid Objects".

In order to avoid this problem you have to make all those objects
hollow by either making sure the camera is outside these objects
(using the inverse keyword) or by adding the hollow to them
(which is much easier).


2.9.4     The Rainbow
The rainbow feature can be used to create rainbows and maybe
other more strange effects. The rainbow is a fog like effect that
is restricted to a cone-like volume.


2.9.4.1   Starting With a Simple Rainbow
The rainbow is specified with a lot of parameters: the angle
under which it is visible, the width of the color band, the
direction of the incoming light, the fog-like distance based
particle density and last but not least the color map to be used.

The size and shape of the rainbow are determined by the angle and
width keywords. The direction keyword is used to set the
direction of the incoming light, thus setting the rainbow's
position. The rainbow is visible when the angle between the
direction vector and the incident light direction is larger than
angle-width/2 and smaller than angle+width/2.

The incoming light is the virtual light source that is
responsible for the rainbow. There needn't be a real light source
to create the rainbow effect.

The rainbow is a fog-like effect, i.e. the rainbow's color is
mixed with the background color based on the distance to the
intersection point. If you choose small distance values the
rainbow will be visible on objects, not just in the background.
You can avoid this by using a very large distance value.

The color map is the crucial part of the rainbow since it
contains all the colors that normally can be seen in a rainbow.
The color of the innermost color band is taken from the color map
entry 0 while the outermost band is take from entry 1. You should
note that due to the limited color range any monitor can display
it is impossible to create a real rainbow. There are just some
colors that you cannot display.

The filter channel of the rainbow's color map is used in the same
way as with fogs. It determines how much of the light passing
through the rainbow is filtered by the color.

The following example shows a simple scene with a ground plane,
three spheres and a somewhat exaggerated rainbow (rainbow1.pov).

  #include "colors.inc"
  camera {
    location <0, 20, -100>
    look_at <0, 25, 0>
    angle 80
  }
  background { color SkyBlue }
  plane { y, -10 pigment { color Green } }
  light_source {<100, 120, 40> color White}
  // declare rainbow's colors
  #declare r_violet1 = color rgbf<1.0, 0.5, 1.0, 1.0>;
  #declare r_violet2 = color rgbf<1.0, 0.5, 1.0, 0.8>;
  #declare r_indigo  = color rgbf<0.5, 0.5, 1.0, 0.8>;
  #declare r_blue    = color rgbf<0.2, 0.2, 1.0, 0.8>;
  #declare r_cyan    = color rgbf<0.2, 1.0, 1.0, 0.8>;
  #declare r_green   = color rgbf<0.2, 1.0, 0.2, 0.8>;
  #declare r_yellow  = color rgbf<1.0, 1.0, 0.2, 0.8>;
  #declare r_orange  = color rgbf<1.0, 0.5, 0.2, 0.8>;
  #declare r_red1    = color rgbf<1.0, 0.2, 0.2, 0.8>;
  #declare r_red2    = color rgbf<1.0, 0.2, 0.2, 1.0>;
  // create the rainbow
  rainbow {
    angle 42.5
    width 5
    distance 1.0e7
    direction <-0.2, -0.2, 1>
    jitter 0.01
    color_map {
      [0.000  color r_violet1]
      [0.100  color r_violet2]
      [0.214  color r_indigo]
      [0.328  color r_blue]
      [0.442  color r_cyan]
      [0.556  color r_green]
      [0.670  color r_yellow]
      [0.784  color r_orange]
      [0.900  color r_red1]
    }
  }
Some irregularity is added to the color bands using the jitter
keyword.

                                
                                
                       A colorful rainbow.
                                
The rainbow in our sample is much too bright. You'll never see a
rainbow like this in reality. You can decrease the rainbow's
colors by decreasing the RGB values in the color map.


2.9.4.2   Increasing the Rainbow's Translucency
The result we have so far looks much too bright. Just reducing
the rainbow's color helps but it's much better to increase the
translucency of the rainbow because it is more realistic if the
background is visible through the rainbow.

We can use the transmittance channel of the colors in the color
map to specify a minimum translucency, just like we did with the
fog. To get realistic results we have to use very large
transmittance values as you can see in the following example
(rainbow2.pov).

  rainbow {
    angle 42.5
    width 5
    distance 1.0e7
    direction <-0.2, -0.2, 1>
    jitter 0.01
    color_map {
      [0.000  color r_violet1 transmit 0.98]
      [0.100  color r_violet2 transmit 0.96]
      [0.214  color r_indigo  transmit 0.94]
      [0.328  color r_blue    transmit 0.92]
      [0.442  color r_cyan    transmit 0.90]
      [0.556  color r_green   transmit 0.92]
      [0.670  color r_yellow  transmit 0.94]
      [0.784  color r_orange  transmit 0.96]
      [0.900  color r_red1    transmit 0.98]
    }
  }
The transmittance values increase at the outer bands of the
rainbow to make it softly blend into the background.

                                
                                
                 A much more realistic rainbow.
                                
The resulting image looks much more realistic than our first
rainbow.


2.9.4.3   Using a Rainbow Arc
Currently our rainbow has a circular shape, even though most of
it is hidden below the ground plane. You can easily create a
rainbow arc by using the arc_angle keyword with an angle below
360 degrees.

If you use arc_angle 120 for example you'll get a rainbow arc
that abruptly vanishes at the arc's ends. This does not look
good. To avoid this the falloff_angle keyword can be used to
specify a region where the arc smoothly blends into the
background.

As explained in the rainbow's reference section (see "Rainbow")
the arc extends from -arc_angle/2 to arc_angle/2 while the
blending takes place from -arc_angle/2 to -falloff_angle/2 and
falloff_angle/2 to arc_angle/2. This is the reason why the
falloff_angle has to be smaller or equal to the arc_angle.

In the following examples we use an 120 degrees arc with a 45
degree falloff region on both sides of the arc (rainbow3.pov).

  rainbow {
    angle 42.5
    width 5
    arc_angle 120
    falloff_angle 30
    distance 1.0e7
    direction <-0.2, -0.2, 1>
    jitter 0.01
    color_map {
      [0.000  color r_violet1 transmit 0.98]
      [0.100  color r_violet2 transmit 0.96]
      [0.214  color r_indigo  transmit 0.94]
      [0.328  color r_blue    transmit 0.92]
      [0.442  color r_cyan    transmit 0.90]
      [0.556  color r_green   transmit 0.92]
      [0.670  color r_yellow  transmit 0.94]
      [0.784  color r_orange  transmit 0.96]
      [0.900  color r_red1    transmit 0.98]
    }
  }
The arc angles are measured against the rainbows up direction
which can be specified using the up keyword. By default the up
direction is the y-axis.

                                
                                
                         A rainbow arc.
                                
We finally have a realistic looking rainbow arc.


2.9.5     Animation
There are a number of programs available that will take a series
of still image files (such as POV-Ray outputs) and assemble them
into animations.  Such programs can produce AVI, MPEG, FLI/FLC,
QuickTime, or even animated GIF files (for use on the World Wide
Web). The trick, therefore, is how to produce the frames. That,
of course, is where POV-Ray comes in. In earlier versions
producing an animation series was no joy, as everything had to be
done manually. We had to set the clock variable, and handle
producing unique file names for each individual frame by hand. We
could achieve some degree of automation by using batch files or
similar scripting devices, but still, We had to set it all up by
hand, and that was a lot of work (not to mention frustration...
imagine forgetting to set the individual file names and coming
back 24 hours later to find each frame had overwritten the last).

Now, at last, with POV-Ray 3, there is a better way. We no longer
need a separate batch script or external sequencing programs,
because a few simple settings in our INI file (or on the command
line) will activate an internal animation sequence which will
cause POV-Ray to automatically handle the animation loop details
for us.

Actually, there are two halves to animation support: those
settings we put in the INI file (or on the command line), and
those code modifications we work into our scene description file.
If we've already worked with animation in previous versions of
POV-Ray, we can probably skip ahead to the section "INI File
Settings" below. Otherwise, let's start with basics. Before we
get to how to activate the internal animation loop, let's look at
a couple examples of how a couple of keywords can set up our code
to describe the motions of objects over time.


2.9.5.1   The Clock Variable: Key To It All
POV-Ray supports an automatically declared floating point
variable identified as clock (all lower case). This is the key to
making image files that can be automated. In command line
operations, the clock variable is set using the +k switch. For
example, +k3.4 from the command line would set the value of clock
to 3.4. The same could be accomplished from the INI file using
Clock=3.4 in an INI file.

If we don't set clock for anything, and the animation loop is not
used (as will be described a little later) the clock variable is
still there - it's just set for the default value of 0.0, so it
is possible to set up some POV code for the purpose of animation,
and still render it as a still picture during the object/world
creation stage of our project.

The simplest example of using this to our advantage would be
having an object which is travelling at a constant rate, say,
along the x-axis. We would have the statement

  translate <clock, 0, 0>
in our object's declaration, and then have the animation loop
assign progressively higher values to clock. And that's fine, as
long as only one element or aspect of our scene is changing, but
what happens when we want to control multiple changes in the same
scene simultaneously?

The secret here is to use normalized clock values, and then make
other variables in your scene proportional to clock. That is,
when we set up our clock, (we're getting to that, patience!) have
it run from 0.0 to 1.0, and then use that as a multiplier to some
other values. That way, the other values can be whatever we need
them to be, and clock can be the same 0 to 1 value for every
application. Let's look at a (relatively) simple example

  #include "colors.inc"
  camera {
    location <0, 3, -6>
    look_at <0, 0, 0>
  }
  light_source { <20, 20, -20> color White }
  plane { y, 0
    pigment { checker color White color Black }
  }
  sphere { <0, 0, 0> , 1
    pigment {
      gradient x
      color_map {
        [0.0 Blue  ]
        [0.5 Blue  ]
        [0.5 White ]
        [1.0 White ]
      }
      scale .25
    }
    rotate <0, 0, -clock*360>
    translate <-pi, 1, 0>
    translate <2*pi*clock, 0, 0>
  }
Assuming that a series of frames is run with the clock
progressively going from 0.0 to 1.0, the above code will produce
a striped ball which rolls from left to right across the screen.
We have two goals here:


2.  Translate the ball from point A to point B, and,
2.  Rotate the ball in exactly the right proportion to its linear
  movement to imply that it is rolling -- not gliding -- to its
  final position.
Taking the second goal first, we start with the sphere at the
origin, because anywhere else and rotation will cause it to orbit
the origin instead of rotating. Throughout the course of the
animation, the ball will turn one complete 360 degree turn.
Therefore, we used the formula, 360*clock to determine the
rotation in each frame. Since clock runs 0 to 1, the rotation of
the sphere runs from 0 degrees through 360.

Then we used the first translation to put the sphere at its
initial starting point. Remember, we couldn't have just declared
it there, or it would have orbited the origin, so before we can
meet our other goal (translation), we have to compensate by
putting the sphere back where it would have been at the start.
After that, we re-translate the sphere by a clock relative
distance, causing it to move relative to the starting point.
We've chosen the formula of 2*pi* r*clock (the widest
circumference of the sphere times current clock value) so that it
will appear to move a distance equal to the circumference of the
sphere in the same time that it rotates a complete 360 degrees.
In this way, we've synchronized the rotation of the sphere to its
translation, making it appear to be smoothly rolling along the
plane.

Besides allowing us to coordinate multiple aspects of change over
time more cleanly, mathematically speaking, the other good reason
for using normalized clock values is that it will not matter
whether we are doing a ten frame animated GIF, or a three hundred
frame AVI. Values of the clock are proportioned to the number of
frames, so that same POV code will work without regard to how
long the frame sequence is. Our rolling ball will still travel
the exact same amount no matter how many frames our animation
ends up with.


2.9.5.2   Clock Dependant Variables And Multi-Stage Animations
Okay, what if we wanted the ball to roll left to right for the
first half of the animation, then change direction 135 degrees
and roll right to left, and toward the back of the scene. We
would need to make use of POV-Ray's new conditional rendering
directives, and test the clock value to determine when we reach
the halfway point, then start rendering a different clock
dependant sequence. But our goal, as above, it to be working in
each stage with a variable in the range of 0 to 1 (normalized)
because this makes the math so much cleaner to work with when we
have to control multiple aspects during animation. So let's
assume we keep the same camera, light, and plane, and let the
clock run from 0 to 2! Now, replace the single sphere declaration
with the following...

  #if ( clock <= 1 )
    sphere { <0, 0, 0> , 1
      pigment {
        gradient x
        color_map {
          [0.0 Blue  ]
          [0.5 Blue  ]
          [0.5 White ]
          [1.0 White ]
        }
        scale .25
      }
      rotate <0, 0, -clock*360>
      translate <-pi, 1, 0>
      translate <2*pi*clock, 0, 0>
    }
  #else
    // (if clock is > 1, we're on the second phase)
    // we still want to work with  a value from 0 - 1
    #declare ElseClock = clock - 1;
    sphere { <0, 0, 0> , 1
      pigment {
        gradient x
        color_map {
          [0.0 Blue  ]
          [0.5 Blue  ]
          [0.5 White ]
          [1.0 White ]
        }
        scale .25
      }
      rotate <0, 0, ElseClock*360>
      translate <-2*pi*ElseClock, 0, 0>
      rotate <0, 45, 0>
      translate <pi, 1, 0>
    }
  #end
If we spotted the fact that this will cause the ball to do an
unrealistic snap turn when changing direction, bonus points for
us - we're a born animator. However, for the simplicity of the
example, let's ignore that for now. It will be easy enough to fix
in the real world, once we examine how the existing code works.

All we did differently was assume that the clock would run 0 to
2, and that we wanted to be working with a normalized value
instead. So when the clock goes over 1.0, POV assumes the second
phase of the journey has begun, and we declare a new variable
Elseclock which we make relative to the original built in clock,
in such a way that while clock is going 1 to 2, Elseclock is
going 0 to 1. So, even though there is only one clock, there can
be as many additional variables as we care to declare (and have
memory for), so even in fairly complex scenes, the single clock
variable can be made the common coordinating factor which
orchestrates all other motions.


2.9.5.3   The Phase Keyword
There is another keyword we should know for purposes of
animations: the phase keyword. The phase keyword can be used on
many texture elements, especially those that can take a color,
pigment, normal or texture map.  Remember the form that these
maps take. For example:

  color_map {
    [0.00 White ]
    [0.25 Blue ]
    [0.76 Green ]
    [1.00 Red ]
  }
The floating point value to the left inside each set of brackets
helps POV-Ray to map the color values to various areas of the
object being textured.  Notice that the map runs cleanly from 0.0
to 1.0?

Phase causes the color values to become shifted along the map by
a floating point value which follows the keyword phase. Now, if
we are using a normalized clock value already anyhow, we can make
the variable clock the floating point value associated with
phase, and the pattern will smoothly shift over the course of the
animation. Let's look at a common example using a gradient normal
pattern

  #include "colors.inc"
  #include "textures.inc"
  #background { rgb<0.8, 0.8, 0.8> }
  camera {
    location <1.5, 1, -30>
    look_at <0, 1, 0>
    angle 10
  }
  light_source { <-100, 20, -100> color White }
  // flag
  polygon { 5, <0, 0>, <0, 1>, <1, 1>, <1, 0>, <0, 0>
    pigment { Blue }
    normal {
      gradient x
      phase clock
      scale <0.2, 1, 1>
      sine_wave
    }
    scale <3, 2, 1>
    translate <-1.5, 0, 0>
  }
  // flagpole
  cylinder { <-1.5, -4, 0>, <-1.5, 2.25, 0>, 0.05
    texture { Silver_Metal }
  }
  // polecap
  sphere { <-1.5, 2.25, 0>, 0.1
    texture { Silver_Metal }
  }
Now, here we've created a simple blue flag with a gradient normal
pattern on it. We've forced the gradient to use a sine-wave type
wave so that it looks like the flag is rolling back and forth as
though flapping in a breeze. But the real magic here is that
phase keyword. It's been set to take the clock variable as a
floating point value which, as the clock increments slowly toward
2.0, will cause the crests and troughs of the flag's wave to
shift along the x-axis.  Effectively, when we animate the frames
created by this code, it will look like the flag is actually
rippling in the wind.

This is only one, simple example of how a clock dependant phase
shift can create interesting animation effects. Trying phase will
all sorts of texture patterns, and it is amazing the range of
animation effects we can create simply by phase alone, without
ever actually moving the object.


2.9.5.4   Do Not Use Jitter Or Crand
 One last piece of basic information to save frustration. Because
jitter is an element of anti-aliasing, we could just as easily
have mentioned this under the INI file settings section, but
there are also forms of anti-aliasing used in area lights, and
the new atmospheric effects of POV-Ray, so now is as good a time
as any.

Jitter is a very small amount of random ray perturbation designed
to diffuse tiny aliasing errors that might not otherwise totally
disappear, even with intense anti-aliasing. By randomizing the
placement of erroneous pixels, the error becomes less noticeable
to the human eye, because the eye and mind are naturally inclined
to look for regular patterns rather than random distortions.

This concept, which works fantastically for still pictures, can
become a nightmare in animations. Because it is random in nature,
it will be different for each frame we render, and this becomes
even more severe if we dither the final results down to, say 256
color animations (such as FLC's). The result is jumping pixels
all over the scene, but especially concentrated any place where
aliasing would normally be a problem (e.g., where an infinite
plane disappears into the distance).

For this reason, we should always set jitter to off in area
lights and anti-aliasing options when preparing a scene for an
animation. The (relatively) small extra measure quality due to
the use of jitter will be offset by the ocean of jumpies that
results. This general rule also applies to any truly random
texture elements, such as crand.


2.9.5.5   INI File Settings
Okay, so we have a grasp of how to code our file for animation.
We know about the clock variable, user declared clock-relative
variables, and the phase keyword. We know not to jitter or crand
when we render a scene, and we're all set build some animations.
Alright, let's have at it.

The first concept we'll need to know is the INI file settings,
Initial_Frame and Final_Frame. These are very handy settings that
will allow us to render a particular number of frames and each
with its own unique frame number, in a completely hands free way.
It is of course, so blindingly simple that it barely needs
explanation, but here's an example anyway. We just add the
following lines to our favorite INI file settings

  Initial_Frame = 1
  Final_Frame = 20
and we'll initiate an automated loop that will generate 20 unique
frames.  The settings themselves will automatically append a
frame number onto the end of whatever we have set the output file
name for, thus giving each frame an unique file number without
having to think about it. Secondly, by default, it will cycle the
clock variable up from 0 to 1 in increments proportional to the
number of frames. This is very convenient, since, no matter
whether we are making a five frame animated GIF or a 300 frame
MPEG sequence, we will have a clock value which smoothly cycles
from exactly the same start to exactly the same finish.

Next, about that clock. In our example with the rolling ball
code, we saw that sometimes we want the clock to cycle through
values other than the default of 0.0 to 1.0. Well, when that's
the case, there are setting for that too.  The format is also
quite simple. To make the clock run, as in our example, from 0.0
to 2.0, we would just add to your INI file the lines

  Initial_Clock = 0.0
  Final_Clock = 2.0
Now, suppose we were developing a sequence of 100 frames, and we
detected a visual glitch somewhere in frames, say 51 to 75. We go
back over our code and we think we've fixed it. We'd like to
render just those 25 frames instead of redoing the whole sequence
from the beginning. What do we change?

If we said make Initial_Frame = 51, and Final_Frame = 75, we're
wrong. Even though this would re-render files named with numbers
51 through 75, they will not properly fit into our sequence,
because the clock will begin at its initial value starting with
frame 51, and cycle to final value ending with frame 75. The only
time Initial_Frame and Final_Frame should change is if we are
doing an essentially new sequence that will be appended onto
existing material.

If we wanted to look at just 51 through 75 of the original
animation, we need two new INI settings

  Subset_Start_Frame = 51
  Subset_End_Frame = 75
Added to settings from before, the clock will still cycle through
its values proportioned from frames 1 to 100, but we will only be
rendering that part of the sequence from the 51st to the 75th
frames.

This should give us a basic idea of how to use animation.
Although, this introductory tutorial doesn't cover all the
angles. For example, the last two settings we just saw, subset
animation, can take fractional values, like 0.5 to 0.75, so that
the number of actual frames will not change what portion of the
animation is being rendered. There is also support for efficient
odd-even field rendering as would be useful for animations
prepared for display in interlaced playback such as television
(see the reference section for full details).

With POV-Ray 3 now fully supporting a complete host of animation
options, a whole fourth dimension is added to the raytracing
experience. Whether we are making a FLIC, AVI, MPEG, or simply an
animated GIF for our web site, animation support takes a lot of
the tedium out of the process. And don't forget that phase and
clock can be used to explore the range of numerous texture
elements, as well as some of the more difficult to master objects
(hint: the julia fractal for example). So even if we are
completely content with making still scenes, adding animation to
our repertoire can greatly enhance our understanding of what POV-
Ray is capable of. Adventure awaits!




3.0    POV-Ray Options
The reference section describes all command line switches and INI
file keywords that are used to set the options of POV-Ray. It is
supposed to be used as a reference for looking up things. It does
not contain detailed explanations on how scenes are written or
how POV-Ray is used. It just explains all features, their syntax,
applications, limits, drawbacks, etc.

POV-Ray was originally created as a command-line program for
operating systems without graphical interfaces, dialog boxes and
pull-down menus. Most versions of POV-Ray still use command-line
switches to tell it what to do. This documentation assumes you
are using the command-line version. If you are using Macintosh,
MS-Windows or other GUI versions, there will be dialog boxes or
menus which do the same thing. There is system-specific
documentation for each system describing the specific commands.


3.1  Setting POV-Ray Options
There are two distinct ways of setting POV-Ray options: command
line switches and INI file keywords. Both are explained in detail
in the following sections.


3.1.1     Command Line Switches
Command line switches consist of a + (plus) or - (minus) sign,
followed by one or more alphabetic characters and possibly a
numeric value. Here is a typical command line with switches.

  POVRAY +Isimple.pov +V +W80 +H60
povray is the name of the program and it is followed by several
switches. Each switch begins with a plus or minus sign. The +I
switch with the filename tells POV-Ray what scene file it should
use as input and +V tells the program to output its status to the
text screen as it's working. The +W and +H switches set the width
and height of the image in pixels. This image will be 80 pixels
wide by 60 pixels high.

In switches which toggle a feature, the plus turns it on and
minus turns it off. For example +P turns on the pause for
keypress   when finished option while -P turns it off. Other
switches are used to specify values and do not toggle a feature.
Either plus or minus may be used in that instance. For example
+W320 sets the width to 320 pixels. You could also use -W320 and
get the same results.

Switches may be specified in upper or lower case. They are read
left to right but in general may be specified in any order. If
you specify a switch more than once, the previous value is
generally overwritten with the last specification. The only
exception is the +L switch for setting library paths. Up to ten
unique paths may be specified.

Almost all + or - switches have an equivalent option which can be
used in an INI file which is described in the next section. A
detailed description of each switch is given in the option
reference section.


3.1.2     Using INI Files
Because it is difficult to set more than a few options on a
command line, you have the ability to put multiple options in one
or more text files. These initialization files or INI files have
.ini as their default extension. Previous versions of POV-Ray
called them default files or DEF files. You may still use
existing DEF files with this version of POV-Ray.

The majority of options you use will be stored in INI files. The
command line switches are recommended for options which you will
turn off or on frequently as you perform test renderings of a
scene you are developing. The file povray.ini is automatically
read if present.  You may specify additional INI files on the
command-line by simply typing the file name on the command line.
For example:

  POVRAY MYOPTS.INI
If no extension is given, then .ini is assumed. POV-Ray knows
this is not a switch because it is not preceded by a plus or
minus. In fact a common error among new users is that they forget
to put the +I switch before the input file name. Without the
switch, POV-Ray thinks that the scene file simple.pov is an INI
file. Don't forget! If no plus or minus precedes a command line
switch, it is assumed to be an INI file name.

You may have multiple INI files on the command line along with
switches. For example:

  POVRAY MYOPTS +V OTHER
This reads options from myopts.ini, then sets the +V switch, then
reads options from other.ini.

An INI file is a plain ASCII text file with options of the
form...

  Option_keyword=VALUE ; Text after semicolon is a comment
For example the INI equivalent of the switch +Isimple.pov is...

  Input_File_Name=simple.pov
Options are read top to bottom in the file but in general may be
specified in any order. If you specify an option more than once,
the previous values are generally overwritten with the last
specification. The only exception is the Library_Path=path
options. Up to ten unique paths may be specified.

Almost all INI-style options have equivalent + or - switches. The
option reference section gives a detailed description of all POV-
Ray options. It includes both the INI-style settings and the +/-
switches.

The INI keywords are not case sensitive. Only one INI option is
permitted per line of text. You may also include switches in your
INI file if they are easier for you. You may have multiple
switches per line but you should not mix switches and INI options
on the same line. You may nest INI files by simply putting the
file name on a line by itself with no equals sign after it.
Nesting may occur up to ten levels deep.

For example:

  ; This is a sample INI file. This entire line is a comment.
  ; Blank lines are permitted.
  Input_File_Name=simple.pov ;This sets the input file name
  +W80 +H60 ; Traditional +/- switches are permitted too
  MOREOPT   ; Read MOREOPT.INI and continue with next line
  +V        ; Another switch
  ; That's all folks!
INI files may have labeled sections so that more than one set of
options may be stored in a single file. Each section begins with
a label in [] brackets. For example:

  ; RES.INI
  ; This sample INI file is used to set resolution.
  +W120 +H100  ; This section has no label.
               ; Select it with "RES"
  [Low]
  +W80 +H60    ; This section has a label.
               ; Select it with "RES[Low]"
  [Med]
  +W320 +H200  ; This section has a label.
               ; Select it with "RES[Med]"
  [High]
  +W640 +H480  ; Labels are not case sensitive.
               ; "RES[high]" works
  [Really High]
  +W800 +H600  ; Labels may contain blanks
When you specify the INI file you should follow it with the
section label in brackets. For example...

  POVRAY RES[Med] +Imyfile.pov
POV-Ray reads res.ini and skips all options until it finds the
label Med. It processes options after that label until it finds
another label and then it skips. If no label is specified on the
command line then only the unlabeled area at the top of the file
is read. If a label is specified, the unlabeled area is ignored.

Because a blank space is considered a delimiter for command-line
switches, POV-Ray has a difficult time reading file names or INI
labels containing blanks.  The rule is that INI-style options
allow blanks in INI files but switches do not allow blanks
whether in INI files or on the command line.  For example:

 +Imy file.pov               ;doesn't work anywhere
 Input_File=my file.pov      ;works only in INI file
To nest INI files which have blanks in the file name or labels
use the Include_INI option like this:

  Input_File=my file.pov
  Include_Ini=my options[this section]

3.1.3     Using the POVINI Environment Variable
The environment variable POVINI is used to specify the location
and name of a default INI file that is read every time POV-Ray is
executed. If POVINI is not specified, or if your computer
platform does not use environment variables, a default INI file
may be read. If the specified file does not exist, a warning
message is printed.

To set the environment variable under MS-DOS you might put the
following line in your autoexec.bat file...

  set POVINI=c:\povray3\default.ini
On most operating systems the sequence of reading options is as
follows:

  1.  Read options from default INI file specified by the POVINI
  environment variable or platform specific INI file.
  2.  Read switches from command line (this includes reading any
  specified INI/DEF files).
The POVRAYOPT environment variable supported by previous POV-Ray
versions is no longer available.


3.2  Options Reference
As explained in the previous section, options may be specified by
switches or INI-style options. Almost all INI-style options have
equivalent  +/ - switches and most switches have equivalent INI-
style option. The following sections give a detailed description
of each POV-Ray option. It includes both the INI-style settings
and the +/ - switches.

The notation and terminology used is described in the tables
below.
Keyword=bool     Turn Keyword on if bool equals true,
                 yes, on or 1 and    Turn it off if
                 it is any other value.
Keyword=true     Do this option if true, yes, on or 1 is
               specified.
Keyword=false    Do this option if false, no, off or 0 is
               specified.
Keyword=filen  Set Keyword to filename where filename
ame              is any valid file name. Note: some
                 options prohibit the use of any of
                 the above true or false values as a
                 file name. They are noted in later
                 sections.
n              Any integer such as in +W320
n.n              Any float such as in Clock=3.45
0.n              Any float < 1.0 even if it has no leading
               0
s                Any string of text
x or y         Any single character
path             Any directory name, drive optional, no
               final path separator ("\" or "/",
               depending on the operating system)
Unless otherwise specifically noted, you may assume that either a
plus or minus sign before a switch will produce the same results.


3.2.1     Animation Options
POV-Ray 3.0 greatly improved its animation capability with the
addition of an internal animation loop, automatic output file
name numbering and the ability to shell out to the operating
system to external utilities which can assemble individual frames
into an animation. The internal animation loop is simple yet
flexible. You may still use external programs or batch files to
create animations without the internal loop as you may have done
in POV-Ray 2.


3.2.1.1   External Animation Loop
Clock=n.n      Sets clock float identifier
               to n.n
+Kn.n          Same as Clock=n.n
The Clock=n.n option or the +Kn.n switch may be used to pass a
single float value to the program for basic animation. The value
is stored in the float identifier clock.  If an object had a
rotate <0,clock,0> attached then you could rotate the object by
different amounts over different frames by setting
+K10.0,+K20.0... etc. on successive renderings. It is up to the
user to repeatedly invoke POV-Ray with a different Clock value
and a different Output_File_Name for each frame.


3.2.1.2   Internal Animation Loop
Initial_Frame  Sets initial frame number to
=n             n
Final_Frame=n  Sets final frame number to n
Initial_Clock  Sets initial clock value to
=n.n           n.n
Final_Clock=n  Sets final clock value to
.n             n.n
+KFIn          Same as Initial_Frame=n
+KFFn          Same as Final_Frame=n
+KIn.n         Same as Initial_Clock=n.n
+KFn.n         Same as Final_Clock=n.n
The internal animation loop new to POV-Ray 3.0 relieves the user
of the task of generating complicated sets of batch files to
invoke POV-Ray multiple times with different settings. While the
multitude of options may look intimidating, the clever set of
default values means that you will probably only need to specify
the Final_Frame=n or the +KFFn option to specify the number of
frames. All other values may remain at their defaults.

Any Final_Frame setting other than -1 will trigger POV-Ray's
internal animation loop. For example Final_Frame=10 or +KFF10
causes POV-Ray to render your scene 10 times. If you specified
Output_File_Name=file.tga then each frame would be output as
file01.tga, file02.tga, file03.tga etc. The number of zero-padded
digits in the file name depends upon the final frame number. For
example +KFF100 would generate file001.tga through file100.tga.
The frame number may encroach upon the file name. On MS-DOS with
an eight character limit, myscene.pov would render to
mysce001.tga through mysce100.tga.

The default Initial_Frame=1 will probably never have to be
changed. You would only change it if you were assembling a long
animation sequence in pieces. One scene might run from frame 1 to
50 and the next from 51 to 100. The Initial_Frame=n or +KFIn
option is for this purpose.

Note that if you wish to render a subset of frames such as 30
through 40 out of a 1 to 100 animation, you should not change
Frame_Initial or Frame_Final. Instead you should use the subset
commands described in section "Subsets of Animation Frames".

Unlike some animation packages, the action in POV-Ray animated
scenes does not depend upon the integer frame numbers. Rather you
should design your scenes based upon the float identifier clock.
By default, the clock value is 0.0 for the initial frame and 1.0
for the final frame. All other frames are interpolated between
these values. For example if your object is supposed to rotate
one full turn over the course of the animation, you could specify
rotate 360*clock*y. Then as clock runs from 0.0 to 1.0, the
object rotates about the y-axis from 0 to 360 degrees.

The major advantage of this system is that you can render a 10
frame animation or a 100 frame or 500 frame or 329 frame
animation yet you still get one full 360 degree rotation. Test
renders of a few frames work exactly like final renders of many
frames.

In effect you define the motion over a continuous float valued
parameter (the clock) and you take discrete samples at some fixed
intervals (the frames). If you take a movie or video tape of a
real scene it works the same way. An object's actual motion
depends only on time.  It does not depend on the frame rate of
your camera.

Many users have already created scenes for POV-Ray 2 that expect
clock values over a range other than the default 0.0 to 1.0. For
this reason we provide the Initial_Clock=n.n or +KIn.n and
Final_Clock=n.n or +KFn.n options. For example to run the clock
from 25.0 to 75.0 you would specify Initial_Clock=25.0 and
Final_Clock=75.0. Then the clock would be set to 25.0 for the
initial frame and 75.0 for the final frame. In-between frames
would have clock values interpolated from 25.0 through 75.0
proportionally.

Users who are accustomed to using frame numbers rather than clock
values could specify Initial_Clock=1.0 and Final_Clock=10.0 and
Frame_Final=10 for a 10 frame animation.

For new scenes, we recommend you do not change the Initial_Clock
or Final_Clock from their default 0.0 to 1.0 values. If you want
the clock to vary over a different range than the default 0.0 to
3.0, we recommend you handle this inside your scene file as
follows...

  #declare Start    = 25.0;
  #declare End      = 75.0;
  #declare My_Clock = Start+(End-Start)*clock;
Then use My_Clock in the scene description. This keeps the
critical values 25.0 and 75.0 in your .pov file.

Note that more details concerning the inner workings of the
animation loop are in the section on shell-out operating system
commands in section "Shell-out to Operating System".


3.2.1.3   Subsets of Animation Frames

Subset_Start_Frame  Set subset starting frame to
=n                  n
Subset_Start_Frame  Set subset starting frame to
=0.n                n percent
Subset_End_Frame=n  Set subset ending frame to n
Subset_End_Frame=0  Set subset ending frame to n
.n                  percent
+SFn or +SF0.n      Same as Subset_Start_Frame
+EFn or +EF0.n      Same as Subset_End_Frame
When creating a long animation, it may be handy to render only a
portion of the animation to see what it looks like. Suppose you
have 100 frames but only want to render frames 30 through 40. If
you set Initial_Frame=30 and Final_Frame=40 then the clock would
vary from 0.0 to 1.0 from frames 30 through 40 rather than 0.30
through 0.40 as it should. Therefore you should leave
Initial_Frame=1 and Final_Frame=100 and use Subset_Start_Frame=30
and Subset_End_Frame=40 to selectively render part of the scene.
POV-Ray will then properly compute the clock values.

Usually you will specify the subset using the actual integer
frame numbers however an alternate form of the subset commands
takes a float value in the range 0.0 <=n.nnn <=1.0 which is
interpreted as a fraction of the whole animation. For example,
Subset_Start_Frame=0.333 and Subset_End_Frame=0.667 would render
the middle 1/3rd of a sequence regardless of the number of
frames.


3.2.1.4   Cyclic Animation
Cyclic_Animation=b       Turn cyclic animation
ool                 on/off
+KC                      Turn cyclic animation
                    on
-KC                      Turn cyclic animation
                    off
Many computer animation sequences are designed to be run in a
continuous loop. Suppose you have an object that rotates exactly
360 degrees over the course of your animation and you did rotate
360*clock*y to do so. Both the first and last frames would be
identical. Upon playback there would be a brief one frame
jerkiness. To eliminate this problem you need to adjust the clock
so that the last frame does not match the first. For example a
ten frame cyclic animation should not use clock 0.0 to 1.0. It
should run from 0.0 to 0.9 in 0.1 increments. However if you
change to 20 frames it should run from 0.0 to 0.95 in 0.05
increments. This complicates things because you would have to
change the final clock value every time you changed Final_Frame.
Setting Cyclic_Animation=on or using +KC will cause POV-Ray to
automatically adjust the final clock value for cyclic animation
regardless of how many total frames. The default value for this
setting is off.


3.2.1.5   Field Rendering
Field_Render=boo Turn field rendering on/off
l
Odd_Field=bool   Set odd field flag
+UF              Turn field rendering on
-UF              Turn field rendering off
+UO              Set odd field flag on
-UO              Set odd field flag off
Field rendering is sometimes used for animations when the
animation is being output for television. TVs only display
alternate scan lines on each vertical refresh. When each frame is
being displayed the fields are interlaced to give the impression
of a higher resolution image. The even scan lines make up the
even field, and are drawn first (i.e. scan lines 0, 2, 4, etc.),
followed by the odd field, made up of the odd numbered scan lines
are drawn afterwards. If objects in an animation are moving
quickly, their position can change noticeably from one field to
the next. As a result, it may be desirable in these cases to have
POV-Ray render alternate fields at the actual field rate (which
is twice the frame rate), rather than rendering full frames at
the normal frame rate. This would save a great deal of time
compared to rendering the entire animation at twice the frame
rate, and then only using half of each frame.

By default, field rendering is not used. Setting Field_Render=on
or using +UF will cause alternate frames in an animation to be
only the even or odd fields of an animation. By default, the
first frame is the even field, followed by the odd field. You can
have POV-Ray render the odd field first by specifying
Odd_Field=on, or by using the +UO switch.


3.2.2     Output Options

3.2.2.1   General Output Options

3.2.2.1.1 Height and Width of Output
Height=n       Sets screen height to n
               pixels
Width=n        Sets screen width to n
               pixels
+Hn            Same as Height=n (when n >
               8)
+Wn            Same as Width=n
These switches set the height and width of the image in pixels.
This specifies the image size for file output. The preview
display, if on, will generally attempt to pick a video mode to
accommodate this size but the display settings do not in any way
affect the resulting file output.


3.2.2.1.2 Partial Output Options

Start_Column=n     Set first column to n pixels
Start_Column=0.n   Set first column to n
                 percent of width
+SCn or +SC0.n     Same as Start_Column
Start_Row=n        Set first row to n pixels
Start_Row=0.n      Set first row to n percent
                 of height
+SRn or +Sn        Same as Start_Row=n
+SR0.n or +S0.n    Same as Start_Row=0.n
End_Column=n       Set last column to n pixels
End_Column=0.n     Set last column to n percent
                 of width
+ECn or +EC0.n     Same as End_Column
End_Row=n          Set last row to n pixels
End_Row=0.n        Set last row to n percent of
                 height
+ERn or +En        Same as End_Row=n
+ER0.n or +E0.n    Same as End_Row=0.n
When doing test rendering it is often convenient to define a
small, rectangular sub-section of the whole screen so you can
quickly check out one area of the image. The Start_Row, End_Row,
Start_Column and End_Column options allow you to define the
subset area to be rendered. The default values are the full size
of the image from (1,1) which is the upper left to (w,h) on the
lower right where w and h are the Width=n and Height=n values you
have set.

Note if the number specified is greater than 1 then it is
interpreted as an absolute row or column number in pixels. If it
is a decimal value between 0.0 and 1.0 then it is interpreted as
a percent of the total width or height of the image. For example:
Start_Row=0.75 and Start_Column=0.75 starts on a row 75% down
from the top at a column 75% from the left. Thus it renders only
the lower-right 25% of the image regardless of the specified
width and height.

The +SR, +ER, +SC and +EC switches work in the same way as the
corresponding INI-style settings for both absolute settings or
percentages. Early versions of POV-Ray allowed only start and end
rows to be specified with +Sn and +En so they are still supported
in addition to +SR and +ER.


3.2.2.1.3 Interrupting Options
Test_Abort=bool  Turn test for user abort
                 on/off
+X               Turn test abort on
-X               Turn test abort off
Test_Abort_Count Set to test for abort every
=n               n pixels
+Xn              Set to test for abort every
                 n pixels on
-Xn              Set to test for abort off
                 (in future test every n
                 pixels)
On some operating systems once you start a rendering you must let
it finish. The Test_Abort=on option or +X switch causes POV-Ray
to test the keyboard for keypress. If you have pressed a key, it
will generate a controlled user abort. Files will be flushed and
closed but only data through the last full row of pixels is
saved. POV-Ray exits with an error code 2 (normally POV-Ray
returns 0 for a successful run or 1 for a fatal error).

When this option is on, the keyboard is polled on every line
while parsing the scene file and on every pixel while rendering.
Because polling the keyboard can slow down a rendering, the
Test_Abort_Count=n option or +Xn switch causes the test to be
performed only every n pixels rendered or scene lines parsed.


3.2.2.1.4 Resuming Options
Continue_Trace=b Sets continued trace on/off
ool
+C               Sets continued trace on
-C               Sets continued trace off
Create_Ini=file  Generate an INI file to file
Create_Ini=true  Generate file.ini where file
                 is scene name.
Create_Ini=false Turn off generation of
                 previously set file.ini
+GIfile          Same as Create_Ini=file
If you abort a render while it's in progress or if you used the
End_Row option to end the render prematurely, you can use
Continue_Trace=on or +C option to continue the render later at
the point where you left off. This option reads in the previously
generated output file, displays the partial image rendered so
far, then proceeds with the ray-tracing. This option cannot be
used if file output is disabled with Output_to_file=off or -F.

The Continue_Trace option may not work if the Start_Row option
has been set to anything but the top of the file, depending on
the output format being used.

POV-Ray tries to figure out where to resume an interrupted trace
by reading any previously generated data in the specified output
file. All file formats contain the image size, so this will
override any image size settings specified. Some file formats
(namely TGA and PNG) also store information about where the file
started (i. e. +SCn and +SRn options), alpha output +UA, and bit-
depth +FNn, which will override these settings. It is up to the
user to make sure that all other options are set the same as the
original render.

The Create_Ini option or +GI switch provides an easy way to
create an INI file with all of the rendering options, so you can
re-run files with the same options, or ensure you have all the
same options when resuming. This option creates an INI file with
every option set at the value used for that rendering. This
includes default values which you have not specified. For example
if you run POV-Ray with...

 POVRAY +Isimple.pov MYOPTS +GIrerun.ini MOREOPTS
POV-Ray will create a file called rerun.ini with all of the
options used to generate this scene. The file is not written
until all options have been processed. This means that in the
above example, the file will include options from both myopts.ini
and moreopts.ini despite the fact that the +GI switch is
specified between them. You may now re-run the scene with...

 POVRAY RERUN
or resume an interrupted trace with

 POVRAY RERUN +C
If you add other switches with the rerun.ini reference, they will
be included in future re-runs because the file is re-written
every time you use it.

The Create_Ini option is also useful for documenting how a scene
was rendered. If you render waycool.pov with Create_Ini=on then
it will create a file waycool.ini that you could distribute along
with your scene file so other users can exactly re-create your
image.


3.2.2.2   Display Output Options

3.2.2.2.1 Display Hardware Settings
Display=bool     Turns graphic display on/off
+D               Turns graphic display on
-D               Turns graphic display off
Video_Mode=x     Set video mode to x; does
                 not affect on/off
+Dx              Set display on; Set mode to
                 x
-Dx              Set display off; but for
                 future use mode x
Palette=y        Set display palette to y;
                 does not affect on/off
+Dxy             Set display on; Set mode x;
                 Set palette y
-Dxy             Set display off; use mode x,
                 palette y in future
Display_Gamma=n. Sets the display gamma to
n                n.n
The Display=on or +D switch will turn on the graphics display of
the image while it is being rendered. Even on some non-graphics
systems, POV-Ray may display an 80 by 24 character  "ASCII-Art"
version of your image. Where available, the display may be full,
24-bit true color. Setting Display=off or using the -D switch
will turn off the graphics display which is the default.

The Video_Mode=x option sets the display mode or hardware type
chosen where x is a single digit or letter that is machine
dependent. Generally Video_Mode=0 means the default or an auto-
detected setting should be used. When using switches, this
character immediately follows the switch. For example the +D0
switch will turn on the graphics display in the default mode.

The Palette=y option selects the palette to be used. Typically
the single character parameter y is a digit which selects one of
several fixed palettes or a letter such G for gray scale, H for
15-bit or 16-bit high color or T for 24-bit true color. When
using switches, this character is the 2nd character after the
switch. For example the +D0T switch will turn on the graphics
display in the default mode with a true color palette.

The Display_Gamma=n.n setting is new with POV-Ray 3.0, and is not
available as a command-line switch. The Display_Gamma setting
overcomes the problem of images (whether ray-traced or not)
having different brightness when being displayed on different
monitors, different video cards, and under different operating
systems. Note that the Display_Gamma is a setting based on your
computer's display hardware, and should be set correctly once and
not changed. The Display_Gamma INI setting works in conjunction
with the new assumed_gamma global setting to ensure that POV
scenes and the images they create look the same on all systems.
See section "Assumed_Gamma" which describes the assumed_gamma
global setting and describes gamma more thoroughly.

While the Display_Gamma can be different for each system, there
are a few general rules that can be used for setting
Display_Gamma if you don't know it exactly. If the Display_Gamma
keyword does not appear in the INI file, POV-Ray assumes that the
display gamma is 2.2. This is because most PC monitors have a
gamma value in the range 1.6 to 2.6 (newer models seem to have a
lower gamma value). Mac has the ability to do gamma correction
inside the system software (based on a user setting in the gamma
control panel). If the gamma control panel is turned off, or is
not available, the default Macintosh system gamma is 1.8. Some
high-end PC graphics cards can do hardware gamma correction and
should use the current Display_Gamma setting, usually 1.0. A
gamma test image is also available to help users to set their
Display_Gamma accurately.

For scene files that do not contain an assumed_gamma global
setting the INI file option Display_Gamma will not have any
affect on the preview output of POV-Ray or for most output file
formats. However, the Display_Gamma value is used when creating
PNG format output files, and also when rendering the POV-Ray
example files (because they have an assumed_gamma), so it should
still be correctly set for your system to ensure proper results.


3.2.2.2.2 Display Related Settings
Pause_When_Done=bo  Sets pause when done
ol                  on/off
+P                  Sets pause when done on
-P                  Sets pause when done off
Verbose=bool        Set verbose messages
                    on/off
+V                  Set verbose messages on
-V                  Set verbose messages off
Draw_Vistas=bool    Turn draw vistas on/off
+UD                 Turn draw vistas on
-UD                 Turn draw vistas off
On some systems, when the image is complete, the graphics display
is cleared and POV-Ray switches back into text mode to print the
final statistics and to exit. Normally when the graphics display
is on, you want to look at the image awhile before continuing.
Using Pause_When_Done=on or +P causes POV-Ray to pause in
graphics mode until you press a key to continue. The default is
not to pause (-P).

When the graphics display is not used, it is often desirable to
monitor progress of the rendering. Using Verbose=on or +V turns
on verbose reporting of your rendering progress. This reports the
number of the line currently being rendered, the elapsed time for
the current frame and other information. On some systems, this
textual information can conflict with the graphics display. You
may need to turn this off when the display is on. The default
setting is off (-V).

The option Draw_Vistas=on or +UD was originally a debugging help
for POV-Ray's vista buffer feature but it was such fun we decided
to keep it. Vista buffering is a spatial sub-division method that
projects the 2-D extents of bounding boxes onto the viewing
window. POV-Ray tests the 2-D x, y pixel location against these
rectangular areas to determine quickly which objects, if any, the
viewing ray will hit. This option shows you the 2-D rectangles
used. The default setting is off (-UD) because the drawing of the
rectangles can take considerable time on complex scenes and it
serves no critical purpose. See section "Automatic Bounding
Control" for more details.


3.2.2.2.3 Mosaic Preview
Preview_Start_Size=n  Set mosaic preview start
                    size to n
+SPn                Same as Preview_Start_Size=n
Preview_End_Size=n  Set mosaic preview end size
                    to n
+EPn                Same as Preview_End_Size=n
Typically, while you are developing a scene, you will do many low
resolution test renders to see if objects are placed properly.
Often this low resolution version doesn't give you sufficient
detail and you have to render the scene again at a higher
resolution. A feature called "mosaic preview" solves this problem
by automatically rendering your image in several passes.

The early passes paint a rough overview of the entire image using
large blocks of pixels that look like mosaic tiles. The image is
then refined using higher resolutions on subsequent passes. This
display method very quickly displays the entire image at a low
resolution, letting you look for any major problems with the
scene. As it refines the image, you can concentrate on more
details, like shadows and textures. You don't have to wait for a
full resolution render to find problems, since you can interrupt
the rendering early and fix the scene, or if things look good,
you can let it continue and render the scene at high quality and
resolution.

To use this feature you should first select a Width and Height
value that is the highest resolution you will need. Mosaic
preview is enabled by specifying how big the mosaic blocks will
be on the first pass using Preview_Start_Size=n or +SPn. The
value n should be a number greater than zero that is a power of
two (1, 2, 4, 8, 16, 32, etc.) If it is not a power of two, the
nearest power of two less than n is substituted. This sets the
size of the squares, measured in pixels. A value of 16 will draw
every 16th pixel as a 16*16 pixel square on the first pass.
Subsequent passes will use half the previous value (such as 8*8,
4*4 and so on.)

The process continues until it reaches 1*1 pixels or until it
reaches the size you set with Preview_End_Size=n or +EPn. Again
the value n should be a number greater than zero that is a power
of two and less than or equal to Preview_Start_Size. If it is not
a power of two, the nearest power of two less than n is
substituted. The default ending value is 1. If you set
Preview_End_Size to a value greater than 1 the mosaic passes will
end before reaching 1*1, but POV-Ray will always finish with a
1*1. For example, if you want a single 8*8 mosaic pass before
rendering the final image, set Preview_Start_Size=8 and
Preview_End_Size=8.

No file output is performed until the final 1*1 pass is reached.
Although the preliminary passes render only as many pixels as
needed, the 1*1 pass re-renders every pixel so that anti-aliasing
and file output streams work properly. This makes the scene take
up to 25% longer than the regular 1*1 pass to render, so it is
suggested that mosaic preview not be used for final rendering.
Also, the lack of file output until the final pass means that
renderings which are interrupted before the 1*1 pass can not be
resumed without starting over from the beginning.

Future versions of POV-Ray will include some system of temporary
files or buffers which will eliminate these inefficiencies and
limitations. Mosaic preview is still a very useful feature for
test renderings.


3.2.2.3   File Output Options
Output_to_File=b Sets file output on/off
ool
+F               Sets file output on (use
                 default type)
-F               Sets file output off
By default, POV-Ray writes an image file to disk. When you are
developing a scene and doing test renders, the graphic preview
may be sufficient. To save time and disk activity you may turn
file output off with Output_to_File=off or -F.


3.2.2.3.1 Output File Type
Output_File_Type Sets file output format to x
=x
+Fxn             Sets file output on; sets
                 format x, depth n
-Fxn             Sets file output off; but in
                 future use format x, depth n
Output_Alpha=boo Sets alpha output on/off
l
+UA              Sets alpha output on
-UA              Sets alpha output off
Bits_Per_Color=n Sets file output bits/color to
                 n
The default type of image file depends on which platform you are
using. MS-DOS and most others default to 24-bit uncompressed
Targa. See your platform-specific documentation to see what your
default file type is. You may select one of several different
file types using Output_File_Type=x or +Fx where x is one of the
following...
+FC Compressed Targa-24 format (RLE,
    run length encoded)
+FN New PNG (portable network
    graphics) format
+FP Unix PPM format
+FS System-specific such as Mac Pict
    or Windows BMP
+FT Uncompressed Targa-24 format
Note that the obsolete +FD dump format and +FR raw format have
been dropped from POV-Ray 3.0 because they were rarely used and
no longer necessary. PPM, PNG, and system specific formats have
been added. PPM format images are uncompressed, and have a simple
text header, which makes it a widely portable image format. PNG
is a new image format designed not only to replace GIF, but to
improve on its shortcomings. PNG offers the highest compression
available without loss for high quality applications, such as ray-
tracing. The system specific format depends on the platform used
and is covered in the appropriate system specific documentation.

Most of these formats output 24 bits per pixel with 8 bits for
each of red, green and blue data. PNG allows you to optionally
specify the output bit depth from 5 to 16 bits for each of the
red, green, and blue colors, giving from 15 to 48 bits of color
information per pixel. The default output depth for all formats
is 8 bits/color (16 million possible colors), but this may be
changed for PNG format files by setting Bits_Per_Color=n or by
specifying +FNn, where n is the desired bit depth.

Specifying a smaller color depth like 5 bits/color (32768 colors)
may be enough for people with 8- or 16-bit (256 or 65536 color)
displays, and will improve compression of the PNG file. Higher
bit depths like 10 or 12 may be useful for video or publishing
applications, and 16 bits/color is good for grayscale height
field output (See section "Height Field" for details on height
fields).

Targa format also allows 8 bits of alpha transparency data to be
output, while PNG format allows 5 to 16 bits of alpha
transparency data, depending on the color bit depth as specified
above. You may turn this option on with Output_Alpha=on or +UA.
The default is off or -UA. See section "Using the Alpha Channel"
for further details on transparency.

In addition to support for variable bit-depths, alpha channel,
and grayscale formats, PNG files also store the Display_Gamma
value so the image displays properly on all systems (see section
"Display Hardware Settings"). The hf_gray_16 global setting, as
described in section "HF_Gray_16" will also affect the type of
data written to the output file.


3.2.2.3.2 Output File Name
Output_File_Name=fi Sets output file to
le                  file
+Ofile              Same as
                    Output_File_Name=file
The default output filename is created from the scene name and
need not be specified. The scene name is the input name with all
drive, path, and extension information stripped. For example if
the input file name is c:\povray3\mystuff\myfile.pov the scene
name is myfile. The proper extension is appended to the scene
name based on the file type. For example myfile.tga or myfile.png
might be used.

You may override the default output name using
Output_File_Name=file or +Ofile. For example:

 Input_File_Name=myinput.pov
 Output_File_Name=myoutput.tga
If an output file name of "-" is specified (a single minus sign),
then the image will be written to standard output, usually the
screen. The output can then be piped into another program or to a
GUI if desired.

If the file specified is actually a path or directory or folder
name and not a file name, then the default output name is used
but it is written to the specified directory.  For example:

 Input_File_Name=myscene.pov
 Output_File_Name=c:\povray3\myimages\
This will create c:\povray3\myimages\myscene.tga as the output
file.


3.2.2.3.3 Output File Buffer
Buffer_Output=b  Turn output buffering on/off
ool
+B               Turn output buffering on
-B               Turn output buffering off
Buffer_Size=n    Set output buffer size to n
                 kilobytes.  If n is zero, no
                 buffering. If n < system
                 default, the system default
                 is used.
+Bn              Turn buffer on, set size n
-Bn              Turn buffer off, but for
                 future set size n
The Buffer_Output and Buffer_Size options and the +B switch
allows you to assign large buffers to the output file. This
reduces the amount of time spent writing to the disk. If this
parameter is not specified, then as each row of pixels is
finished, the line is written to the file and the file is
flushed. On most systems, this operation ensures that the file is
written to the disk so that in the event of a system crash or
other catastrophic event, at least a part of the picture has been
stored properly and retrievable on disk. The default is not to
use any buffer.


3.2.2.4   CPU Utilization Histogram
The CPU utilization histogram is a way of finding out where POV-
Ray is spending its rendering time, as well as an interesting way
of generating heightfields. The histogram splits up the screen
into a rectangular grid of blocks. As POV-Ray renders the image,
it calculates the amount of time it spends rendering each pixel
and then adds this time to the total rendering time for each grid
block. When the rendering is complete, the histogram is a file
which represents how much time was spent computing the pixels in
each grid block.

Not all versions of POV-Ray allow the creation of histograms. The
histogram output is dependent on the file type and the system
that POV-Ray is being run on.


3.2.2.4.1 File Type
Histogram_Type=y Set histogram type to y
                 (Turn off if type is 'X')
+HTy             Same as Histogram_Type=y
The histogram output file type is nearly the same as that used
for the image output file types in "Output File Type". The
available histogram file types are as follows.
+HTC      Comma separated values (CSV)
          often used in spreadsheets
+HTN      New PNG (portable network
          graphics) format grayscale
+HTP      Unix PPM format
+HTS      System-specific such as Mac Pict
          or Windows BMP
+HTT      Uncompressed Targa-24 format
          (TGA)
+HTX      No histogram file output is
          generated
Note that +HTC does not generate a compressed Targa-24 format
output file but rather a text file with a comma-separated list of
the time spent in each grid block, in left-to-right and top-to
bottom order. The units of time output to the CSV file are system
dependent. See the system specific documentation for further
details on the time units in CSV files.

The Targa and PPM format files are in the POV heightfield format
(see "Height Field"), so the histogram information is stored in
both the red and green parts of the image, which makes it
unsuitable for viewing. When used as a height field, lower values
indicate less time spent calculating the pixels in that block,
while higher indicate more time spent in that block.

PNG format images are stored as grayscale images and are useful
for both viewing the histogram data as well as for use as a
heightfield. In PNG files, the darker (lower) areas indicate less
time spent in that grid block, while the brighter (higher) areas
indicate more time spent in that grid block.


3.2.2.4.2 File Name
Histogram_Name=f Set histogram name to file
ile
+HNfile          Same as Histogram_Name=file
The histogram file name is the name of the file in which to write
the histogram data. If the file name is not specified it will
default to histgram.ext, where ext is based on the file type
specified previously. Note that if the histogram name is
specified the file name extension should match the file type.


3.2.2.4.3 Grid Size
Histogram_Grid_Size=n  Set histogram grid to nn by
n.mm                   mm
+HSnn.mm               Same as
                       Histogram_Grid_Size=nn.mm
The histogram grid size gives the number of times the image is
split up in both the horizontal and vertical directions. For
example

 povray +Isample +W640 +H480 +HTN +HS160.120 +HNhistogrm.png
will split the image into 160*120 grid blocks, each of size 4*4
pixels, and output a PNG file, suitable for viewing or for use as
a heightfield. Smaller numbers for the grid size mean more pixels
are put into the same grid block. With CSV output, the number of
values output is the same as the number of grid blocks specified.
For the other formats the image size is identical to the rendered
image rather than the specified grid size, to allow easy
comparison between the histogram and the rendered image. If the
histogram grid size is not specified, it will default to the same
size as the image, so there will be one grid block per pixel.

Note that on systems that do task-switching or multi-tasking the
histogram may not exactly represent the amount of time POV-Ray
spent in a given grid block since the histogram is based on real
time rather than CPU time. As a result, time may be spent for
operating system overhead or on other tasks running at the same
time. This will cause the histogram to have speckling, noise or
large spikes. This can be reduced by decreasing the grid size so
that more pixels are averaged into a given grid block.


3.2.3     Scene Parsing Options
POV-Ray reads in your scene file and processes it to create an
internal model of your scene. The process is called parsing. As
your file is parsed other files may be read along the way. This
section covers options concerning what to parse, where to find it
and what version specific assumptions it should make while
parsing it.


3.2.3.1   Input File Name
Input_File_Name=fi  Sets input file name to
le                  file
+Ifile              Same as
                    Input_File_Name=file
You will probably always set this option but if you do not the
default input filename is object.pov. If you do not have an
extension then .pov is assumed. On case-sensitive operating
systems both .pov and .POV are tried. A full path specification
may be used (on MS-DOS systems +Ic:\povray3\mystuff\myfile.pov is
allowed for example). In addition to specifying the input file
name this also establishes the scene name.

The scene name is the input name with drive, path and extension
stripped. In the above example the scene name is myfile. This
name is used to create a default output file name and it is
referenced other places.

If you use "-" as the input file name the input will be read from
standard input. Thus you can pipe a scene created by a program to
POV-Ray and render it without having a scene file.

Under MS-DOS you can try this feature by typing.

 type ANYSCENE.POV | povray +I-

3.2.3.2   Library Paths
Library_Path=pat Add path to list of
h                library paths
+Lpath           Same as Library_Path=path
POV-Ray looks for files in the current directory. If it does not
find a file it needs it looks in various other library
directories which you specify. POV-Ray does not search your
operating system path. It only searches the current directory and
directories which you specify with this option. For example the
standard include files are usually kept in one special directory.
You tell POV-Ray to look there with...

 Library_Path=c:\povray3\include
You must not specify any final path separators ("\" or "/") at
the end.

Multiple uses of this option switch do not override previous
settings. Up to twenty unique paths may be specified. If you
specify the exact same path twice it is only counts once. The
current directory will be searched first followed by the
indicated library directories in the order in which you specified
them.


3.2.3.3   Language Version
Version=n.n    Set initial language
               compatibility to version n.n
+MVn.n         Same as Version=n.n
As POV-Ray as evolved from version 1.0 through 3.1 we have made
every effort to maintain some amount of backwards compatibility
with earlier versions.  Some old or obsolete features can be
handled directly without any special consideration by the user.
Some old or obsolete features can no longer be handled at all.
However some old features can still be used if you warn POV-Ray
that this is an older scene.  In the POV-Ray scene language you
can use the #version directive to switch version compatibility to
different setting.  See section "The #version Directive" for more
details about the language version directive.  Additionally you
may use the Version=n.n option or the +MVn.n switch to establish
the initial setting.  For example one feature introduced in 2.0
that was incompatible with any 1.0 scene files is the parsing of
float expressions. Setting Version=1.0 or using +MV1.0 turns off
expression parsing as well as many warning messages so that
nearly all 1.0 files will still work. Naturally the default
setting for this option is Version=3.1.

NOTE: Some obsolete or re-designed features are totally
unavailable in POV-Ray 3.1 REGARDLES OF THE VERSION SETTING.
Details on these features are noted throughout this
documentation.


3.2.4     Shell-out to Operating System
Pre_Scene_Command=  Set command before entire
s                   scene
Pre_Frame_Command=  Set command before each
s                   frame
Post_Scene_Command  Set command after entire
=s                  scene
Post_Frame_Command  Set command after each frame
=s
User_Abort_Command  Set command when user aborts
=s                  POV-Ray
Fatal_Error_Comman  Set command when POV-Ray has
d=s                 fatal error
Note that no + or - switches are available for these options.
They cannot be used from the command line. They may only be used
from INI files.

POV-Ray offers you the opportunity to shell-out to the operating
system at several key points to execute another program or batch
file. Usually this is used to manage files created by the
internal animation loop however the shell commands are available
for any scene. The string s is a single line of text which is
passed to the operating system to execute a program. For example

 Post_Scene_Command=tga2gif -d -m myfile
would use the utility tga2gif with the -D and -M parameters to
convert myfile.tga to myfile.gif after the scene had finished
rendering.


3.2.4.1   String Substitution in Shell Commands
It could get cumbersome to change the Post_Scene_Command every
time you changed scene names. POV-Ray can substitute various
values into a command string for you. For example:

 Post_Scene_Command=tga2gif -d -m %s
POV-Ray will substitute the %s with the scene name in the
command. The scene name is the Input_File_Name or +I setting with
any drive, directory and extension removed. For example:

 Input_File_Name=c:\povray3\scenes\waycool.pov
is stripped down to the scene name waycool which results in...

 Post_Scene_Command=tga2gif -d -m waycool
In an animation it may be necessary to have the exact output file
name with the frame number included. The string %o will
substitute the output file name. Suppose you want to save your
output files in a zip archive using the utility program pkzip.
You could do...

 Post_Frame_Command=pkzip -m %s %o
After rendering frame 12 of myscene.pov POV-Ray would shell to
the operating system with

 pkzip -m myscene mysce012.tga
The -M switch in pkzip moves mysce012.tga to myscene.zip and
removes it from the directory. Note that %o includes frame
numbers only when in an animation loop. During the
Pre_Scene_Command and Post_Scene_Command there is no frame number
so the original, unnumbered Output_File_Name is used. Any
User_Abort_Command or Fatal_Error_Command not inside the loop
will similarly give an unnumbered %o substitution.

Here is the complete list of substitutions available for a
command string.
%o   Output file name with extension and
     embedded frame number if any
%s   Scene name derived by stripping path
     and ext from input name
%n   Frame number of this frame
%k   Clock value of this frame
%h   Height of image in pixels
%w   Width of image in pixels
%%   A single % sign.

3.2.4.2   Shell Command Sequencing
Here is the sequence of events in an animation loop. Non-animated
scenes work the exact same way except there is no loop.

1)Process all INI file keywords and command line switches just
  once.
2)Open any text output streams and do Create_INI if any.
3)Execute Pre_Scene_Command if any.
4)Loop through frames (or just do once on non-animation).
  a)Execute Pre_Frame_Command if any.
  b)Parse entire scene file, open output file and read settings,
     turn on display, render the frame, destroy all objects,
     textures etc., close output file, close display.
  c)Execute Post_Frame_Command if any.
  d)Go back to (4a) until all frames are done.
5)Execute Post_Scene_Command if any.
6)Exit POV-Ray.
If the user interrupts processing the User_Abort_Command, if any,
is executed. User aborts can only occur during the parsing and
rendering parts of step (4b) above.

If a fatal error occurs that POV-Ray notices the
Fatal_Error_Command, if any, is executed. Sometimes an unforeseen
bug or memory error could cause a total crash of the program in
which case there is no chance to shell out. Fatal errors can
occur just about anywhere including during the processing of
switches or INI files. If a fatal error occurs before POV-Ray has
read the Fatal_Error_Command string then obviously no shell can
occur.

Note that the entire scene is re-parsed for every frame. Future
versions of POV-Ray may allow you to hold over parts of a scene
from one frame to the next but for now it starts from scratch
every time. Note also that the Pre_Frame_Command occurs before
the scene is parsed. You might use this to call some custom scene
generation utility before each frame. This utility could rewrite
your .pov or .inc files if needed. Perhaps you will want to
generate new .gif or .tga files for image maps or height fields
on each frame.


3.2.4.3   Shell Command Return Actions
Pre_Scene_Return=s  Set pre scene return
                    actions
Pre_Frame_Return=s  Set pre frame return
                    actions
Post_Scene_Return=  Set post scene return
s                   actions
Post_Frame_Return=  Set post frame return
s                   actions
User_Abort_Return=  Set user abort return
s                   actions
Fatal_Error_Return  Set fatal return actions
=s
Note that no + or - switches are available for these options.
They cannot be used from the command line. They may only be used
from INI files.

Most operating systems allow application programs to return an
error code if something goes wrong. When POV-Ray executes a shell
command it can make use of this error code returned from the
shell process and take some appropriate action if the code is
zero or non-zero. POV-Ray itself returns such codes. It returns 0
for success, 1 for fatal error and 2 for user abort.

The actions are designated by a single letter in the different
..._Return=s options. The possible actions are:
I  ignore the code
S  skip one step
A  all steps skipped
Q  quit POV-Ray
   immediately
U  generate a user abort
   in POV-Ray
F  generate a fatal error
   in POV-Ray
For example if your Pre_Frame_Command calls a program which
generates your height field data and that utility fails then it
will return a non-zero code. We would probably want POV-Ray to
abort as well. The option Pre_Frame_Return=F will cause POV-Ray
to do a fatal abort if the Pre_Frame_Command returns a non-zero
code.

Sometimes a non-zero code from the external process is a good
thing. Suppose you want to test if a frame has already been
rendered. You could use the S action to skip this frame if the
file is already rendered. Most utilities report an error if the
file is not found. For example the command...

 pkzip -V myscene mysce012.tga
tells pkzip you want to view the catalog of myscene.zip for the
file mysce012.tga. If the file isn't in the archive pkzip returns
a non-zero code.

However we want to skip if the file is found. Therefore we need
to reverse the action so it skips on zero and doesn't skip on non-
zero. To reverse the zero vs. non-zero triggering of an action
precede it with a "-" sign (note a "!" will also work since it is
used in many programming languages as a negate operator).

Pre_Frame_Return=S will skip if the code shows error (non-zero)
and will proceed normally on no error (zero). Pre_Frame_Return=-S
will skip if there is no error (zero) and will proceed normally
if there is an error (non-zero).

The default for all shells is I which means that the return
action is ignored no matter what. POV-Ray simply proceeds with
whatever it was doing before the shell command. The other actions
depend upon the context. You may want to refer back to the
animation loop sequence chart in the previous section "Shell
Command Sequencing". The action for each shell is as follows.

On return from any User_Abort_Command if there is an action
triggered...

and you have     ... then POV-Ray will..
specified...
F                Then turn this user abort
                 into a fatal error.
                 Do the
                 Fatal_Error_Command, if
                 any.
                 Exit POV-Ray with error
                 code 1.
S, A, Q, or U    Then proceed with the user
                 abort.
                 Exit POV-Ray with error
                 code 2.
On return from any Fatal_Error_Command then POV-Ray will proceed
with the fatal error no matter what. It will exit POV-Ray with
error code 1.

On return from any Pre_Scene_Command, Pre_Frame_Command,
Post_Frame_Command or Post_Scene_Commands if there is an action
triggered...
...and you have  ... then POV-Ray will...
specified...
F                ...turn this user abort into
                    a fatal error. Do the
                    Fatal_Error_Command, if
                    any. Exit POV-Ray with
                    error code 1.
U                ...generate a user abort. Do
                    the User_Abort_Command, if
                    any. Exit POV-Ray with an
                    error code 2.
Q                ..quit POV-Ray immediately.
                    Acts as though POV-Ray
                    never really ran. Do no
                    further shells, (not even
                    a Post_Scene_Command) and
                    exit POV-Ray with an error
                    code 0.
On return from a Pre_Scene_Command if there is an action
triggered...
...and you have  ... then POV-Ray will...
specified...
S                ...skip rendering all
                    frames. Acts as though the
                    scene completed all frames
                    normally. Do not do any
                    Pre_Frame_Command or
                    Post_Frame_Commands. Do
                    the Post_Scene_Command, if
                    any. Exit POV-Ray with
                    error code 0. On the
                    earlier chart this means
                    skip step #4.
A                ...skip all scene activity.
                    Works exactly like Q quit.
                    On the earlier chart this
                    means skip to step #6.
                    Acts as though POV-Ray
                    never really ran. Do no
                    further shells, (not even
                    a Post_Scene_Command) and
                    exit POV-Ray with an error
                    code 0.
On return from a Pre_Frame_Command if there is an action
triggered...
...and you have  ... then POV-Ray will...
specified...
S                ...skip only this frame.
                    Acts as though this frame
                    never existed. Do not do
                    the Post_Frame_Command.
                    Proceed with the next
                    frame. On the earlier
                    chart this means skip
                    steps (4b) and (4c) but
                    loop back as needed in
                    (4d).
A                ...skip rendering this frame
                    and all remaining frames.
                    Acts as though the scene
                    completed all frames
                    normally. Do not do any
                    further
                    Post_Frame_Commands. Do
                    the Post_Scene_Command, if
                    any. Exit POV-Ray with
                    error code 0. On the
                    earlier chart this means
                    skip the rest of step (4)
                    and proceed at step (5).
On return from a Post_Frame_Command if there is an action
triggered...
...and you have  ... then POV-Ray will...
specified...
S or A           ...skip all remaining
                    frames. Acts as though the
                    scene completed all frames
                    normally. Do not do any
                    further
                    Post_Frame_Commands. Do
                    the Post_Scene_Command, if
                    any. Exit POV-Ray with
                    error code 0. On the
                    earlier chart this means
                    skip the rest of step (4)
                    and proceed at step (5).
On return from any Post_Scene_Command if there is an action
triggered and you have specified S or A then no special action
occurs.  This is the same as I for this shell command.


3.2.5     Text Output
Text output is an important way that POV-Ray keeps you informed
about what it is going to do, what it is doing and what it did.
New to POV-Ray 3.0, the program splits its text messages into 7
separate streams. Some versions of POV-Ray color-codes the
various types of text. Some versions allow you to scroll back
several pages of messages. All versions allow you to turn some of
these text streams off/on or to direct a copy of the text output
to one or several files. This section details the options which
give you control over text output.


3.2.5.1   Text Streams
There are seven distinct text streams that POV-Ray uses for
output. On some versions each stream is designated by a
particular color. Text from these streams are displayed whenever
it is appropriate so there is often an intermixing of the text.
The distinction is only important if you choose to turn some of
the streams off or to direct some of the streams to text files.
On some systems you may be able to review the streams separately
in their own scroll-back buffer.

Here is a description of each stream.

Banner: This stream displays the program's sign-on banner,
copyright, contributor's list, and some help screens. It cannot
be turned off or directed to a file because most of this text is
displayed before any options or switches are read. Therefore you
cannot use an option or switch to control it. There are switches
which display the help screens. They are covered in section "Help
Screen Switches".

Debug: This stream displays debugging messages. It was primarily
designed for developers but this and other streams may also be
used by the user to display messages from within their scene
files. See section "Text Message Streams" for details on this
feature. This stream may be turned off and/or directed to a text
file.

Fatal: This stream displays fatal error messages. After
displaying this text, POV-Ray will terminate. When the error is a
scene parsing error, you may be shown several lines of scene text
that leads up to the error. This stream may be turned off and/or
directed to a text file.

Render: This stream displays information about what options you
have specified to render the scene. It includes feedback on all
of the major options such as scene name, resolution, animation
settings, anti-aliasing and others. This stream may be turned off
and/or directed to a text file.

Statistics: This stream displays statistics after a frame is
rendered. It includes information about the number of rays
traced, the length of time of the processing and other
information. This stream may be turned off and/or directed to a
text file.

Status: This stream displays one-line status messages that
explain what POV-Ray is doing at the moment. On some systems this
stream is displayed on a status line at the bottom of the screen.
This stream cannot be directed to a file because there is
generally no need to. The text displayed by the Verbose option or
+V switch is output to this stream so that part of the status
stream may be turned off.

Warning: This stream displays warning messages during the parsing
of scene files and other warnings. Despite the warning, POV-Ray
can continue to render the scene. You will be informed if POV-Ray
has made any assumptions about your scene so that it can proceed.
In general any time you see a warning, you should also assume
that this means that future versions of POV-Ray will not allow
the warned action. Therefore you should attempt to eliminate
warning messages so your scene will be able to run in future
versions of POV-Ray. This stream may be turned off and/or
directed to a text file.


3.2.5.2   Console Text Output
Debug_Console=bool   Turn console display of
                     debug info text on/off
+GD                  Same as Debug_Console=On
-GD                  Same as Debug_Console=Off
Fatal_Console=bool   Turn console display of
                     fatal error text on/off
+GF                  Same as Fatal_Console=On
-GF                  Same as Fatal_Console=Off
Render_Console=bool  Turn console display of
                     render info text on/off
+GR                  Same as Render_Console=On
-GR                  Same as Render_Console=Off
Statistic_Console=bo Turn console display of
ol                   statistic text on/off
+GS                  Same as Statistic_Console=On
-GS                  Same as
                     Statistic_Console=Off
Warning_Console=bool Turn console display of
                     warning text on/off
+GW                  Same as Warning_Console=On
-GW                  Same as Warning_Console=Off
All_Console=bool     Turn on/off all debug,
                        fatal, render, statistic
                        and warning text to
                        console.
+GA                  Same as All_Console=On
-GA                  Same as All_Console=Off
You may suppress the output to the console of the debug, fatal,
render, statistic or warning text streams. For example the
Statistic_Console=off option or the -GS switch can turn off the
statistic stream. Using on or +GS you may turn it on again. You
may also turn all five of these streams on or off at once using
the All_Console option or +GA switch.

Note that these options take effect immediately when specified.
Obviously any error or warning messages that might occur before
the option is read are not be affected.


3.2.5.3   Directing Text Streams to Files
Debug_File=true    Echo debug info text to DEBUG.OUT
Debug_File=false   Turn off file output of debug info
Debug_File=file      Echo debug info text to file
+GDfile            Both Debug_Console=On, Debug_File=file
-GDfile              Both Debug_Console=Off,
                   Debug_File=file
Fatal_File=true    Echo fatal text to FATAL.OUT
Fatal_File=false   Turn off file output of fatal
Fatal_File=file      Echo fatal info text to file
+GFfile            Both Fatal_Console=On, Fatal_File=file
-GFfile              Both Fatal_Console=Off,
                   Fatal_File=file
Render_File=true   Echo render info text to RENDER.OUT
Render_File=false  Turn off file output of render info
Render_File=file     Echo render info text to file
+GRfile            Both Render_Console=On,
                   Render_File=file
-GRfile              Both Render_Console=Off,
                   Render_File=file
Statistic_File=tr  Echo statistic text to STATS.OUT
ue
Statistic_File=fa  Turn off file output of statistics
lse
Statistic_File=file  Echo statistic text to file
+GSfile            Both Statistic_Console=On,
                     Statistic_File=file
-GSfile            Both Statistic_Console=Off,
                     Statistic_File=file
Warning_File=true  Echo warning info text to
                   WARNING.OUT
Warning_File=fals  Turn off file output of warning info
e
Warning_File=file    Echo warning info text to file
+GWfile            Both Warning_Console=On,
                   Warning_File=file
-GWfile              Both Warning_Console=Off,
                   Warning_File=file
All_File=true      Echo all debug, fatal, render,
                     statistic, and warning text to
                     ALLTEXT.OUT
All_File=false     Turn off file output of all debug,
                     fatal, render, statistic, and
                     warning text.
All_File=file        Echo all debug, fatal, render,
                   statistic, and warning text to file
+GAfile            Both All_Console=On, All_File=file
-GAfile              Both All_Console=Off, All_File=file
You may direct a copy of the text streams to a text file for the
debug, fatal, render, statistic, or warning text streams. For
example the Statistic_File=s option or the +GSs switch. If the
string s is true or any of the other valid true strings then that
stream is redirected to a file with a default name. Valid true
values are true, yes, on or 1. If the value is false the
direction to a text file is turned off. Valid false values are
false, no, off or 0. Any other string specified turns on file
output and the string is interpreted as the output file name.

Similarly you may specify such a true, false or file name string
after a switch such as +GSfile. You may also direct all five
streams to the same file using the All_File option or +GA switch.
You may not specify the same file for two or more streams because
POV-Ray will fail when it tries to open or close the same file
twice.

Note that these options take effect immediately when specified.
Obviously any error or warning messages that might occur before
the option is read will not be affected.


3.2.5.4   Help Screen Switches
+H or +?       Show help screen 0 if this
               is the only switch
+H0 to +H8     Show help screen 0 to 8 if
               this is the only switch
+?0 to +?8     Same as +H0 to +H8
Note that there are no INI style equivalents to these options.

Graphical interface versions of POV-Ray such as Mac or Windows
have extensive online help. Other versions of POV-Ray have only a
few quick-reference help screens. The +? switch, optionally
followed by a single digit from 0 to 8, will display these help
screens to the banner text stream. After displaying the help
screens, POV-Ray terminates. Because some operating systems do
not permit a question mark as a command line switch you may also
use the +H switch. Note however that this switch is also used to
specify the height of the image in pixels. Therefore the +H
switch is only interpreted as a help switch if it is the only
switch on the command line and if the value after the switch is
less than or equal to 8.


3.2.6     Tracing Options
There is more than one way to trace a ray. Sometimes there is a
trade-off between quality and speed. Sometimes options designed
to make tracing faster can slow things down. This section covers
options that tell POV-Ray how to trace rays with the appropriate
speed and quality settings.


3.2.6.1   Quality Settings
Quality=  Set quality value to n
n         (0 <= n <= 11)
+Qn       Same as Quality=n
The Quality=n option or +Qn switch allows you to specify the
image rendering quality. You may choose to lower the quality for
test rendering and raise it for final renders. The quality
adjustments are made by eliminating some of the calculations that
are normally performed. For example settings below 4 do not
render shadows. Settings below 8 do not use reflection or
refraction. The duplicate values allow for future expansion.  The
values correspond to the following quality levels:
0,  Just show quick colors. Use
1      full ambient lighting only.
       Quick colors are used only at
       5 or below.
2,  Show specified diffuse and
3      ambient light.
4   Render shadows, but no extended
       lights.
5   Render shadows, including
       extended lights.
6,  Compute texture patterns.
7
8   Compute reflected, refracted,
       and transmitted rays.
9   Compute media.
10  Compute radiosity but no media
11  Compute radiosity and media
The default is 9 if not specified.


3.2.6.2   Radiosity Setting
Radiosity=boo Turns radiosity
l             on/off
+QR           Turns radiosity on
-QR           Turns radiosity on
Radiosity is an additional calculation which computes diffuse
inter-reflection. It is an extremely slow calculation that is
somewhat experimental. By default, radiosity is off.  The
parameters which control how radiosity calculations are performed
are specified in the radiosity section of the global_settings
statement. See section "Radiosity" for further details.


3.2.6.3   Automatic Bounding Control
Bounding=bool       Turn bounding on/off
+MB                 Turn bounding on; Set
                      threshold to 25 or
                      previous amount
-MB                 Turn bounding off
Bounding_Threshold  Set bound threshold to n
=n
+MBn                Turn bounding on; bound
                      threshold to n
-MBn                Turn bounding off; for
                      future threshold to n
Light_Buffer=bool   Turn light buffer on/off
+UL                 Turn light buffer on
-UL                 Turn light buffer off
Vista_Buffer=bool   Turn vista buffer on/off
+UV                 Turn vista buffer on
-UV                 Turn vista buffer off
POV-Ray uses a variety of spatial sub-division systems to speed
up ray-object intersection tests. The primary system uses a
hierarchy of nested bounding boxes. This system compartmentalizes
all finite objects in a scene into invisible rectangular boxes
that are arranged in a tree-like hierarchy. Before testing the
objects within the bounding boxes the tree is descended and only
those objects are tested whose bounds are hit by a ray. This can
greatly improve rendering speed. However for scenes with only a
few objects the overhead of using a bounding system is not worth
the effort. The Bounding=off option or -MB switch allows you to
force bounding off. The default value is on.

The Bounding_Threshold=n or +MBn switch allows you to set the
minimum number of objects necessary before bounding is used. The
default is +MB25 which means that if your scene has fewer than 25
objects POV-Ray will automatically turn bounding off because the
overhead isn't worth it. Generally it's a good idea to use a much
lower threshold like +MB5.

Additionally POV-Ray uses systems known as vista buffers and
light buffers to further speed things up. These systems only work
when bounding is on and when there are a sufficient number of
objects to meet the bounding threshold. The vista buffer is
created by projecting the bounding box hierarchy onto the screen
and determining the rectangular areas that are covered by each of
the elements in the hierarchy. Only those objects whose
rectangles enclose a given pixel are tested by the primary
viewing ray. The vista buffer can only be used with perspective
and orthographic cameras because they rely on a fixed viewpoint
and a reasonable projection (i. e. straight lines have to stay
straight lines after the projection).

The light buffer is created by enclosing each light source in an
imaginary box and projecting the bounding box hierarchy onto each
of its six sides. Since this relies on a fixed light source,
light buffers will not be used for area lights.

Reflected and transmitted rays do not take advantage of the light
and vista buffer.

The default settings are Vista_Buffer=on or +UV and
Light_Buffer=on or +UL. The option to turn these features off is
available to demonstrate their usefulness and as protection
against unforeseen bugs which might exist in any of these
bounding systems.

In general, any finite object and many types of CSG of finite
objects will properly respond to this bounding system. In
addition blobs and meshes use an additional internal bounding
system. These systems are not affected by the above switch. They
can be switched off using the appropriate syntax in the scene
file (see "Blob" and "Mesh" for details). Text objects are split
into individual letters that are bounded using the bounding box
hierarchy. Some CSG combinations of finite and infinite objects
are also automatically bound. The end result is that you will
rarely need to add manual bounding objects as was necessary in
earlier versions of POV-Ray unless you use many infinite objects.


3.2.6.4   Removing User Bounding
Remove_Bounds=bo Turn unnecessary bounds
ol               removal on/off
+UR              Turn unnecessary bounds
                 removal on
-UR              Turn unnecessary bounds
                 removal off
Split_Unions=boo Turn split bounded unions
l                on/off
+SU              Turn split bounded unions on
-SU              Turn split bounded unions
                 off
Early versions of POV-Ray had no system of automatic bounding or
spatial sub-division to speed up ray-object intersection tests.
Users had to manually create bounding boxes to speed up the
rendering. Since version 3.0, POV-Ray has had more sophisticated
automatic bounding than any previous version. In many cases the
manual bounding on older scenes is slower than the new automatic
systems. Therefore POV-Ray removes manual bounding when it knows
it will help. In rare instances you may want to keep manual
bounding. Some older scenes incorrectly used bounding when they
should have used clipping. If POV-Ray removes the bounds in these
scenes the image will not look right. To turn off the automatic
removal of manual bounds you should specify Remove_Bounds=off or
use -UR. The default is Remove_Bounds=on.

One area where the jury is still out is the splitting of manually
bounded unions. Unbounded unions are always split into their
component parts so that automatic bounding works better. Most
users do not bound unions because they know that doing so is
usually slower. If you do manually bound a union we presume you
really want it bound. For safety sake we do not presume to remove
such bounds. If you want to remove manual bounds from unions you
should specify Split_Unions=on or use +SU. The default is
Split_Unions=off.


3.2.6.5   Anti-Aliasing Options
Antialias=bool        Turns anti-aliasing on/off
+A                    Turns aa on with threshold 0.3 or
                      previous amount
-A                    Turns anti-aliasing off
Sampling_Method=n     Sets aa-sampling method (only 1 or 2
                      are valid)
+AMn                  Same as Sampling_Method=n
Antialias_Threshold=n Sets anti-aliasing threshold
.n
+An.n                 Sets aa on with aa-threshold at n.n
-An.n                 Sets aa off (aa-threshold n.n in
                      future)
Jitter=bool           Sets aa-jitter on/off
+J                    Sets aa-jitter on with 1.0 or previous
                      amount
-J                    Sets aa-jitter off
Jitter_Amount=n.n     Sets aa-jitter amount to n.n. If n.n
                      <= 0 aa-jitter is set off
+Jn.n                 Sets aa-jitter on; jitter amount to
                      n.n. If n.n <= 0 aa-jitter is set off
-Jn.n                 Sets aa-jitter off (jitter amount n.n
                      in future)
Antialias_Depth=n     Sets aa-depth (1 <= n <= 9)
+Rn                   Same as Antialias_Depth=n
The ray-tracing process is in effect a discrete, digital sampling
of the image with typically one sample per pixel. Such sampling
can introduce a variety of errors. This includes a jagged, stair-
step appearance in sloping or curved lines, a broken look for
thin lines, moiré patterns of interference and lost detail or
missing objects, which are so small they reside between adjacent
pixels. The effect that is responsible for those errors is called
aliasing.

Anti-aliasing is any technique used to help eliminate such errors
or to reduce the negative impact they have on the image. In
general, anti-aliasing makes the ray-traced image look smoother.
The Antialias=on option or +A switch turns on POV-Ray's anti-
aliasing system.

When anti-aliasing is turned on, POV-Ray attempts to reduce the
errors by shooting more than one viewing ray into each pixel and
averaging the results to determine the pixel's apparent color.
This technique is called super-sampling and can improve the
appearance of the final image but it drastically increases the
time required to render a scene since many more calculations have
to be done.

POV-Ray gives you the option to use one of two alternate super-
sampling methods. The Sampling_Method=n option or +AMn switch
selects either type 1 or type 2. Selecting one of those methods
does not turn anti-aliasing on. This has to be done by using the
+A command line switch or Antialias=on option.

Type 1 is an adaptive, non-recursive super-sampling method.  It
is adaptive because not every pixel is super-sampled.  Type 2 is
an adaptive and recursive super-sampling method.  It is recursive
because the pixel is sub-divided and sub-sub-divided recursively.
The adaptive nature of type 2 is the variable depth of recursion.

In the default, non-recursive method (+AM1), POV-Ray initially
traces one ray per pixel. If the color of a pixel differs from
its neighbors (to the left or above) by more than a threshold
value then the pixel is super-sampled by shooting a given, fixed
number of additional rays. The default threshold is 0.3 but it
may be changed using the Antialias_Threshold=n.n option. When the
switches are used, the threshold may optionally follow the +A.
For example +A0.1 turns anti-aliasing on and sets the threshold
to 0.1.

The threshold comparison is computed as follows. If r1, g1, b1
and r2, g2, b2 are the rgb components of two pixels then the
difference between pixels is computed by

  diff = abs(r1-r2) + abs(g1-g2) + abs(b1-b2)
If this difference is greater than the threshold then both pixels
are super-sampled. The rgb values are in the range from 0.0 to
3.0 thus the most two pixels can differ is 3.0. If the anti-
aliasing threshold is 0.0 then every pixel is super-sampled. If
the threshold is 3.0 then no anti-aliasing is done. Lower
threshold means more anti-aliasing and less speed. Use anti-
aliasing for your final version of a picture, not the rough
draft. The lower the contrast, the lower the threshold should be.
Higher contrast pictures can get away with higher tolerance
values. Good values seem to be around 0.2 to 0.4.

When using the non-recursive method, the default number of super-
samples is nine per pixel, located on a 3*3 grid. The
Antialias_Depth=n option or +Rn switch controls the number of
rows and columns of samples taken for a super-sampled pixel. For
example +R4 would give 4*4=16 samples per pixel.

The second, adaptive, recursive super-sampling method starts by
tracing four rays at the corners of each pixel. If the resulting
colors differ more than the threshold amount additional samples
will be taken. This is done recursively, i.e. the pixel is
divided into four sub-pixels that are separately traced and
tested for further subdivision. The advantage of this method is
the reduced number of rays that have to be traced. Samples that
are common among adjacent pixels and sub-pixels are stored and
reused to avoid re-tracing of rays. The recursive character of
this method makes the super-sampling concentrate on those parts
of the pixel that are more likely to need super-sampling (see
figure below).

                                
                                
       Example of how the recursive super-sampling works.
                                
The maximum number of subdivisions is specified by the
Antialias_Depth=n option or +Rn switch. This is different from
the adaptive, non-recursive method were the total number of super-
samples is specified. A maximum number of n subdivisions results
in a maximum number of samples per pixel that is given by the
following table.
+Rn     Number of      Maximum number of
       samples per          samples
      super-sampled    per super-sampled
      pixel for the        pixel for
      non-recursive      the recursive
       method +AM1        method +AM2
 1          1                  9
 2          4                 25
 3          9                 81
 4         16                 289
 5         25                1089
 6         36                4225
 7         49                16641
 8         64                66049
 9         81               263169
You should note that the maximum number of samples in the
recursive case is hardly ever reached for a given pixel. If the
recursive method is used with no anti-aliasing each pixel will be
the average of the rays traced at its corners. In most cases a
recursion level of three is sufficient.

Another way to reduce aliasing artifacts is to introduce noise
into the sampling process. This is called jittering and works
because the human visual system is much more forgiving to noise
than it is to regular patterns. The location of the super-samples
is jittered or wiggled a tiny amount when anti-aliasing is used.
Jittering is used by default but it may be turned off with the
Jitter=off option or -J switch. The amount of jittering can be
set with the Jitter_Amount=n.n option. When using switches the
jitter scale may be specified after the +Jn.n switch. For example
+J0.5 uses half the normal jitter. The default amount of 1.0 is
the maximum jitter which will insure that all super-samples
remain inside the original pixel. Note that the jittering noise
is random and non-repeatable so you should avoid using jitter in
animation sequences as the anti-aliased pixels will vary and
flicker annoyingly from frame to frame.

If anti-aliasing is not used one sample per pixel is taken
regardless of the super-sampling method specified.



4.0    Scene Description Language
The reference section describes the POV-Ray scene description
language.  It is supposed to be used as a reference for looking
up things. It does not contain detailed explanations on how
scenes are written or how POV-Ray is used. It just explains all
features, their syntax, applications, limits, drawbacks, etc.

The scene description language allows you to describe the world
in a readable and convenient way. Files are created in plain
ASCII text using an editor of your choice. The input file name is
specified using the Input_File_Name=file option or +Ifile switch.
By default the files have the extension .pov. POV-Ray reads the
file, processes it by creating an internal model of the scene and
then renders the scene.

The overall syntax of a scene is shown below.  See "Notation and
Basic Assumptions" for more information on syntax notation.

SCENE:
  SCENE_ITEM...
SCENE_ITEM:
  LANGUAGE_DIRECTIVES      |
  camera { CAMERA_ITEMS... }    |
  OBJECTS                  |
  ATMOSPHERIC_EFFECTS      |
  global_settings { GLOBAL_ITEMS }
In plain English, this means that a scene contains one or more
scene items and that a scene item may be any of the five items
listed below it.  The items may appear in any order.  None is a
required item.  In addition to the syntax depicted above, a
LANGUAGE_DIRECTIVE may also appear anywhere embedded in other
statements between any two tokens.  There are some restrictions
on nesting directives also.

For details on those five items see section "Language
Directives", section "Objects", section "Camera", section
"Atmospheric Effects" and section "Global Settings" for details.


4.1  C41-Language Basics
The POV-Ray language consists of identifiers, reserved keywords,
floating point expressions, strings, special symbols and
comments. The text of a POV-Ray scene file is free format. You
may put statements on separate lines or on the same line as you
desire. You may add blank lines, spaces or indentations as long
as you do not split any keywords or identifiers.


4.1.1     Identifiers and Keywords
POV-Ray allows you to define identifiers for later use in the
scene file. An identifier may be 1 to 40 characters long. It may
consist of upper or lower case letters, the digits 0 through 9 or
an underscore character ("_"). The first character must be an
alphabetic character. The declaration of identifiers is covered
later.

POV-Ray has a number of reserved keywords which are listed below.
abs        dimension_s  merge        sky_sphere
absorption ize          mesh         slice
acos       direction    metallic     slope_map
acosh      disc         min          smooth
adaptive   distance     minimum_reu  smooth_tri
adc_bailou distance_ma  se           angle
t          ximum        mod          sor
agate      div          mortar       specular
agate_turb eccentricit  nearest_cou  sphere
all        y            nt           spherical
alpha      else         no           spiral1
ambient    emission     normal       spiral2
ambient_li end          normal_map   spotlight
ght        error        no_shadow    spotted
angle      error_bound  number_of_w  sqr
aperture   exp          aves         sqrt
append     extinction   object       statistics
arc_angle  fade_distan  octaves      str
area_light ce           off          strcmp
array      fade_power   offset       strength
asc        falloff      omega        strlen
asin       falloff_ang  omnimax      strlwr
asinh      le           on           strupr
assumed_ga false        once         sturm
mma        fclose       onion        substr
atan       file_exists  open         superellip
atan2      filter       orthographi  soid
atanh      finish       c            switch
average    fisheye      panoramic    sys
background flatness     perspective  t
bezier_spl flip         pgm          tan
ine        floor        phase        tanh
bicubic_pa focal_point  phong        text
tch        fog          phong_size   texture
black_hole fog_alt      pi           texture_ma
blob       fog_offset   pigment      p
blue       fog_type     pigment_map  tga
blur_sampl fopen        planar       thickness
es         frequency    plane        threshold
bounded_by gif          png          tightness
box        global_sett  point_at     tile2
boxed      ings         poly         tiles
bozo       gradient     polygon      torus
break      granite      poly_wave    track
brick      gray_thresh  pot          transform
brick_size old          pow          translate
brightness green        ppm          transmit
brilliance height_fiel  precision    triangle
bumps      d            prism        triangle_w
bump_map   hexagon      pwr          ave
bump_size  hf_gray_16   quadratic_s  true
camera     hierarchy    pline        ttf
case       hollow       quadric      turbulence
caustics   hypercomple  quartic      turb_depth
ceil       x            quaternion   type
checker    if           quick_color  u
chr        ifdef        quick_colou  ultra_wide
clipped_by iff          r            _angle
clock      ifndef       quilted      undef
clock_delt image_map    radial       union
a          include      radians      up
color      int          radiosity    use_color
color_map  interior     radius       use_colour
colour     interpolate  rainbow      use_index
colour_map intersectio  ramp_wave    u_steps
component  n            rand         v
composite  intervals    range        val
concat     inverse      ratio        variance
cone       ior          read         vaxis_rota
confidence irid         reciprocal   te
conic_swee irid_wavele  recursion_l  vcross
p          ngth         imit         vdot
control0   jitter       red          version
control1   julia_fract  reflection   vlength
cos        al           reflection_  vnormalize
cosh       lambda       exponent     vrotate
count      lathe        refraction   v_steps
crackle    leopard      render       warning
crand      light_sourc  repeat       warp
cube       e            rgb          water_leve
cubic      linear_spli  rgbf         l
cubic_spli ne           rgbft        waves
ne         linear_swee  rgbt         while
cubic_wave p            right        width
cylinder   local        ripples      wood
cylindrica location     rotate       wrinkles
l          log          roughness    write
debug      looks_like   samples      x
declare    look_at      scale        y
default    low_error_f  scallop_wav  yes
defined    actor        e            z
degrees    macro        scattering
density    mandel       seed
density_fi map_type     shadowless
le         marble       sin
density_ma material     sine_wave
p          material_ma  sinh
dents      p            sky
difference matrix
diffuse    max
dimensions max_interse
           ctions
           max_iterati
           on
           max_trace_l
           evel
           media
           media_atten
           uation
           media_inter
           action
All reserved words are fully lower case. Therefore it is
recommended that your identifiers contain at least one upper case
character so it is sure to avoid conflict with reserved words.


4.1.2     Comments
Comments are text in the scene file included to make the scene
file easier to read or understand. They are ignored by the ray-
tracer and are there for your information. There are two types of
comments in POV-Ray.

Two slashes are used for single line comments. Anything on a line
after a double slash (//) is ignored by the ray-tracer. For
example:

 // This line is ignored
You can have scene file information on the line in front of the
comment as in:

 object { FooBar } // this is an object
The other type of comment is used for multiple lines. It starts
with "/*" and ends with "*/". Everything in-between is ignored.
For example:

 /* These lines
   are ignored
   by the
   ray-tracer */
This can be useful if you want to temporarily remove elements
from a scene file. /* ... */ comments can comment out lines
containing other // comments and thus can be used to temporarily
or permanently comment out parts of a scene. /* ... */ comments
can be nested, the following is legal:

 /* This is a comment
 // This too
 /* This also */
 */
Use comments liberally and generously. Well used, they really
improve the readability of scene files.


4.1.3     Float Expressions
Many parts of the POV-Ray language require you to specify one or
more floating point numbers. A floating point number is a number
with a decimal point. Floats may be specified using literals,
identifiers or functions which return float values. You may also
create very complex float expressions from combinations of any of
these using various familiar operators.

Where POV-Ray needs an integer value it allows you to specify a
float value and it truncates it to an integer. When POV-Ray needs
a logical or boolean value it interprets any non-zero float as
true and zero as false. Because float comparisons are subject to
rounding errors POV-Ray accepts values extremely close to zero as
being false when doing boolean functions. Typically values whose
absolute values are less than a preset value epsilon are
considered false for logical expressions. The value of epsilon is
system dependent but is generally about 1.0e-10. Two floats a and
b are considered to be equal if abs(a-b) < epsilon.

The full syntax for float expressions is given below.  Detailed
explanations are given in the following sub-sections.

FLOAT:
  NUMERIC_TERM  [SIGN  NUMERIC_TERM]
SIGN:
  +    |    -
NUMERIC_TERM:
  NUMERIC_FACTOR  [MULT  NUMERIC_FACTOR]
MULT:
  *    |    /
NUMERIC_FACTOR:
  FLOAT_LITERAL       |
  FLOAT_IDENTIFIER         |
  SIGN  NUMERIC_FACTOR     |
  FLOAT_FUNCTION      |
  FLOAT_BUILT-IN_IDENT     |
  ( FULL_EXPRESSION ) |
  !  NUMERIC_FACTOR   |
  VECTOR DECIMAL_POINT DOT_ITEM
  
FLOAT_LITERAL:
  [DIGIT...] [DECIMAL_POINT] DIGIT... [EXP [SIGN] DIGIT...]
DIGIT:
  0   |   1   |   2   |   3   |   4   |   5   |   6   |   7   |
  8   |   9
DECIMAL_POINT:
  .
EXP:
  e   |   E
DOT_ITEM:
  x   |   y   |   z   |   t   |   u   |   v   |   red   |   blue
  |   green   |   filter   |   transmit
FLOAT_FUNCTION:
  abs( FLOAT )   |   acos( FLOAT )   |   val( STRING )   |
  asc( STRING )   |
  asin( FLOAT )   |   atan2( FLOAT , FLOAT )   |   ceil( FLOAT )
  |   cos( FLOAT )   |
  defined(IDENTIFIER )   |   degrees( FLOAT )   |   div( FLOAT ,
  FLOAT )   |   exp( FLOAT )   |
  file_exists( STRING )   |   floor( FLOAT )   |   int( FLOAT )
  |   log( FLOAT )   |
  max( FLOAT , FLOAT )   |   min( FLOAT , FLOAT )   |   mod(
  FLOAT , FLOAT )   |
  pow( FLOAT , FLOAT )   |   radians( FLOAT )   |   sin( FLOAT )
  |   sqrt( FLOAT )   |
  strcmp( STRING , STRING )   |   strlen( STRING )   |   tan(
  FLOAT )   |
  vdot( VECTOR , VECTOR )   |   vlength( VECTOR )   |   seed(
  FLOAT )   |   rand( FLOAT )   |
  dimensions( ARRAY_IDENTIFIER )   |   dimension_size(
  ARRAY_IDENTIFIER , FLOAT )
FLOAT_BUILT-IN_IDENT:
  clock   |   pi   |   version   |   true   |   yes   |   on   |
  false   |   no   |
  off   |   clock_delta
FULL_EXPRESSION:
  LOGICAL_EXPRESSION  [? FULL_EXPRESSION : FULL_EXPRESSION]
LOGICAL_EXPRESSION:
  REL_TERM  [LOGICAL_OPERATOR  REL_TERM]
LOGICAL_OPERATOR:
  &   |   |        (note this means an ampersand or a vertical
  bar is a logical operator)
REL_TERM:
  FLOAT  [REL_OPERATOR  FLOAT]
REL_OPERATOR:
  <   |   <=   |   =   |   >=   |   >   |   !=
INT:
  FLOAT     (note any syntax which requires a integer INT will
  accept a FLOAT and it will be truncated
            to an integer internally by POV-Ray).
Note: FLOAT_IDENTIFIERS are identifiers previously declared to
have float values.  The DOT_ITEM syntax is actually a vector or
color operator but it returns a float value.  See "Vector
Operators" or "Color Operators" for details.  An ARRAY_IDENTIFIER
is just the identifier name of a previously declared array, it
does not include the [] braces nor the index.  The syntax for
STRING is in the section "Strings".


4.1.3.1   Float Literals
Float literals are represented by an optional sign ("+" or "-")
digits, an optional decimal point and more digits. If the number
is an integer you may omit the decimal point and trailing zero.
If it is all fractional you may omit the leading zero. POV-Ray
supports scientific notation for very large or very small
numbers. The following are all valid float literals:

 -2.0  -4  34  3.4e6  2e-5  .3  0.6

4.1.3.2   Float Identifiers
Float identifiers may be declared to make scene files more
readable and to parameterize scenes so that changing a single
declaration changes many values. An identifier is declared as
follows.

FLOAT_DECLARATION:
  #declare IDENTIFIER = EXPRESSION;  |
  #local IDENTIFIER = EXPRESSION;
Where IDENTIFIER is the name of the identifier up to 40
characters long and EXPRESSION is any valid expression which
evaluates to a float value. Note that there should be a semi-
colon after the expression in a float declaration. This semi-
colon is new with POV-Ray version 3.1. If omitted, it generates a
warning and some macros may not work properly. See "#declare vs.
#local" for information on identifier scope.  Here are some
examples.

 #declare Count = 0;
 #declare Rows = 5.3;
 #declare Cols = 6.15;
 #declare Number = Rows*Cols;
 #declare Count = Count+1;
As the last example shows, you can re-declare a float identifier
and may use previously declared values in that re-declaration.
There are several built-in identifiers which POV-Ray declares for
you. See "Built-in Float Identifiers" for details.


4.1.3.3   Float Operators
Arithmetic expressions: Basic math expressions can be created
from float literals, identifiers or functions using the following
operators in this order of precedence...
(  )      expressions in
          parentheses first
+A  -A    unary minus, unary plus
!A        and logical "not"
A*B A/B   multiplication and
          division
A+B A-B   addition and
          subtraction
Relational, logical and conditional expressions may also be
created. However there is a restriction that these types of
expressions must be enclosed in parentheses first. This
restriction, which is not imposed by most computer languages, is
necessary because POV-Ray allows mixing of float and vector
expressions. Without the parentheses there is an ambiguity
problem. Parentheses are not required for the unary logical not
operator "!" as shown above. The operators and their precedence
are shown here.

Relational expressions: The operands are arithmetic expressions
and the result is always boolean with 1 for true and 0 for false.
All relational operators have the same precedence.


(A < B)   A is less than B
(A <= B)  A is less than or equal to B
(A = B)   A is equal to B (actually abs(A-
          B)<EPSILON)
(A != B)  A is not equal to B (actually
          abs(A-B)>=EPSILON)
(A >= B)  A is greater than or equal to B
(A > B)   A is greater than B
Logical expressions: The operands are converted to boolean values
of 0 for false and 1 for true. The result is always boolean. All
logical operators have the same precedence. Note that these are
not bit-wise operations, they are logical.
(A & B)   true only if both A and B are
          true, false otherwise
(A | B)   true if either A or B or both
          are true
Conditional expressions: The operand C is boolean while operands
A and B are any expressions. The result is of the same type as A
and B.
(C ? A : B) if C then A else B
Assuming the various identifiers have been declared, the
following are examples of valid expressions...

1+2+3    2*5     1/3     Row*3    Col*5
(Offset-5)/2      This/That+Other*Thing
((This<That) & (Other>=Thing)?Foo:Bar)
Expressions are evaluated left to right with innermost
parentheses evaluated first, then unary +, - or !, then multiply
or divide, then add or subtract, then relational, then logical,
then conditional.


4.1.3.4   Built-in Float Identifiers
There are several built-in float identifiers. You can use them to
specify values or to create expressions but you cannot re-declare
them to change their values.  They are:

FLOAT_BUILT-IN_IDENT:
  clock   |   pi   |   version   |   true   |   yes   |   on   |
  false   |   no   |
  off   |   clock_delta
Most built-in identifiers never change value. They are defined as
though the following lines were at the start of every scene.

 #declare pi = 3.1415926535897932384626;
 #declare true = 1;
 #declare yes = 1;
 #declare on = 1;
 #declare false = 0;
 #declare no = 0;
 #declare off = 0;
The built-in float identifier pi is obviously useful in math
expressions involving circles.  The built-in float identifiers
on, off, yes, no, true, and false are designed for use as boolean
constants.

The built-in float identifier clock is used to control animations
in POV-Ray. Unlike some animation packages, the action in POV-Ray
animated scenes does not depend upon the integer frame numbers.
Rather you should design your scenes based upon the float
identifier clock. For non-animated scenes its default value is 0
but you can set it to any float value using the INI file option
Clock=n.n or the command-line switch +Kn.n to pass a single float
value your scene file.

Other INI options and switches may be used to animate scenes by
automatically looping through the rendering of frames using
various values for clock. By default, the clock value is 0 for
the initial frame and 1 for the final frame. All other frames are
interpolated between these values. For example if your object is
supposed to rotate one full turn over the course of the animation
you could specify rotate 360*clock*y. Then as clock runs from 0
to 1, the object rotates about the y-axis from 0 to 360 degrees.

Although the value of clock will change from frame-to-frame, it
will never change throughout the parsing of a scene.

The built-in float identifier clock_delta returns the amount of
time between clock values in animations in POV-Ray. While most
animations only need the clock value itself, some animation
calculations are easier if you know how long since the last
frame. Caution must be used when designing such scenes. If you
render a scene with too few frames, the results may be different
than if you render with more frames in a given time period.  On
non-animated scenes, clock_delta defaults to 1.0.  See section
"Animation Options" for more details.

The built-in float identifier version contains the current
setting of the version compatibility option. Although this value
defaults to 3.1 which is the current POV-Ray version number, the
initial value of version may be set by the INI file option
Version=n.n or by the +MVn.n command-line switch. This tells POV-
Ray to parse the scene file using syntax from an earlier version
of POV-Ray.

The INI option or switch only affects the initial setting. Unlike
other built-in identifiers, you may change the value of version
throughout a scene file. You do not use #declare to change it
though. The #version language directive is used to change modes.
Such changes may occur several times within scene files.

Together with the built-in version identifier the #version
directive allows you to save and restore the previous values of
this compatibility setting. The new #local identifier option is
especially useful here. For example suppose mystuff.inc is in
version 1 format. At the top of the file you could put:

 #local Temp_Vers = version;  // Save previous value
 #version 1.0;         // Change to 1.0 mode
 ... // Version 1.0 stuff goes here...
 #version Temp_Vers;      // Restore previous version
Note that there should be a semi-colon after the float expression
in a #version directive. This semi-colon is new with POV-Ray
version 3.1. If omitted, it generates a warning and some macros
may not work properly.


4.1.3.5   Boolean Keywords
The built-in float identifiers on, off, yes, no, true, and false
are most often used as boolean values with object modifiers or
parameters such as sturm, hollow, hierarchy, smooth,
media_attenuation, and media_interaction.  Whenever you see
syntax of the form keyword [Bool], if you simply specify the
keyword without the optional boolean then it assumes keyword on.
You need not use the boolean but for readability it is a good
idea.  You must use one of the false booleans or an expression
which evaluates to zero to turn it off.  Note some of these
keywords default on if no keyword is specified.  For example:

  object{MyBlob}  //sturm defaults off but hierarchy defaults on
  object{MyBlob sturm}      //turn sturm on
  object{MyBlob sturm on}   //turn sturm on
  object{MyBlob sturm off}  //turn sturm off
  object{MyBlob hierarchy}  //does nothing, hierarchy was already
on
  object{MyBlob hierarchy off}  //turn hierarchy off

4.1.3.6   Float Functions
POV-Ray defines a variety of built-in functions for manipulating
floats, vectors and strings. Function calls consist of a keyword
which specifies the name of the function followed by a parameter
list enclosed in parentheses. Parameters are separated by commas.
For example:

 keyword(param1,param2)
The following are the functions which return float values. They
take one or more float, integer, vector, or string parameters.
Assume that A and B are any valid expression that evaluates to a
float; I is a float which is truncated to integer internally, S,
S1, S2 etc. are strings, and V, V1, V2 etc. are any vector
expressions.

abs(A)    Absolute value of A. If A is negative, returns -A
otherwise returns A.

acos(A)   Arc-cosine of A. Returns the angle, measured in
radians, whose cosine is A.

asc(S)    Returns an integer value in the range 0 to 255 that is
the ASCII value of the first character of the string S. For
example asc("ABC") is 65 because that is the value of the
character "A".

asin(A)   Arc-sine of A. Returns the angle, measured in radians,
whose sine is A.

atan2(A,B)     Arc-tangent of (A/B). Returns the angle, measured
in radians, whose tangent is (A/B). Returns appropriate value
even if B is zero. Use atan2(A,1) to compute usual atan(A)
function.

ceil(A)   Ceiling of A. Returns the smallest integer greater than
A. Rounds up to the next higher integer.

cos(A)    Cosine of A. Returns the cosine of the angle A, where A
is measured in radians.

defined(IDENTIFIER )     Returns true if the identifier is
currently defined, false otherwise.  This is especially useful
for detecting end-of-file after a #read directive because the
file identifer is automatically undefined when end-of-file is
reached.  See "The #read Directive" for details.

degrees(A)     Convert radians to degrees. Returns the angle
measured in degrees whose value in radians is A. Formula is
degrees=A/pi*180.0.

dimensions( ARRAY_IDENTIFIER )     Returns the number of
dimensions of a previously declared array identifier.  For
example if you do #declare MyArray=array[6][10] then
dimensions(MyArray) returns the value 2.

dimension_size( ARRAY_IDENTIFIER, FLOAT )    Returns the size of
a given dimension of a previously declared array identifier.
Dimensions are numbered left-to-right starting with 1. For
example if you do #declare MyArray=array[6][10] then
dimension_size(MyArray,2) returns the value 10.

div(A,B)  Integer division. The integer part of (A/B).

exp(A)    Exponential of A. Returns the value of e raised to the
power A where e is the base of the natural logarithm, i.e. the
non-repeating value approximately equal to 2.71828182846.

file_exists(S) Attempts to open the file specified by the string
S. The current directory and all library directories specified by
the Library_Path or +L options are also searched.  See "Library
Paths" for details.  Returns 1 if successful and 0 if
unsuccessful.

floor(A)  Floor of A. Returns the largest integer less than A.
Rounds down to the next lower integer.

int(A)    Integer part of A. Returns the truncated integer part
of A. Rounds towards zero.

log(A)    Natural logarithm of A. Returns the natural logarithm
base e of the value A.

max(A,B)  Maximum of A and B. Returns A if A larger than B.
Otherwise returns B.

min(A,B)  Minimum of A and B. Returns A if A smaller than B.
Otherwise returns B.

mod(A,B)  Value of A modulo B. Returns the remainder after the
integer division of A/B. Formula is mod=((A/B)-int(A/B))*B.

pow(A,B)  Exponentiation. Returns the value of A raised to the
power B.

radians(A)     Convert degrees to radians. Returns the angle
measured in radians whose value in degrees is A. Formula is
radians=A*pi/180.0.

rand(I)   Returns the next pseudo-random number from the stream
specified by the positive integer I. You must call seed() to
initialize a random stream before calling rand(). The numbers are
uniformly distributed, and have values between 0.0 and 1.0,
inclusively. The numbers generated by separate streams are
independent random variables.

seed(A)   Initializes a new pseudo-random stream with the initial
seed value A. The number corresponding to this random stream is
returned. Any number of pseudo-random streams may be used as
shown in the example below:

 #declare R1 = seed(0);
 #declare R2 = seed(12345);
 #sphere { <rand(R1), rand(R1), rand(R1)>, rand(R2) }
Multiple random generators are very useful in situations where
you use rand() to place a group of objects, and then decide to
use rand() in another location earlier in the file to set some
colors or place another group of objects. Without separate rand()
streams, all of your objects would move when you added more calls
to rand(). This is very annoying.

sin(A)    Sine of A. Returns the sine of the angle A, where A is
measured in radians.

strcmp(S1,S2)  Compare string S1 to S2. Returns a float value
zero if the strings are equal, a positive number if S1 comes
after S2 in the ASCII collating sequence, else a negative number.

strlen(S) Length of S. Returns an integer value that is the
number of characters in the string S.

sqrt(A)   Square root of A. Returns the value whose square is A.

tan(A)    Tangent of A. Returns the tangent of the angle A, where
A is measured in radians.

val(S)    Convert string S to float. Returns a float value that
is represented by the text in string S. For example val("123.45")
is 123.45 as a float.

vdot(V1,V2)    Dot product of V1 and V2. Returns a float value
that is the dot product (sometimes called scalar product of V1
with V2. Formula is vdot=V1.x*V2.x + V1.y*V2.y + V1.z*V2.z. See
the animated demo scene VECT2.POV for an illustration.

vlength(V)     Length of V. Returns a float value that is the
length of vector V. Formula is vlength=sqrt(vdot(A,A)).  Can be
used to compute the distance between two points. Dist=vlength(V2-
V1).

See section "Vector Functions" and section "String Functions" for
other functions which are somewhat float-related but which return
vectors and strings.  In addition to the above built-in
functions, you may also define your own functions using the new
#macro directive. See the section "User Defined Macros" for more
details.


4.1.4     Vector Expressions
POV-Ray often requires you to specify a vector. A vector is a set
of related float values. Vectors may be specified using literals,
identifiers or functions which return vector values. You may also
create very complex vector expressions from combinations of any
of these using various familiar operators.

POV-Ray vectors may have from two to five components but the vast
majority of vectors have three components. Unless specified
otherwise, you should assume that the word "vector" means a three
component vector. POV-Ray operates in a 3D x, y, z coordinate
system and you will use three component vectors to specify x, y
and z values. In some places POV-Ray needs only two coordinates.
These are often specified by a 2D vector called an UV vector.
Fractal objects use 4D vectors. Color expressions use 5D vectors
but allow you to specify 3, 4 or 5 components and use default
values for the unspecified components. Unless otherwise noted,
all 2, 4 or 5 component vectors work just like 3D vectors but
they have a different number of components.

The syntax for combining vector literals into vector expressions
is almost identical to the rules for float expressions.  In the
syntax for vector expressions below, some of the syntax items are
defined in the section for float expressions.  See "Float
Expressions" for those definitions.  Detailed explanations of
vector-specific issues are given in the following sub-sections.

VECTOR:
  NUMERIC_TERM  [SIGN  NUMERIC_TERM]
NUMERIC_TERM:
  NUMERIC_FACTOR  [MULT  NUMERIC_FACTOR]
NUMERIC_FACTOR:
  VECTOR_LITERAL      |
  VECTOR_IDENTIFIER   |
  SIGN  NUMERIC_FACTOR     |
  VECTOR_FUNCTION     |
  VECTOR_BUILT-IN_IDENT    |
  ( FULL_EXPRESSION ) |
  !  NUMERIC_FACTOR   |
  FLOAT
VECTOR_LITERAL:
  < FLOAT , FLOAT , FLOAT >
VECTOR_FUNCTION:
  vaxis_rotate( VECTOR , VECTOR , FLOAT )   |
  vcross( VECTOR , VECTOR )   |
  vrotate( VECTOR , VECTOR )   |
  vnormalize( VECTOR )
VECTOR_BUILT-IN_IDENT:
  x   |   y   |   z   |   t   |   u   |   v
Note: VECTOR_IDENTIFIERS are identifiers previously declared to
have vector values.


4.1.4.1   Vector Literals
Vectors literals consist of two to five float expressions that
are bracketed by angle brackets < and >. The terms are separated
by commas. For example here is a typical three component vector:

 < 1.0, 3.2, -5.4578 >
The commas between components are necessary to keep the program
from thinking that the 2nd term is the single float expression
3.2-5.4578 and that there is no 3rd term. If you see an error
message such as "Float expected but '>' found instead" then you
probably have missed a comma.

Sometimes POV-Ray requires you to specify floats and vectors side-
by-side. The rules for vector expressions allow for mixing of
vectors with vectors or vectors with floats so commas are
required separators whenever an ambiguity might arise. For
example <1,2,3>-4 evaluates as a mixed float and vector
expression where 4 is subtracted from each component resulting in
<-3,-2,-1>. However the comma in <1,2,3>,-4 means this is a
vector followed by a float.

Each component may be a full float expression. For example
<This+3,That/3,5*Other_Thing> is a valid vector.


4.1.4.2   Vector Identifiers
Vector identifiers may be declared to make scene files more
readable and to parameterize scenes so that changing a single
declaration changes many values. An identifier is declared as
follows.

VECTOR_DECLARATION:
  #declare IDENTIFIER = EXPRESSION;  |
  #local IDENTIFIER = EXPRESSION;
Where IDENTIFIER is the name of the identifier up to 40
characters long and EXPRESSION is any valid expression which
evaluates to a vector value. Note that there should be a semi-
colon after the expression in a vector declaration. This semi-
colon is new with POV-Ray version 3.1. If omitted, it generates a
warning and some macros may not work properly. See "#declare vs.
#local" for information on identifier scope.  Here are some
examples....

 #declare Here = <1,2,3>;
 #declare There = <3,4,5>;
 #declare Jump = <Foo*2,Bar-1,Bob/3>;
 #declare Route = There-Here;
 #declare Jump = Jump+<1,2,3>;
Note that you invoke a vector identifier by using its name
without any angle brackets. As the last example shows, you can re-
declare a vector identifier and may use previously declared
values in that re-declaration. There are several built-in
identifiers which POV-Ray declares for you. See section "Built-in
Vector Identifiers" for details.


4.1.4.3   Vector Operators
Vector literals, identifiers and functions may also be combined
in expressions the same as float values. Operations are performed
on a component-by-component basis. For example <1,2,3> + <4,5,6>
evaluates the same as <1+4,2+5,3+6> or <5,7,9>. Other operations
are done on a similar component-by-component basis. For example
(<1,2,3> = <3,2,1>) evaluates to <0,1,0> because the middle
components are equal but the others are not. Admittedly this
isn't very useful but its consistent with other vector
operations.

Conditional expressions such as (C ? A : B) require that C is a
float expression but A and B may be vector expressions. The
result is that the entire conditional evaluates as a valid
vector. For example if Foo and Bar are floats then (Foo < Bar ?
<1,2,3> : <5,6,7>) evaluates as the vector <1,2,3> if Foo is less
than Bar and evaluates as <5,6,7> otherwise.

You may use the dot operator to extract a single float component
from a vector. Suppose the identifier Spot was previously defined
as a vector. Then Spot.x is a float value that is the first
component of this x, y, z vector. Similarly Spot.y and Spot.z
reference the 2nd and 3rd components. If Spot was a two component
UV vector you could use Spot.u and Spot.v to extract the first
and second component. For a 4D vector use .x, .y, .z, and .t to
extract each float component. The dot operator is also used in
color expressions which are covered later.


4.1.4.4   Operator Promotion
You may use a lone float expression to define a vector whose
components are all the same. POV-Ray knows when it needs a vector
of a particular type and will promote a float into a vector if
need be. For example the POV-Ray scale statement requires a three
component vector. If you specify scale 5 then POV-Ray interprets
this as scale <5,5,5> which means you want to scale by 5 in every
direction.

Versions of POV-Ray prior to 3.0 only allowed such use of a float
as a vector in various limited places such as scale and
turbulence. However you may now use this trick anywhere. For
example...

 box{0,1}  // Same as box{<0,0,0>,<1,1,1>}
 sphere{0,1} // Same as sphere{<0,0,0>,1}
When promoting a float into a vector of 2, 3, 4 or 5 components,
all components are set to the float value, however when promoting
a vector of a lower number of components into a higher order
vector, all remaining components are set to zero. For example if
POV-Ray expects a 4D vector and you specify 9 the result is
<9,9,9,9> but if you specify <7,6> the result is <7,6,0,0>.


4.1.4.5   Built-in Vector Identifiers
There are several built-in vector identifiers. You can use them
to specify values or to create expressions but you cannot re-
declare them to change their values.  They are:

VECTOR_BUILT-IN_IDENT:
  x   |   y   |   z   |   t   |   u   |   v
All built-in vector identifiers never change value. They are
defined as though the following lines were at the start of every
scene.

 #declare x = <1, 0, 0>;
 #declare y = <0, 1, 0>;
 #declare z = <0, 0, 1>;
 #declare t = <0, 0, 0, 1>;
 #declare u = <1, 0>;
 #declare v = <0, 1>;
The built-in vector identifiers x, y, and z provide much greater
readability for your scene files when used in vector expressions.
For example....

 plane { y, 1}    // The normal vector is obviously "y".
 plane { <0,1,0>, 1} // This is harder to read.
 translate 5*x    // Move 5 units in the "x" direction.
 translate <5,0,0>  // This is less obvious.
An expression like 5*x evaluates to 5*<1,0,0> or <5,0,0>.

Similarly u and v may be used in 2D vectors. When using 4D
vectors you should use x, y, z, and t and POV-Ray will promote x,
y, and z to 4D when used where 4D is required.


4.1.4.6   Vector Functions
POV-Ray defines a variety of built-in functions for manipulating
floats, vectors and strings. Function calls consist of a keyword
which specifies the name of the function followed by a parameter
list enclosed in parentheses. Parameters are separated by commas.
For example:

 keyword(param1,param2)
The following are the functions which return vector values. They
take one or more float, integer, vector, or string parameters.
Assume that A and B are any valid expression that evaluates to a
vector; and F is any float expression.

vaxis_rotate(A,B,F) Rotate A about B by F. Given the x,y,z
coordinates of a point in space designated by the vector A,
rotate that point about an arbitrary axis defined by the vector
B. Rotate it through an angle specified in degrees by the float
value F. The result is a vector containing the new x,y,z
coordinates of the point.

vcross(A,B)    Cross product of A and B. Returns a vector that is
the vector cross product of the two vectors. The resulting vector
is perpendicular to the two original vectors and its length is
proportional to the angle between them. See the animated demo
scene VECT2.POV for an illustration.

vnormalize(A)  Normalize vector A. Returns a unit length vector
that is the same direction as A. Formula is
vnormalize=A/vlength(A).

vrotate(A,B)   Rotate A about origin by B. Given the x,y,z
coordinates of a point in space designated by the vector A,
rotate that point about the origin by an amount specified by the
vector B. Rotate it about the x-axis by an angle specified in
degrees by the float value B.x. Similarly B.y and B.z specify the
amount to rotate in degrees about the y-axis and z-axis. The
result is a vector containing the new x,y,z coordinates of the
point.

See section "Float Functions" for other functions which are
somewhat vector-related but which return floats.  In addition to
the above built-in functions, you may also define your own
functions using the new #macro directive. See the section "User
Defined Macros" for more details.


4.1.5     Specifying Colors
POV-Ray often requires you to specify a color. Colors consist of
five values or color components. The first three are called red,
green, and blue. They specify the intensity of the primary colors
red, green and blue using an additive color system like the one
used by the red, green and blue color phosphors on a color
monitor.

The 4th component, called filter, specifies the amount of
filtered transparency of a substance. Some real-world examples of
filtered transparency are stained glass windows or tinted
cellophane. The light passing through such objects is tinted by
the appropriate color as the material selectively absorbs some
frequencies of light while allowing others to pass through. The
color of the object is subtracted from the light passing through
so this is called subtractive transparency.

The 5th component, called transmit, specifies the amount of non-
filtered light that is transmitted through a surface. Some real-
world examples of non-filtered transparency are thin see-through
cloth, fine mesh netting and dust on a surface. In these
examples, all frequencies of light are allowed to pass through
tiny holes in the surface. Although the amount of light passing
through is diminished, the color of the light passing through is
unchanged. The color of the object is added to the light passing
through so this is called additive transparency.

Note that early versions of POV-Ray used the keyword alpha to
specify filtered transparency. However that word is often used to
describe non-filtered transparency. For this reason alpha is no
longer used.

Each of the five components of a color are float values which are
normally in the range between 0.0 and 1.0. However any values,
even negatives may be used.

Under most circumstances the keyword color is optional and may be
omitted. We also support the British or Canadian spelling colour.
Colors may be specified using vectors, keywords with floats or
identifiers. You may also create very complex color expressions
from combinations of any of these using various familiar
operators. The syntax for specifying a color has evolved since
POV-Ray was first released. We have maintained the original
keyword-based syntax and added a short-cut vector notation.
Either the old or new syntax is acceptable however the vector
syntax is easier to use when creating color expressions.

The syntax for combining color literals into color expressions is
almost identical to the rules for vector and float expressions.
In the syntax for vector expressions below, some of the syntax
items are defined in the section for float expressions.  See
"Float Expressions" for those definitions.  Detailed explanations
of color-specific issues are given in the following sub-sections.

COLOR:
  COLOR_BODY               |
  color COLOR_BODY         |    (this means the keyword color or
  colour may
  colour COLOR_BODY               optionally precede any color
  specification)
COLOR_BODY:
  COLOR_VECTOR             |
  COLOR_KEYWORD_GROUP      |
  COLOR_IDENTIFIER
COLOR_VECTOR:
  rgb <3_Term_Vector>      |
  rgbf <4_Term_Vector>          |
  rgbt <4_Term_Vector>          |
  [ rgbft ] <5_Term_Vector>
COLOR_KEYWORD_GROUP:
  [ COLOR_KEYWORD_ITEM ]...
COLOR_KEYWORD_ITEM:
  COLOR_IDENTIFIER         |
  red Red_Amount   |   blue Blue_Amount   |   green Green_Amount
  |
  filter Filter_Amount   |   transmit Transmit_Amount
Note: COLOR_IDENTIFIERS are identifiers previously declared to
have color values.  The 3, 4, and 5 term vectors are usually
vector literals but may be vector expressions or floats promoted
to vectors.  See "Operator Promotion" and the sections below.


4.1.5.1   Color Vectors
The syntax for a color vector is...

COLOR_VECTOR:
  rgb <3_Term_Vector>      |
  rgbf <4_Term_Vector>          |
  rgbt <4_Term_Vector>          |
  [ rgbft ] <5_Term_Vector>
...where the vectors are any valid vector expressions of 3, 4 or
5 components. For example

 color rgb <1.0, 0.5, 0.2>
This specifies a color whose red component is 1.0 or 100% of full
intensity. The green component is 0.5 or 50% of full intensity
and the blue component is 0.2 or 20% of full intensity. Although
the filter and transmit components are not explicitly specified,
they exist and are set to their default values of 0 or no
transparency.

The rgbf keyword requires a four component vector. The 4th
component is the filter component and the transmit component
defaults to zero. Similarly the rgbt keyword requires four
components where the 4th value is moved to the 5th component
which is transmit and then the filter component is set to zero.

The rgbft keyword allows you to specify all five components.
Internally in expressions all five are always used.

Under some circumstances, if the vector expression is a 5
component expression or there is a color identifier in the
expression then the rgbtf keyword is optional.


4.1.5.2   Color Keywords
The older keyword method of specifying a color is still useful
and many users prefer it.

COLOR_KEYWORD_GROUP:
  [ COLOR_KEYWORD_ITEM ]...
COLOR_KEYWORD_ITEM:
  COLOR_IDENTIFIER         |
  red Red_Amount   |   blue Blue_Amount   |   green Green_Amount
  |
  filter Filter_Amount   |   transmit Transmit_Amount
Although the color keyword at the beginning is optional, it is
more common to see it in this usage. This is followed by any of
five additional keywords red, green, blue, filter, or transmit.
Each of these component keywords is followed by a float
expression. For example

 color red 1.0 green 0.5
This specifies a color whose red component is 1.0 or 100% of full
intensity and the green component is 0.5 or 50% of full
intensity. Although the blue, filter and transmit components are
not explicitly specified, they exist and are set to their default
values of 0. The component keywords may be given in any order and
if any component is unspecified its value defaults to zero.  A
COLOR_IDENTIFIER can also be specified but it should always be
first in the group.  See "Common Color Pitfalls" for details.


4.1.5.3   Color Identifiers
Color identifiers may be declared to make scene files more
readable and to parameterize scenes so that changing a single
declaration changes many values. An identifier is declared as
follows.

COLOR_DECLARATION:
  #declare IDENTIFIER = COLOR;  |
  #local IDENTIFIER = COLOR;
Where IDENTIFIER is the name of the identifier up to 40
characters long and COLOR is any valid specification. Note that
there should be a semi-colon at the end of the declaration. This
semi-colon is new with POV-Ray version 3.1. If omitted, it
generates a warning and some macros may not work properly. See
"#declare vs. #local" for information on identifier scope.  Here
are some examples....

 #declare White = rgb <1,1,1>;
 #declare Cyan = color blue 1.0 green 1.0;
 #declare Weird = rgb <Foo*2,Bar-1,Bob/3>;
 #declare LightGray = White*0.8;
 #declare LightCyan = Cyan red 0.6;
As the LightGray example shows you do not need any color keywords
when creating color expressions based on previously declared
colors. The last example shows you may use a color identifier
with the keyword style syntax. Make sure that the identifier
comes first before any other component keywords.

Like floats and vectors, you may re-define colors throughout a
scene but the need to do so is rare.


4.1.5.4   Color Operators
Color vectors may be combined in expressions the same as float or
vector values. Operations are performed on a component-by-
component basis. For example rgb <1.0,0.5,0.2>*0.9 evaluates the
same as rgb<1.0,0.5,0.2>*<0.9,0.9,0.9> or rgb<0.9,0.45,0.18>.
Other operations are done on a similar component-by-component
basis.

You may use the dot operator to extract a single component from a
color. Suppose the identifier Shade was previously defined as a
color. Then Shade.red is the float value of the red component of
Shade. Similarly Shade.green, Shade.blue, Shade.filter and
Shade.transmit extract the float value of the other color
components.


4.1.5.5   Common Color Pitfalls
The variety and complexity of color specification methods can
lead to some common mistakes. Here are some things to consider
when specifying a color.

When using filter transparency, the colors which come through are
multiplied by the primary color components. For example if gray
light such as rgb<0.9,0.9,0.9> passes through a filter such as
rgbf<1.0,0.5,0.0,1.0> the result is rgb<0.9,0.45,0.0> with the
red let through 100%, the green cut in half from 0.9 to 0.45 and
the blue totally blocked. Often users mistakenly specify a clear
object by

 color filter 1.0
but this has implied red, green and blue values of zero. You've
just specified a totally black filter so no light passes through.
The correct way is either

 color red 1.0  green 1.0  blue 1.0  filter 1.0
or

 color transmit 1.0
In the 2nd example it doesn't matter what the rgb values are. All
of the light passes through untouched.

Another pitfall is the use of color identifiers and expressions
with color keywords. For example...

 color My_Color red 0.5
this substitutes whatever was the red component of My_Color with
a red component of 0.5 however...

 color My_Color + red 0.5
adds 0.5 to the red component of My_Color and even less
obvious...

 color My_Color * red 0.5
that cuts the red component in half as you would expect but it
also multiplies the green, blue, filter and transmit components
by zero! The part of the expression after the multiply operator
evaluates to rgbft<0.5,0,0,0,0> as a full 5 component color.

The following example results in no change to My_Color.

 color red 0.5 My_Color
This is because the identifier fully overwrites the previous
value. When using identifiers with color keywords, the identifier
should be first.

Another issue to consider: some POV-Ray syntax allows full color
specifications but only uses the rgb part. In these cases it is
legal to use a float where a color is needed. For example:

 finish { ambient 1 }
The ambient keyword expects a color so the value 1 is promoted to
<1,1,1,1,1> which is no problem. However

 pigment { color 0.4 }
is legal but it may or may not be what you intended. The 0.4 is
promoted to <0.4,0.4,0.4,0.4,0.4> with the filter and transmit
set to 0.4 as well. It is more likely you wanted...

 pigment { color rgb 0.4 }
in which case a 3 component vector is expected. Therefore the 0.4
is promoted to <0.4,0.4,0.4,0.0,0.0> with default zero for filter
and transmit.

Finally there is another problem which arises when using color
dot operators in #declare or #local directives.  Consider the
directive:

 #declare MyColor = rgb <0.75, 0.5, 0.75>;
 #declare RedAmt = MyColor.red;
Now RedAmt should be a float but unfortunately it is a color.
POV-Ray looks at the first keyword after the equals to try to
guess what type of identifier you want.  It sees the color
identifier MyColor and assumes you want to declare a color.  It
then computes the float value as 0.75 then promotes that into
rgbft<0.75,0.75,0.75,0.75,0.75>.

It would take a major rewrite to fix this problem so we're just
warning you about it.  Any of the following work-arounds will
work properly.

 #declare RedAmt = 0.0+MyColor.red;
 #declare RedAmt = 1.0*MyColor.red;
 #declare RedAmt = (MyColor.red);

4.1.6     Strings
The POV-Ray language requires you to specify a string of
characters to be used as a file name, text for messages or text
for a text object. Strings may be specified using literals,
identifiers or functions which return string values. See "String
Functions" for details on string functions.  Although you cannot
build string expressions from symbolic operators such as are used
with floats, vectors or colors, you may perform various string
operations using string functions. Some applications of strings
in POV-Ray allow for non-printing formatting characters such as
newline or form-feed.

STRING:
  STRING_FUNCTION          |
  STRING_IDENTIFIER   |
  STRING_LITERAL
STRING_LITERAL:
  "up to 256 ASCII characters"
STRING_FUNCTION:
  str( FLOAT , INT , INT )   |   concat( STRING , STRING ,
  [STRING ,...])   |   chr( INT )   |
  substr( STRING , INT , INT )   |   strupr( STRING )   |
  strlwr( STRING )

4.1.6.1   String Literals
String literals begin with a double quote mark '"' which is
followed by up to 256 printable ASCII characters and are
terminated by another double quote mark. The following are all
valid string literals:

 "Here"  "There"  "myfile.gif"  "textures.inc"
Note if you need to specify a quote mark in a string literal you
must precede it with a backslash. For example

 "Joe said \"Hello\" as he walked in."
is converted to

 Joe said "Hello" as he walked in.
If you need to specify a backslash, most of the time you need do
nothing special. However if the string ends in a backslash, you
will have to specify two. For example:

 "This is a backslash \ and so is this\\"
Is converted to:

 This is a backslash \ and so is this\
The substitution of \" with a " occurs in all POV-Ray string
literals regardless usage however other formatting codes such as
\n for new line are only supported in user message streams. See
"Text Formatting" for details.


4.1.6.2   String Identifiers
String identifiers may be declared to make scene files more
readable and to parameterize scenes so that changing a single
declaration changes many values. An identifier is declared as
follows.

STRING_DECLARATION:
  #declare IDENTIFIER = STRING  |
  #local IDENTIFIER = STRING
Where IDENTIFIER is the name of the identifier up to 40
characters long and STRING is any valid string specification.
Note that unlike floats, vectors, or colors, there need not be a
semi-colon at the end of the declaration. See "#declare vs.
#local" for information on identifier scope.  Here are some
examples...

 #declare Font_Name = "ariel.ttf"
 #declare Inc_File = "myfile.inc"
 #declare Name = "John"
 #declare Name = concat(Name," Doe")
As the last example shows, you can re-declare a string identifier
and may use previously declared values in that re-declaration.


4.1.6.3   String Functions
POV-Ray defines a variety of built-in functions for manipulating
floats, vectors and strings. Function calls consist of a keyword
which specifies the name of the function followed by a parameter
list enclosed in parentheses. Parameters are separated by commas.
For example:

 keyword(param1,param2)
The following are the functions which return string values. They
take one or more float, integer, vector, or string parameters.
Assume that A is any valid expression that evaluates to a float;
B, L, and P are floats which are truncated to integers
internally, S, S1, S2 etc are strings.

chr(B)    Character whose ASCII value is B. Returns a single
character string. The ASCII value of the character is specified
by an integer B which must be in the range 0 to 255. For example
chr(70) is the string "F". When rendering text objects you should
be aware that the characters rendered for values of B > 127 are
dependent on the (TTF) font being used. Many (TTF) fonts use the
Latin-1 (ISO 8859-1) character set, but not all do.

concat(S1,S2,...)   Concatenate strings S1 and S2. Returns a
string that is the concatenation of all parameter strings. Must
have at least 2 parameters but may have more. For example:

 concat("Value is ", str(A,3,1), " inches")
If the float value A was 12.34321 the result is "Value is 12.3
inches" which is a string.

str(A,L,P): Convert float A to a formatted string. Returns a
formatted string representation of float value A. The integer
parameter L specifies the minimum length of the string and the
type of left padding used if the string's representation is
shorter than the minimum. If L is positive then the padding is
with blanks. If L is negative then the padding is with zeros. The
overall minimum length of the formatted string is abs(L). If the
string needs to be longer, it will be made as long as necessary
to represent the value.

The integer parameter P specifies the number of digits after the
decimal point. If P is negative then a compiler-specific default
precision is use. Here are some examples:

 str(123.456,0,3)  "123.456"
 str(123.456,4,3)  "123.456"
 str(123.456,9,3)  "  123.456"
 str(123.456,-9,3) "00123.456"
 str(123.456,0,2)  "123.46"
 str(123.456,0,0)  "123"
 str(123.456,5,0)  "  123"
 str(123.000,7,2)  "  123.00"
 str(123.456,0,-1) "123.456000" (platform specific)
strlwr(S) Lower case of S. Returns a new string in which all
upper case letters in the string S1 are converted to lower case.
The original string is not affected. For example strlwr("Hello
There!") results in "hello there!".

substr(S,P,L)  Sub-string from S. Returns a string that is a
subset of the characters in parameter S starting at the position
specified by the integer value P for a length specified by the
integer value L. For example substr("ABCDEFGHI",4,2) evaluates to
the string "EF". If P+L>strlen(S) an error occurs.

strupr(S) Upper case of S. Returns a new string in which all
lower case letters in the string S are converted to upper case.
The original string is not affected. For example strupr("Hello
There!") results in "HELLO THERE!".

See section "Float Functions" for other functions which are
somewhat string-related but which return floats.  In addition to
the above built-in functions, you may also define your own
functions using the new #macro directive. See the section "User
Defined Macros" for more details.


4.1.7     Array Identifiers
New in POV-Ray 3.1 you may now declare arrays of identifiers of
up to five dimensions. Any item that can be declared as an
identifier can be declared in an array.


4.1.7.1   Declaring Arrays
The syntax for declaring an array is as follows:

STRING_DECLARATION:
  #declare IDENTIFIER = array[ INT ][ [ INT ]
  ]...[ARRAY_INITIALIZER]  |
  #local IDENTIFIER = array[ INT ][ [ INT ]
  ]...[ARRAY_INITIALIZER]
ARRAY_INITIALIZER:
  {ARRAY_ITEM, [ARRAY_ITEM, ]... }
ARRAY_ITEM:
  RVALUE              |
  ARRAY_INITIALIZER
Where IDENTIFIER is the name of the identifier up to 40
characters long and INT is a valid float expression which is
internally truncated to an integer which specifies the size of
the array. The optional ARRAY_INITIALIZER is discussed in the
next section "Array Initalizers".  Here is an example of a one-
dimensional, uninitalized array.

 #declare MyArray = array[10]
This declares an uninitalized array of ten elements. The elements
are referenced as MyArray[0] through MyArray[9]. As yet, the type
of the elements are undetermined. Once you have initialized any
element of the array, all other elements can only be defined as
that type. An attempt to reference an uninitalized element
results in an error. For example:

 #declare MyArray = array[10];
 #declare MyArray[5] = pigment{White}  //all other elements must
be
                     //pigments too.
 #declare MyArray[2] = normal{bumps 0.2} //generates an error
 #declare Thing = MyArray[4] //error: uninitalized array element
Multi-dimensional arrays up to five dimensions may be declared.
For example:

 #declare MyGrid = array[4][5]
declares a 20 element array of 4 rows and 5 columns. Elements are
referenced from MyGrid[0][0] to MyGrid[3][4]. Although it is
permissible to reference an entire array as a whole, you may not
reference just one dimension of a multi-dimensional array. For
example:

 #declare MyArray = array[10]
 #declare MyGrid = array[4][5]
 #declare YourArray = MyArray  //this is ok
 #declare YourGrid = MyGrid   //so is this
 #declare OneRow  = MyGrid[2] //this is illegal
Large uninitalized arrays do not take much memory. Internally
they are arrays of pointers so they probably use just 4 bytes per
element. Once initialized with values, they consume memory
depending on what you put in them.

The rules for local vs. global arrays are the same as any other
identifier. Note that this applies to the entire array. You
cannot mix local and global elements in the same array.  See
"#declare vs. #local" for information on identifier scope.


4.1.7.2   Array Initalizers
Because it is cumbersome to individually initialize the elements
of an array, you may initialize it as it is created using array
initializer syntax. For example:

 #include "colors.inc"
 #declare FlagColors = array[3] {Red,White,Blue}
Multi-dimensional arrays may also be initialized this way. For
example:

 #declare Digits =
 array[4][10]
 {
  {7,6,7,0,2,1,6,5,5,0},
  {1,2,3,4,5,6,7,8,9,0},
  {0,9,8,7,6,5,4,3,2,1},
  {1,1,2,2,3,3,4,4,5,5}
 }
The commas are required between elements and between dimensions
as shown in the example.



4.2  Language Directives
The POV Scene Language contains several statements called
language directives which tell the file parser how to do its job.
These directives can appear in almost any place in the scene file
- even in the middle of some other statements. They are used to
include other text files in the stream of commands, to declare
identifiers, to define macros, conditional, or looped parsing and
to control other important aspects of scene file processing.

Each directive begins with the hash character # (often called a
number sign or pound sign). It is followed by a keyword and
optionally other parameters.

In versions of POV-Ray prior to 3.0, the use of this # character
was optional. Language directives could only be used between
objects, camera or light_source statements and could not appear
within those statements. The exception was the #include which
could appear anywhere. Now that all language directives can be
used almost anywhere, the # character is mandatory.

The following keywords introduce language directives.
#break      #case        #debug      #declare
#default    #else        #end        #fclose
#fopen      #local       #macro      #read
#render     #statistics  #switch     #undef
#version    #warning     #write      
Earlier versions of POV-Ray considered the keyword
#max_intersections and the keyword #max_trace_level to be
language directives but they have been moved to the
global_settings statement and should be placed there without the
# sign. Their use as a directive still works but it generates a
warning and may be discontinued in the future.


4.2.1     Include Files and the #include Directive.
The language allows include files to be specified by placing the
line

 #include "filename.inc"
at any point in the input file. The filename may be specified by
any valid string expression but it usually is a literal string
enclosed in double quotes. It may be up to 40 characters long (or
your computer's limit), including the two double-quote
characters.

The include file is read in as if it were inserted at that point
in the file. Using include is almost the same as cutting and
pasting the entire contents of this file into your scene.

Include files may be nested. You may have at most 10 nested
include files. There is no limit on un-nested include files.

Generally, include files have data for scenes but are not scenes
in themselves. By convention scene files end in .pov and include
files end with .inc.

It is legal to specify drive and directory information in the
file specification however it is discouraged because it makes
scene files less portable between various platforms.  Use of full
lower case is also recommended but not required.

It is typical to put standard include files in a special sub-
directory. POV-Ray can only read files in the current directory
or one referenced by the Library_Path option or +L switch.  See
section "Library Paths".

You may use the #local directive to declare identifiers which are
temporary in duration and local to the include file in scope. For
details see "#declare vs. #local".


4.2.2     The #declare and #local Directives
Identifiers may be declared and later referenced to make scene
files more readable and to parameterize scenes so that changing a
single declaration changes many values. There are several built-
in identifiers which POV-Ray declares for you. See section "Built-
in Float Identifiers" and "Built-in Vector Identifiers" for
details.


4.2.2.1   Declaring identifiers
An identifier is declared as follows.

DECLARATION:
  #declare IDENTIFIER = RVALUE  |
  #local IDENTIFIER = RVALUE
RVALUE:
  FLOAT;   |   VECTOR;   |   COLOR;   |   STRING   |
  OBJECT   |   TEXTURE   |   PIGMENT   |   NORMAL   |   FINISH
  |
  INTERIOR   |   MEDIA   |   DENSITY
  COLOR_MAP   |   PIGMENT_MAP   |   SLOPE_MAP   |   NORMAL_MAP
  |   DENSITY_MAP   |
  CAMERA   |   LIGHT_SOURCE   |
  FOG   |    RAINBOW   |    SKY_SPHERE   |    TRANSFORM
Where IDENTIFIER is the name of the identifier up to 40
characters long and RVALUE is any of the listed items.  They are
called that because they are values that can appear to the right
of the equals sign.  The syntax for each is in the corresponding
section of this language reference.

Here are some examples.

 #declare Rows = 5;
 #declare Count = Count+1;
 #local  Here = <1,2,3>;
 #declare White = rgb <1,1,1>;
 #declare Cyan = color blue 1.0 green 1.0;
 #declare Font_Name = "ariel.ttf"
 #declare Rod = cylinder {-5*x,5*x,1}
 #declare Ring = torus {5,1}
 #local  Checks = pigment { checker White, Cyan }
 object{ Rod scale y*5 }     // not "cylinder { Rod }"
 object {
  Ring
  pigment { Checks scale 0.5 }
  transform Skew
 }
Note that there should be a semi-colon after the expression in
all float, vector and color identifier declarations. This semi-
colon is new with POV-Ray version 3.1. If omitted, it generates a
warning and some macros may not work properly.

Declarations, like most language directives, can appear anywhere
in the file - even within other statements. For example:

 #declare Here=<1,2,3>;
 #declare Count=0;         // initialize Count
 union {
  object { Rod translate Here*Count }
  #declare Count=Count+1;     // re-declare inside union
  object { Rod translate Here*Count }
  #declare Count=Count+1;     // re-declare inside union
  object { Rod translate Here*Count }
 }
As this example shows, you can re-declare an identifier and may
use previously declared values in that re-declaration. However if
you attempt to re-declare an identifier as anything other than
its original type, it will generate a warning message.

Note that object identifiers use the generic wrapper statement
object{ ... }. You do not need to know what kind of object it is.

Declarations may be nested inside each other within limits. In
the example in the previous section you could declare the entire
union as a object. However for technical reasons there are
instances where you may not use any language directive inside the
declaration of floats, vectors or color expressions. Although
these limits have been loosened somewhat for POV-Ray 3.1, they
still exist.

Identifiers declared within #macro ... #end blocks are not
created at the time the macro is defined. They are only created
at the time the macro is actually invoked. Like all other items
inside such a #macro definition, they are ignored when the macro
is defined.


4.2.2.2   #declare vs. #local
Identifiers may be declared either global using #declare or local
using the #local directive.

Those created by the #declare directive are permanent in duration
and global in scope. Once created, they are available throughout
the scene and they are not released until all parsing is complete
or until they are specifically released using #undef. See
"Destroying Identifiers".

Those created by the #local directive are temporary in duration
and local in scope. They temporarily override any identifiers
with the same name. See "Identifier Name ".

If #local is used inside a #macro then the identifier is local to
that macro. When the macro is invoked and the #local directive is
parsed, the identifier is created. It persists until the #end
directive of the macro is reached. At the #end directive, the
identifier is destroyed. Subsequent invocations of the macro
create totally new identifiers.

Use of #local within an include file but not in a macro, also
creates a temporary identifier that is local to that include
file. When the include file is included and the #local directive
is parsed, the identifier is created. It persists until the end
of the include file is reached. At the end of file the identifier
is destroyed. Subsequent inclusions of the file totally new
identifiers.

Use of #local in the main scene file (not in an include file and
not in a macro) is identical to #declare. For clarity sake you
should not use #local in a main file except in a macro.

There is currently no way to create permanent, yet local
identifiers in POV-Ray.

Local identifiers may be specifically released early using #undef
but in general there is no need to do so. See "Destroying
Identifiers".


4.2.2.3   Identifier Name Collisions
Local identifiers may have the same names as previously declared
identifiers. In this instance, the most recent, most local
identifier takes precedence. Upon entering an include file or
invoking a macro, a new symbol table is created. When referencing
identifiers, the most recently created symbol table is searched
first, then the next most recent and so on back to the global
table of the main scene file. As each macro or include file is
exited, its table and identifiers are destroyed. Parameters
passed by value reside in the same symbol table as the one used
for identifiers local to the macro.

The rules for duplicate identifiers may seem complicated when
multiply-nested includes and macros are involved, but in actual
practice the results are generally what you intended.

Consider this example: You have a main scene file called
myscene.pov and it contains

 #declare A = 123;
 #declare B = rgb<1,2,3>;
 #declare C = 0;
 #include "myinc.inc"
Inside the include file you invoke a macro called MyMacro(J,K,L).
Note it isn't important where MyMacro is defined as long as it is
defined before it is invoked. In this example, it is important
that the macro is invoked from within myinc.inc.

The identifiers A, B, and C are generally available at all
levels. If either myinc.inc or MyMacro contain a line such as
#declare C=C+1; then the value C is changed everywhere as you
might expect.

Now suppose inside myinc.inc you do...

 #local A = 546;
The main version of A is hidden and a new A is created. This new
A is also available inside MyMacro because MyMacro is nested
inside myinc.inc. Once you exit myinc.inc, the local A is
destroyed and the original A with its value of 123 is now in
effect. Once you have created the local A inside myinc.inc, there
is no way to reference the original global A unless you #undef A
or exit the include file. Using #undef always undefines the most
local version of an identifier.

Similarly if MyMacro contained...

 #local B = box{0,1}
then a new identifier B is created local to the macro only. The
original value of B remains hidden but is restored when the macro
is finished. Note that the local B need not have the same type as
the original.

The complication comes when trying to assign a new value to an
identifier at one level that was declared local at an earlier
level. Suppose inside myinc.inc you do...

 #local D = 789;
If you are inside myinc.inc and you want to increment D by one,
you might try to do...

 #local D = D + 1;
but if you try to do that inside MyMacro you'll create a new D
which is local to MyMacro and not the D which is external to
MyMacro but local to myinc.inc. Therefore you've said "create a
MyMacro D from the value of myinc.inc's D plus one". That's
probably not what you wanted. Instead you should do...

 #declare D = D + 1;
You might think this creates a new D that is global but it
actually increments the myinc.inc version of D. Confusing isn't
it? Here are the rules:

1.) When referencing an identifier, you always get the most
recent, most local version. By "referencing" we mean using the
value of the identifier in a POV-Ray statement or using it on the
right of an equals sign in either a #declare or #local.

2.) When declaring an identifier using the #local keyword, the
identifier which is created or has a new value assigned, is
ALWAYS created at the current nesting level of macros or include
files.

3.) When declaring a NEW, NON-EXISTANT identifier using #declare,
it is created as fully global. It is put in the symbol table of
the main scene file.

4.) When ASSIGNING A VALUE TO AN EXISTING identifier using
#declare, it assigns it to the most recent, most local version at
the time.

In summary, #local always means "the current level", and #declare
means "global" for new identifiers and "most recent" for existing
identifiers.


4.2.2.4   Destroying Identifiers with #undef
Identifiers created with #declare will generally persist until
parsing is complete. Identifiers created with #local will persist
until the end of the macro or include file in which they were
created. You may however un-define an identifier using the #undef
directive. For example:

 #undef MyValue
If multiple local nested versions of the identifier exist, the
most local most recent version is deleted and any identically
named identifiers which were created at higher levels will still
exist.

See also "The #ifdef and #ifndef Directives".


4.2.3     File I/O Directives
New in POV-Ray 3.1 you may now open, read, write, append, and
close plain ASCII text files while parsing POV-Ray scenes. This
feature is primarily intended to help pass information between
frames of an animation. Values such as an object's position can
be written while parsing the current frame and read back during
the next frame. Clever use of this feature could allow a POV-Ray
scene to generate its own include files or write self-modifying
scripts. We trust that users will come up with other interesting
uses for this feature.


4.2.3.1   The #fopen Directive
Users may open a text file using the #fopen directive. The syntax
is as follows:

FOPEN_DIRECTIVE:
  #fopen IDENTIFIER "filename" OPEN_TYPE
OPEN_TYPE:
  read   |   write   |   append
Where IDENTIFIER is an undefined identifier used to reference
this file as a file handle, "filename" is any string literal or
string expression which specifies the file name.  Files opened
with the read are open for read only. Those opened with write
create a new file with the specified name and it overwrites any
existing file with that name. Those opened with append opens a
file for writing but appends the text to the end of any existing
file.

The file handle identifier created by #fopen is always global and
remains in effect (and the file remains open) until the scene
parsing is complete or until you #fclose the file. You may use
#ifdef FILE_HANDLE_IDENTIFIER to see if a file is open.


4.2.3.2   The #fclose Directive
Files opened with the #fopen directive are automatically closed
when scene parsing completes however you may close a file using
the #fclose directive. The syntax is as follows:

FCLOSE_DIRECTIVE:
  #fclose FILE_HANDLE_IDENTIFIER
Where FILE_HANDLE_IDENTIFIER is previously opened file opened
with the #fopen directive. See "The #fopen Directive".


4.2.3.3   The #read Directive
You may read string, float or vector values from a plain ASCII
text file directly into POV-Ray variables using the #read
directive. The file must first be opened in "read" mode using the
#fopen directive. The syntax for #read is as follows:

READ_DIRECTIVE:
  #read( FILE_HANDLE_IDENTIFIER,
  DATA_IDENTIFIER[,DATA_IDENTIFIER]...)
DATA_IDENTIFIER:
  UNDECLARED_IDENTIFIER   |   FLOAT_IDENTIFIER   |
  VECTOR_IDENTIFIER   |   STRING_IDENTIFIER
Where FILE_HANDLE_IDENTIFIER is the previously opened file. It is
followed by one or more DATA_IDENTIFIERs separated by commas. The
parentheses around the identifier list are required. A
DATA_IDENTIFIER is any undeclared identifier or any previously
declared string identifier, float identifier, or vector
identifier. Undefined identifiers will be turned into global
identifiers of the type determined by the data which is read.
Previously defined identifiers remain at whatever global/local
status they had when originally created. Type checking is
performed to insure that the proper type data is read into these
identifiers.

The format of the data to be read must be a series of valid
string literals, float literals, or vector literals separated by
commas. Expressions or identifiers are not permitted in the data
file however unary minus signs and exponential notation are
permitted on float values.

If you attempt to read past end-of-file, the file is
automatically closed and the FILE_HANDLE_IDENTIFIER is deleted
from the symbol table.  This means that the boolean function
defined(IDENTIFIER) can be used to detect end-of-file.  For
example:

  #fopen MyFile "mydata.txt" read
  #while (defined(MyFile))
    #read (MyFile,Var1,Var2,Var3)
    ...
  #end

4.2.3.4   The #write Directive
You may write string, float or vector values to a plain ASCII
text file from POV-Ray variables using the #write directive. The
file must first be opened in either write or append mode using
the #fopen directive. The syntax for #write is as follows:

WRITE_DIRECTIVE:
  #write( FILE_HANDLE_ITEM, DATA_ITEM[,DATA_ITEM]...)
DATA_ITEM:
  FLOAT   |   VECTOR   |   STRING
Where FILE_HANDLE_IDENTIFIER is the previously opened file. It is
followed by one or more DATA_ITEMs separated by commas. The
parentheses around the identifier list are required. A DATA_ITEM
is any valid string expression, float expression, or vector
expression. Float expressions are evaluated and written as signed
float literals. If you require format control, you should use the
str(VALUE,L,P) function to convert it to a formatted string. See
"String Functions" for details on the str function. Vector
expressions are evaluated into three signed float constants and
are written with angle brackets and commas in standard POV-Ray
vector notation. String expressions are evaluated and written as
specified.

Note that data read by the #read directive must have comma
delimiters between values and quotes around string data but the
#write directive does not automatically output commas or quotes.
For example the following #read directive reads a string, float
and vector.

 #read (MyFile,MyString,MyFloat,MyVect)
It expects to read something like:

 "A quote delimeted string" , -123.45, <1,2,-3>
The POV-Ray code to write this might be:

 #declare Val1 = -123.45;
 #declare Vect1 = <1,2,-3>;
 #write (MyFile,"\"A quote delimited
string\",",Val1,",",Vect1,"\n")
See "String Literals" and "Text Formatting" for details on
writing special characters such as quotes, newline, etc.


4.2.4     The #default Directive
POV-Ray creates a default texture when it begins processing. You
may change those defaults as described below. Every time you
specify a texture statement, POV-Ray creates a copy of the
default texture. Anything you put in the texture statement
overrides the default settings. If you attach a pigment, normal,
or finish to an object without any texture statement then POV-Ray
checks to see if a texture has already been attached. If it has a
texture then the pigment, normal or finish will modify the
existing texture. If no texture has yet been attached to the
object then the default texture is copied and the pigment, normal
or finish will modify that texture.

You may change the default texture, pigment, normal or finish
using the language directive #default as follows:

DEFAULT_DIRECTIVE:
  #default {DEFAULT_ITEM }
DEFAULT_ITEM:
  TEXTURE   |   PIGMENT   |   NORMAL   |   FINISH
For example:

 #default{
   texture{
     pigment{rgb <1,0,0>}
     normal{bumps 0.3}
     finish{ambient 0.4}
   }
 }
means objects will default to red bumps and slightly high ambient
finish.  Note also you may change just part of it like this:

 #default {
  pigment {rgb <1,0,0>}
 }
This still changes the pigment of the default texture. At any
time there is only one default texture made from the default
pigment, normal and finish. The example above does not make a
separate default for pigments alone. Note that the special
textures tiles and material_map or a texture with a texture_map
may not be used as defaults.

You may change the defaults several times throughout a scene as
you wish. Subsequent #default statements begin with the defaults
that were in effect at the time. If you wish to reset to the
original POV-Ray defaults then you should first save them as
follows:

 //At top of file
 #declare Original_Default = texture {}
later after changing defaults you may restore it with...

 #default {texture {Original_Default}}
If you do not specify a texture for an object then the default
texture is attached when the object appears in the scene. It is
not attached when an object is declared. For example:

 #declare My_Object =
  sphere{ <0,0,0>, 1 } // Default texture not applied
  object{ My_Object }  // Default texture added here
You may force a default texture to be added by using an empty
texture statement as follows:

 #declare My_Thing =
  sphere { <0,0,0>, 1 texture {} } // Default texture applied
The original POV-Ray defaults for all items are given throughout
the documentation under each appropriate section.


4.2.5     The #version Directive
As POV-Ray as evolved from version 1.0 through 3.1 we have made
every effort to maintain some amount of backwards compatibility
with earlier versions.  Some old or obsolete features can be
handled directly without any special consideration by the user.
Some old or obsolete features can no longer be handled at all.
However some old features can still be used if you warn POV-Ray
that this is an older scene.  The #version directive can be used
to switch version compatibility to different setting several
times throughout a scene file.  The syntax is:

VERSION_DIRECTIVE:
  #version FLOAT;
Note that there should be a semi-colon after the float expression
in a #version directive. This semi-colon is new with POV-Ray
version 3.1. If omitted, it generates a warning and some macros
may not work properly.

Additionally you may use the Version=n.n option or the +MVn.n
switch to establish the initial setting.  See "Language Version"
for details. For example one feature introduced in 2.0 that was
incompatible with any 1.0 scene files is the parsing of float
expressions. Using #version 1.0 turns off expression parsing as
well as many warning messages so that nearly all 1.0 files will
still work. Naturally the default setting for this option is
#version 3.1.

NOTE: Some obsolete or re-designed features are totally
unavailable in POV-Ray 3.1 REGARDLES OF THE VERSION SETTING.
Details on these features are noted throughout this
documentation.

The built-in float identifier version contains the current
setting of the version compatibility option. See "Built-in Float
Identifiers".  Together with the built-in version identifier the
#version directive allows you to save and restore the previous
values of this compatibility setting. The new #local identifier
option is especially useful here. For example suppose mystuff.inc
is in version 1 format. At the top of the file you could put:

 #local Temp_Vers = version;  // Save previous value
 #version 1.0;         // Change to 1.0 mode
 ... // Version 1.0 stuff goes here...
 #version Temp_Vers;      // Restore previous version
Future versions of POV-Ray may not continue to maintain full
backward compatibility even with the #version directive. We
strongly encourage you to phase in 3.1 syntax as much as
possible.


4.2.6     Conditional Directives
POV-Ray 3.0 allows a variety of new language directives to
implement conditional parsing of various sections of your scene
file. This is especially useful in describing the motion for
animations but it has other uses as well. Also available is a
#while loop directive. You may nest conditional directives 200
levels deep.


4.2.6.1   The #if...#else...#end Directives
The simplest conditional directive is a traditional #if
directive. It is of the form...

IF_DIRECTIVE:
  #if ( Cond ) TOKENS...  [#else TOKENS...] #end
The TOKENS are any number of POV-Ray keyword, identifiers, or
punctuation and ( Cond ) is a float expression that is
interpreted as a boolean value. The parentheses are required.
The #end directive is required.  A value of 0.0 is false and any
non-zero value is true. Note that extremely small values of about
1e-10 are considered zero in case of round off errors. If Cond is
true, the first group of tokens is parsed normally and the second
set is skipped.  If false, the first set is skipped and the
second set is parsed.  For example:

 #declare Which=1;
 #if (Which)
   box{0,1}
 #else
   sphere{0,1}
 #end
The box is parsed and the sphere is skipped.  Changing the value
of Which to 0 means the box is skipped and the sphere is used.
The #else directive and second token group is optional. For
example:

 #declare Which=1;
 #if (Which)
   box{0,1}
 #end
Changing the value of Which to 0 means the box is removed.


4.2.6.2   The #ifdef and #ifndef Directives
The #ifdef and #ifndef directive are similar to the #if directive
however they is used to determine if an identifier has been
previously declared.

IFDEF_DIRECTIVE:
  #ifdef ( IDENTIFIER ) TOKENS...  [#else TOKENS...] #end
IFNDEF_DIRECTIVE:
  #ifndef ( IDENTIFIER ) TOKENS...  [#else TOKENS...] #end
If the IDENTIFIER exists then the first group of tokens is parsed
normally and the second set is skipped.  If false, the first set
is skipped and the second set is parsed.  This is especially
useful for replacing an undefined item with a default.  For
example:

 #ifdef (User_Thing)

  // This section is parsed if the
  // identifier "User_Thing" was
  // previously declared
  object{User_Thing} // invoke identifier
 #else
  // This section is parsed if the
  // identifier "User_Thing" was not
  // previously declared
  box{<0,0,0>,<1,1,1>} // use a default
 #end
  // End of conditional part
The #ifndef directive works the opposite.  The first group is
parsed if the identifier is not defined.  As with the #if
directive, the #else clause is optional and the #end directive is
required.


4.2.6.3   The #switch, #case, #range and #break Directives
A more powerful conditional is the #switch directive. The syntax
is as follows...

SWITCH_DIRECTIVE:
  #switch ( Switch_Value ) SWITCH_CLAUSE...  [#else TOKENS...]
  #end
SWITCH_CLAUSE:
  #case( Case_Value ) TOKENS...  [#break]      |
  #range( Low_Value , High_Value ) TOKENS...  [#break]
The TOKENS are any number of POV-Ray keyword, identifiers, or
punctuation and ( Switch_Value ) is a float expression. The
parentheses are required.  The #end directive is required.  The
SWITCH_CLAUSE comes in two varieties.  In the #case variety, the
float Switch_Value is compared to the float Case_Value.  If they
are equal, the condition is true.  Note that values whose
difference is less than 1e-10 are considered equal in case of
round off errors.  In the #range variety, Low_Value Switch and
High_Value are floats separated by a comma and enclosed in
parentheses.  If Low_Value <= Switch_Value and
Switch_Value<=High_Value then the condition is true.

In either variety, if the clause's condition is true, that
clause's tokens are parsed normally and parsing continues until a
#break, #else or #end directive is reached. If the condition is
false, POV-Ray skips until another #case or #range is found.

There may be any number of #case or #range clauses in any order
you want. If a clause evaluates true but no #break is specified,
the parsing will fall through to the next #case or #range and
that clause conditional is evaluated.  Hitting #break while
parsing a successful section causes an immediate jump to the #end
without processing subsequent sections, even if a subsequent
condition would also have been satisfied.

An optional #else clause may be the last clause.  It is only
executed if the clause before it was a false clause.

Here is an example:

 #switch (VALUE)
  #case (TEST_1)
   // This section is parsed if VALUE=TEST_1
  #break //First case ends
  #case (TEST_2)
   // This section is parsed if VALUE=TEST_2
  #break //Second case ends
  #range (LOW_1,HIGH_1)
   // This section is parsed if (VALUE>=LOW_1)&(VALUE<=HIGH_1)
  #break //Third case ends
  #range (LOW_2,HIGH_2)
   // This section is parsed if (VALUE>=LOW_2)&(VALUE<=HIGH_2)
  #break //Fourth case ends
  #else
   // This section is parsed if no other case or
   // range is true.
 #end // End of conditional part

4.2.6.4   The #while...#end Directive
The #while directive is a looping feature that makes it easy to
place multiple objects in a pattern or other uses.

WHILE_DIRECTIVE:
  #while ( Cond ) TOKENS... #end
The TOKENS are any number of POV-Ray keyword, identifiers, or
punctuation marks which are the body of the loop.  The #while
directive is followed by a float expression that evaluates to a
boolean value. A value of 0.0 is false and any non-zero value is
true. Note that extremely small values of about 1e-10 are
considered zero in case of round off errors. The parentheses
around the expression are required. If the condition is true
parsing continues normally until an #end directive is reached. At
the end, POV-Ray loops back to the #while directive and the
condition is re-evaluated. Looping continues until the condition
fails. When it fails, parsing continues after the #end directive.
Note it is possible for the condition to fail the first time and
the loop is totally skipped.  It is up to the user to insure that
something inside the loop changes so that it eventually
terminates.  Here is a properly constructed loop example:

 #declare Count=0;
 #while (Count < 5)
  object{MyObject translate x*3*Count}
  #declare Count=Count+1;
 #end
This example places five copies of MyObject in a row spaced three
units apart in the x-direction.


4.2.7     User Message Directives
With the addition of conditional and loop directives, the POV-Ray
language has the potential to be more like an actual programming
language. This means that it will be necessary to have some way
to see what is going on when trying to debug loops and
conditionals. To fulfill this need we have added the ability to
print text messages to the screen. You have a choice of five
different text streams to use including the ability to generate a
fatal error if you find it necessary. Limited formatting is
available for strings output by this method.


4.2.7.1   Text Message Streams
The syntax for a text message is any of the following:

TEXT_STREAM_DIRECTIVE:
  #debug STRING       |
  #error STRING       |
  #render STRING      |
  #statistics STRING  |
  #warning STRING
Where STRING is any valid string of text including string
identifiers or functions which return strings. For example:

 #switch (clock*360)
  #range (0,180)
   #render "Clock in 0 to 180 range\n"
  #break
  #range (180,360)
   #render "Clock in 180 to 360 range\n"
  #break
  #else
   #warning "Clock outside expected range\n"
   #warning concat("Value is:",str(clock*360,5,0),"\n")
 #end
There are seven distinct text streams that POV-Ray uses for
output. You may output only to five of them. On some versions of
POV-Ray, each stream is designated by a particular color. Text
from these streams are displayed whenever it is appropriate so
there is often an intermixing of the text. The distinction is
only important if you choose to turn some of the streams off or
to direct some of the streams to text files. On some systems you
may be able to review the streams separately in their own scroll-
back buffer. See "Directing Text Streams to Files" for details on
re-directing the streams to a text file.

Here is a description of how POV-Ray uses each stream. You may
use them for whatever purpose you want except note that use of
the #error stream causes a fatal error after the text is
displayed.

Debug: This stream displays debugging messages. It was primarily
designed for developers but this and other streams may also be
used by the user to display messages from within their scene
files.

Fatal: This stream displays fatal error messages. After
displaying this text, POV-Ray will terminate. When the error is a
scene parsing error, you may be shown several lines of scene text
that leads up to the error.

Render: This stream displays information about what options you
have specified to render the scene. It includes feedback on all
of the major options such as scene name, resolution, animation
settings, anti-aliasing and others.

Statistics: This stream displays statistics after a frame is
rendered. It includes information about the number of rays
traced, the length of time of the processing and other
information.

Warning: This stream displays warning messages during the parsing
of scene files and other warnings. Despite the warning, POV-Ray
can continue to render the scene.

The banner and status streams can not be accessed by the user.


4.2.7.2   Text Formatting
Some escape sequences are available to include non-printing
control characters in your text. These sequences are similar to
those used in string literals in the C programming language. The
sequences are:
"\a" Bell or       0x0
     alarm,        7
"\b" Backspace,    0x0
                   8
"\f" Form feed,    0x0
                   C
"\n" New line      0x0
     (line feed)   A
"\r" Carriage      0x0
     return        D
"\t" Horizontal    0x0
     tab           9
"\v" Vertical      0x0
     tab           B
"\0" Null          0x0
                   0
"\\" Backslash     0x5
                   C
"\'" Single        0x2
     quote         7
"\"" Double        0x2
     quote         2
For example:

 #debug "This is one line.\nBut this is another"
Depending on what platform you are using, they may not be fully
supported for console output. However they will appear in any
text file if you re-direct a stream to a file.

Note that most of these control characters only apply in text
message directives and #write directives which write strings They
are not implemented for other string usage in POV-Ray such as
text objects or file names.


4.2.8     User Defined Macros
New in POV-Ray 3.1 are user defined macros with parameters. This
new feature, along with the ability to declare #local variables,
turns the POV-Ray Language into a fully functional programming
language. It should now be possible to write scene generation
utilities that previously required external utilities.


4.2.8.1   The #macro Directive
The syntax for declaring a macro is:

MACRO_DEFINITION:
  #macro IDENTIFIER ( [PARAM_IDENT] [,  PARAM_IDENT]... )
  TOKENS... #end
Where IDENTIFIER is the name of the macro and PARAM_IDENTs are a
list of zero or more formal parameter identifiers separated by
commas and enclosed by parentheses. The parentheses are required
even if no parameters are specified.

The TOKENS are any number of POV-Ray keyword, identifiers, or
punctuation marks which are the body of the macro.  The body of
the macro may contain almost any POV-Ray syntax items you desire.
It is terminated my the #end directive. Note however that any
conditional directives such as #if...#end, #while...#end, etc.
must be fully nested inside or outside the macro so that the
corresponding #end directives pair-up properly. Also you may not
nest macro declarations.

A macro must be declared before it is invoked.  All macro names
are global in scope and permanent in duration.  You may redefine
a macro by another #macro directive with the same name.  The
previous definition is lost.  Macro names respond to #ifdef,
#ifndef, and #undef directives.  See "The #ifdef and #ifndef
Directives" and "Destroying Identifiers with #undef".


4.2.8.2   Invoking Macros
You invoke the macro by specifying the macro name followed by a
list of zero or more actual parameters enclosed in parentheses
and separated by commas.  The number of actual parameters must
match the number of formal parameters in the definition.  The
parentheses are required even if no parameters are specified.
The syntax is:

MACRO_INVOCATION:
  MACRO_IDENTIFIER ( [ACTUAL_PARAM] [,  ACTUAL_PARAM]... )
ACTUAL_PARAM:
  IDENTIFIER          |
  RVALUE
An RVALUE is any value that can legally appear to the right of an
equals sign in a #declare or #local declaration. See "Declaring
identifiers" for information on RVALUEs.  When the macro is
invoked, a new local symbol table is created.  The actual
parameters are assigned to formal parameter identifiers as local,
temporary variables.  POV-Ray jumps to the body of the macro and
continues parsing until the matching #end directive is reached.
There, the local variables created by the parameters are
destroyed as well as any local identifiers expressly created in
the body of the macro.  It then resumes parsing at the point
where the macro was invoked.  It is as though the body of the
macro was cut and pasted into the scene at the point where the
macro was invoked.

Here is a simple macro that creates a window frame object when
you specify the inner and outer dimensions.

 #macro Make_Frame
(OuterWidth,OuterHeight,InnerWidth,InnerHeight,Depth)
  #local Horz = (OuterHeight-InnerHeight)/2;
  #local Vert = (OuterWidth-InnerWidth)/2;
  difference
  {
   box{<0,0,0>,<OuterWidth,OuterHeight,Depth>}
   box{<Vert,Horz,-0.1>,<OuterWidth-Vert,OuterHeight-
Horz,Depth+0.1>}
  }
 #end
 Make_Frame(8,10,7,9,1) //invoke the macro
In this example, the macro has five float parameters.  The actual
parameters (the values 8, 10, 7, 9, and 1) are assigned to the
five identifiers in the #macro formal parameter list.  It is as
though you had used the following five lines of code.

 #local OuterWidth = 8;
 #local OuterHeight = 10;
 #local InnerWidth, = 7;
 #local InnerHeight = 9;
 #local Depth = 1;
These five identifiers are stored in the same symbol table as any
other local identifier such as Horz or Vert in this example.  The
parameters and local variables are all destroyed when the #end
statement is reached.  See "Identifier Name Collisions" for a
detailed discussion of how local identifiers, parameters, and
global identifiers work when a local identifier has the same name
as a previously declared identifier.


4.2.8.3   Are POV-Ray Macros a Function or a Macro?
POV-Ray macros are a strange mix of macros and functions.  In
traditional computer programming languages, a macro works
entirely by token substitution.  The body of the routine is
inserted into the invocation point by simply copying the tokens
and parsing them as if they had been cut and pasted in place.
Such cut-and-paste substitution is often called macro
substitution because it is what macros are all about.  In this
respect, POV-Ray macros are exactly like traditional macros in
that they use macro substitution for the body of the macro.
However traditional macros also use this cut-and-paste
substitution strategy for parameters but POV-Ray does not.

Suppose you have a macro in the C programming language
Typical_Cmac(Param) and you invoke it as Typical_Cmac(else A=B).
Anywhere that Param appears in the macro body, the four tokens
else, A, =, and B are substituted into the program code using a
cut-and-paste operation.  No type checking is performed because
anything is legal.  The ability to pass an arbitrary group of
tokens via a macro parameter is a powerful (and sadly often
abused) feature of traditional macros.

After careful deliberation, we have decided against this type of
parameters for our macros.  The reason is that POV-Ray uses
commas more frequently in its syntax than do most programming
languages.  Suppose you create a macro that is designed to
operate on one vector and two floats.  It might be defined
OurMac(V,F1,F2).  If you allow arbitrary strings of tokens and
invoke a macro such as OurMac(<1,2,3>,4,5) then it is impossible
to tell if this is a vector and two floats or if its 5 parameters
with the two tokens < and 1 as the first parameter.  If we design
the macro to accept 5 parameters then we cannot invoke it like
this... OurMac(MyVector,4,5).

Function parameters in traditional programming languages do not
use token substitution to pass values.  They create temporary,
local variables to store parameters that are either constant
values or identifier references which are in effect a pointer to
a variable.  POV-Ray macros use this function-like system for
passing parameters to its macros.  In our example
OurMac(<1,2,3>,4,5), POV-Ray sees the < and knows it must be the
start of a vector.  It parses the whole vector expression and
assigns it to the first parameter exactly as though you had used
the statement #local V=<1,2,3>;.

Although we say that POV-Ray parameters are more like traditional
function parameters than macro parameters, there still is one
difference.  Most languages require you to declare the type of
each parameter in the definition before you use it but POV-Ray
does not.  This should be no surprise because Most languages
require you to declare the type of any identifier before you use
it but POV-Ray does not.  This means that if you pass the wrong
type value in a POV-Ray macro parameter, it may not generate an
error until you reference the identifier in the macro body.  No
type checking is performed as the parameter is passed.  So in
this very limited respect, POV-Ray parameters are somewhat macro-
like but are mostly function-like.


4.2.8.4   Returning a Value Like a Function
POV-Ray macros have a variety of uses.  Like most macros, they
provide a parameterized way to insert arbitrary code into a scene
file.  However most POV-Ray macros will be used like functions or
procedures in a traditional programming language.  This is
especially true because the POV-Ray language has no user-defined
functions or procedures.  Macros are designed to fill all of
these roles.

When the body of a macro consists of statements that create an
entire item such as an object, texture, etc. then the macro acts
like a function which returns a single value.  The Make_Frame
macro example in the section "Invoking Macros" above is such a
macro which returns a value that is an object.  Here are some
examples of how you might invoke it.

 union {  //make a union of two objects
   object{ Make_Frame(8,10,7,9,1) translate  20*x}
   object{ Make_Frame(8,10,7,9,1) translate -20*x}
 }
 #declare BigFrame = object{ Make_Frame(8,10,7,9,1)}
 #declare SmallFrame = object{ Make_Frame(5,4,4,3,0.5)}
Because no type checking is performed on parameters and because
the expression syntax for floats, vectors, and colors is
identical, you can create clever macros which work on all three.
See the sample scene MACRO3.POV which includes this macro to
interpolate values.

// Define the macro.  Parameters are:
//   T:  Middle value of time
//   T1: Initial time
//   T2: Final time
//   P1: Initial position (may be float, vector or color)
//   P2: Final position (may be float, vector or color)
//   Result is a value between P1 and P2 in the same proportion
//    as T is between T1 and T2.
#macro Interpolate(T,T1,T2,P1,P2)
   (P1+(T1+T/(T2-T1))*(P2-P1))
#end
You might invoke it with P1 and P2 as floats, vectors, or colors
as follows.

  sphere{
    Interpolate(I,0,15,<2,3,4>,<9,8,7>),  //center location is
vector
    Interpolate(I,0,15,3.0,5.5)           //radius is float
    pigment{
      color Interpolate(I,0,15,rgb<1,1,0>,rgb<0,1,1>)
    }
  }
As the float value I varies from 0 to 15, the location, radius,
and color of the sphere vary accordingly.

There is a danger in using macros as functions.  In a traditional
programming language function, the result to be returned is
actually assigned to a temporary variable and the invoking code
treats it as a variable of a given type.  However macro
substitution may result in invalid or undesired syntax.  Note the
definition of the macro Interpolate above has an outermost set of
parentheses.  If those parentheses are omitted, it will not
matter in the examples above, but what if you do this...

 #declare Value = Interpolate(I,0,15,3.0,5.5)*15;
The end result is as if you had done...

 #declare Value = P1+(T1+T/(T2-T1))*(P2-P1) * 15;
which is syntactically legal but not mathematically correct
because the P1 term is not multiplied.  The parentheses in the
original example solves this problem.  The end result is as if
you had done...

 #declare Value = (P1+(T1+T/(T2-T1))*(P2-P1)) * 15;
which is correct.


4.2.8.5   Returning Values Via Parameters
Sometimes it is necessary to have a macro return more than one
value or you may simply prefer to return a value via a parameter
as is typical in traditional programming language procedures.
POV-Ray macros are capable of returning values this way.  The
syntax for POV-Ray macro parameters says that the actual
parameter may be an IDENTIFIER or an RVALUE.  Values may only be
returned via a parameter if the parameter is an IDENTIFIER.
Parameters that are RVALUES are constant values that cannot
return information.  An RVALUE is anything that legally may
appear to the right of an equals sign in a #declare or #local
directive.  For example consider the following trivial macro
which rotates an object about the x-axis.

 #macro Turn_Me(Stuff,Degrees)
   #declare Stuff = object{Stuff rotate x*Degrees}
 #end
This attempts to re-declare the identifier Stuff as the rotated
version of the object.  However the macro might be invoked with
Turn_Me(box{0,1},30) which uses a box object as an RVALUE
parameter.  This won't work because the box is not an identifier.
You can however do this

   #declare MyObject=box{0,1}
   Turn_Me(MyObject,30)
The identifier MyObject now contains the rotated box.

See "Identifier Name Collisions" for a detailed discussion of how
local identifiers, parameters, and global identifiers work when a
local identifier has the same name as a previously declared
identifier.

While it is obvious that MyObject is an identifier and box{0,1}
is not, it should be noted that Turn_Me(object{MyObject},30) will
not work because object{MyObject} is considered an object
statement and is not a pure identifier.  This mistake is more
likely to be made with float identifiers verses float
expressions.  Consider these examples.

  #declare Value=5.0;
  MyMacro(Value)     //MyMacro can change the value of Value
but...
  MyMacro(+Value)    //This version and the rest are not lone
  MyMacro(Value+0.0) // identifiers. They are float expressions
  MyMacro(Value*1.0) // which cannot be changed.
Although all four invocations of MyMacro are passed the value
5.0, only the first may modify the value of the identifier.


4.3  POV-Ray Coordinate System
Objects, lights and the camera are positioned using a typical 3D
coordinate system. The usual coordinate system for POV-Ray has
the positive y-axis pointing up, the positive x-axis pointing to
the right and the positive z-axis pointing into the screen. The
negative values of the axes point the other direction as shown in
the images in section "Understanding POV-Ray's Coordinate
System".

Locations within that coordinate system are usually specified by
a three component vector. The three values correspond to the x, y
and z directions respectively. For example, the vector <1,2,3>
means the point that's one unit to the right, two units up and
three units in front of the center of the universe at <0,0,0>.

Vectors are not always points though. They can also refer to an
amount to size, move or rotate a scene element or to modify the
texture pattern applied to an object.

The size, location, orientation, and deformation of items within
the coordinate system is controlled by modifiers called
transformations.  The follow sub-sections describe the
transformations and their usage.


4.3.1     Transformations
The supported transformations are rotate, scale, and translate.
They are used to turn, size and move an object or texture. A
transformation matrix may also be used to specify complex
transformations directly. Groups of transformations may be merged
together and stored in a transformation identifier.  The syntax
for transformations is as follows.

TRANSFORMATION:
  rotate <Rotate_Amt>           |
  scale <Scale_Amt>                  |
  translate <Translate_Amt>          |
  transform TRANSFORM_IDENTIFIER     |
  matrix <Val00, Val01, Val02,
     Val10, Val11, Val12,
     Val20, Val21, Val22,
     Val30, Val31, Val32>
TRANSFORM_DECLARATION:
  #declare IDENTIFIER = transform{ TRANSFORMATION... }   |
  #local IDENTIFIER = transform{ TRANSFORMATION... }

4.3.1.1   Translate
Items may be moved by adding a translate modifier. It consists of
the keyword translate followed by a vector expression. The three
terms of the vector specify the number of units to move in each
of the x, y and z directions. Translate moves the element
relative to it's current position. For example

 sphere { <10, 10, 10>, 1
  pigment { Green }
  translate <-5, 2, 1>
 }
will move the sphere from the location <10,10,10> to <5,12,11>.
It does not move it to the absolute location <-5,2,1>.
Translations are always relative to the item's location before
the move.  Translating by zero will leave the element unchanged
on that axis. For example:

 sphere { <10, 10, 10>, 1
  pigment { Green }
  translate 3*x // evaluates to <3,0,0> so move 3 units
         // in the x direction and none along y or z
 }

4.3.1.2   Scale
You may change the size of an object or texture pattern by adding
a scale modifier. It consists of the keyword scale followed by a
vector expression. The three terms of the vector specify the
amount of scaling in each of the x, y and z directions.

Uneven scaling is used to stretch or squish an element. Values
larger than one stretch the element on that axis while values
smaller than one are used to squish it. Scale is relative to the
current element size. If the element has been previously re-sized
using scale then scale will size relative to the new size.
Multiple scale values may used.

For example

 sphere { <0,0,0>, 1
  scale <2,1,0.5>
 }
will stretch and smash the sphere into an ellipsoid shape that is
twice the original size along the x-direction, remains the same
size in the y-direction and is half the original size in the z-
direction.

If a lone float expression is specified it is promoted to a three
component vector whose terms are all the same. Thus the item is
uniformly scaled by the same amount in all directions. For
example:

 object {
  MyObject
  scale 5 // Evaluates as <5,5,5> so uniformly scale
      // by 5 in every direction.
 }

4.3.1.3   Rotate
You may change the orientation of an object or texture pattern by
adding a rotate modifier. It consists of the keyword rotate
followed by a vector expression. The three terms of the vector
specify the number of degrees to rotate about each of the x-, y-
and z-axes.

Note that the order of the rotations does matter. Rotations occur
about the x-axis first, then the y-axis, then the z-axis. If you
are not sure if this is what you want then you should only rotate
on one axis at a time using multiple rotation statements to get a
correct rotation. As in

 rotate <0, 30, 0>  // 30 degrees around Y axis then,
 rotate <-20, 0, 0> // -20 degrees around X axis then,
 rotate <0, 0, 10>  // 10 degrees around Z axis.
Rotation is always performed relative to the axis. Thus if an
object is some distance from the axis of rotation it will not
only rotate but it will orbit about the axis as though it was
swinging around on an invisible string.

POV-Ray uses a left-handed rotation system. Using the famous
"Computer Graphics Aerobics" exercise, you hold up your left hand
and point your thumb in the positive direction of the axis of
rotation. Your fingers will curl in the positive direction of
rotation. Similarly if you point your thumb in the negative
direction of the axis your fingers will curl in the negative
direction of rotation.  See "Understanding POV-Ray's Coordinate
System" for a illustration.


4.3.1.4   Matrix Keyword
The matrix keyword can be used to explicitly specify the
transformation matrix to be used for objects or textures. Its
syntax is:

MATRIX:
  matrix <Val00, Val01, Val02,
     Val10, Val11, Val12,
     Val20, Val21, Val22,
     Val30, Val31, Val32>
Where Val00 through Val32 are float expressions enclosed in angle
brackets and separated by commas.  Note this is not a vector.  It
is a set of 12 float expressions.  These floats specify the
elements of a 4 by 4 matrix with the fourth column implicitly set
to <0,0,0,1>. At any given point P, P=<px, py, pz>, is
transformed into the point Q, Q=<qx, qy, qz> by

 qx = Val00 * px + Val10 * py + Val20 * pz + Val30
 qy = Val01 * px + Val11 * py + Val21 * pz + Val31
 qz = Val02 * px + Val12 * py + Val22 * pz + Val32
Normally you won't use the matrix keyword because it's less
descriptive than the transformation commands and harder to
visualize. However the matrix command allows more general
transformation effects like shearing. The following matrix causes
an object to be sheared along the y-axis.

 object {
  MyObject
  matrix < 1, 1, 0,
       0, 1, 0,
       0, 0, 1,
       0, 0, 0 >
 }

4.3.2     Transformation Order
Because rotations are always relative to the axis and scaling is
relative to the origin, you will generally want to create an
object at the origin and scale and rotate it first. Then you may
translate it into its proper position. It is a common mistake to
carefully position an object and then to decide to rotate it.
However because a rotation of an object causes it to orbit about
the axis, the position of the object may change so much that it
orbits out of the field of view of the camera!

Similarly scaling after translation also moves an object
unexpectedly. If you scale after you translate the scale will
multiply the translate amount. For example

 translate <5, 6, 7>
 scale 4
will translate to <20,24,28> instead of <5,6,7>. Be careful when
transforming to get the order correct for your purposes.


4.3.3     Transform Identifiers
At times it is useful to combine together several transformations
and apply them in multiple places. A transform identifier may be
used for this purpose. Transform identifiers are declared as
follows:

TRANSFORM_DECLARATION:
  #declare IDENTIFIER = transform{ TRANSFORMATION... }   |
  #local IDENTIFIER = transform{ TRANSFORMATION... }
Where IDENTIFIER is the name of the identifier up to 40
characters long and TRANSFORMATION is any valid transformation
modifier.  See "#declare vs. #local" for information on
identifier scope.  Here is an example...

 #declare MyTrans = transform {
   rotate ThisWay
   scale SoMuch
   rotate -ThisWay
   scale Bigger
   translate OverThere
   rotate WayAround
  }
A transform identifier is invoked by the transform keyword
without any brackets as shown here:

 object {
  MyObject      // Get a copy of MyObject
  transform MyTrans // Apply the transformation
  translate -x*5   // Then move it 5 units left
 }
 object {
  MyObject      // Get another copy of MyObject
  transform MyTrans // Apply the same transformation
  translate x*5   // Then move this one 5 units right
 }
On extremely complex CSG objects with lots of components it may
speed up parsing if you apply a declared transformation rather
than the individual translate, rotate, scale, or matrix
modifiers. The transform is attached just once to each component.
Applying each individual translate, rotate, scale, or matrix
modifiers takes longer. This only affects parsing - rendering
works the same either way.


4.3.4     Transforming Textures and Objects
When an object is transformed all textures attached to the object
at that time are transformed as well. This means that if you have
a translate, rotate, scale, or matrix modifier in an object
before a texture, then the texture will not be transformed. If
the transformation is after the texture then the texture will be
transformed with the object. If the transformation is inside the
texture statement then only the texture is affected. The shape
remains the same. For example:

 sphere { 0, 1
  texture { Jade } // texture identifier from TEXTURES.INC
  scale 3      // this scale affects both the
           // shape and texture
 }
 sphere { 0, 1
  scale 3      // this scale affects the shape only
  texture { Jade }
 }
 sphere { 0, 1
  texture {
   Jade
   scale 3     // this scale affects the texture only
  }
 }
Transformations may also be independently applied to pigment
patterns and surface normal patterns. Note that scaling a normal
pattern affects only the width and spacing. It does not affect
the apparent height or depth of the bumps. For example:

 box { <0, 0, 0>, <1, 1, 1>
  texture {
   pigment {
    checker Red, White
    scale 0.25 // This affects only the color pattern
   }
   normal {
    bumps 0.3 // This specifies apparent height of bumps
    scale 0.2 // Scales diameter and space between bumps
          // but not the height. Has no effect on
          // color pattern.
   }
   rotate y*45 // This affects the entire texture but
  }       // not the object.
 }


4.4  Camera
The camera definition describes the position, projection type and
properties of the camera viewing the scene. Its syntax is:

CAMERA:
  camera{ [CAMERA_ITEMS...] }
CAMERA_ITEM:
  CAMERA_TYPE   |   CAMERA_VECTOR   |   CAMERA_MODIFIER   |
  CAMERA_IDENTIFIER
CAMERA_TYPE:
  perspective   |   orthographic   |   fisheye   |
  ultra_wide_angle   |
  omnimax   |   panoramic   |   cylinder CylinderType
CAMERA_VECTOR:
  location <Location>   |   right <Right>   |   up <Up>   |
  direction <Direction>   |
  sky <Sky>
CAMERA_MODIFIER:
  angle Degrees   |   look_at <Look_At>   |
  blur_samples Num_of_Samples   |   aperture Size   |
  focal_point <Point>   |
  confidence Blur_Confidence   |   varience Blur_Varience   |
  NORMAL   |
  TRANSFORMATION
Depending on the projection type some of the parameters are
required, some are optional and some aren't used. If no
projection type is given the perspective camera will be used
(pinhole camera). If no camera is specified a default camera is
used.  CAMERA_ITEMs may legally appear in any order but the order
of some items is critical to the proper functioning of the
camera.  Follow the guidelines in this document closely because
POV-Ray will not stop you from making mistakes.


4.4.1     Placing the Camera
The POV-Ray camera has ten different models, each of which uses a
different projection method to project the scene onto your
screen.  Regardless of the projection type all cameras use the
location, right, up, direction, and keywords to determine the
location and orientation of the camera. The type keywords and
these four vectors fully define the camera.  All other camera
modifiers adjust how the camera does its job.  The meaning of
these vectors and other modifiers differ with the projection type
used. A more detailed explanation of the camera types follows
later.  In the sub-sections which follows, we explain how to
place and orient the camera by the use of these four vectors and
the sky and look_at modifiers.  You may wish to refer to the
illustration of the perspective camera below as you read about
these vectors.



                                
                                
                     The perspective camera.
                                

4.4.1.1   Location and Look_At
Under many circumstances just two vectors in the camera statement
are all you need to position the camera: location and look_at
vectors. For example:

 camera {
  location <3,5,-10>
  look_at <0,2,1>
 }
The location is simply the x, y, z coordinates of the camera. The
camera can be located anywhere in the ray-tracing universe. The
default location is <0,0,0>. The look_at vector tells POV-Ray to
pan and tilt the camera until it is looking at the specified x,
y, z coordinates. By default the camera looks at a point one unit
in the z-direction from the location.

The look_at modifier should almost always be the last item in the
camera statement. If other camera items are placed after the
look_at vector then the camera may not continue to look at the
specified point.


4.4.1.2   The Sky Vector
Normally POV-Ray pans left or right by rotating about the y-axis
until it lines up with the look_at point and then tilts straight
up or down until the point is met exactly. However you may want
to slant the camera sideways like an airplane making a banked
turn. You may change the tilt of the camera using the sky vector.
For example:

 camera {
  location <3,5,-10>
  sky   <1,1,0>
  look_at <0,2,1>
 }
This tells POV-Ray to roll the camera until the top of the camera
is in line with the sky vector. Imagine that the sky vector is an
antenna pointing out of the top of the camera. Then it uses the
sky vector as the axis of rotation left or right and then to tilt
up or down in line with the sky until pointing at the look_at
point. In effect you're telling POV-Ray to assume that the sky
isn't straight up. Note that the sky vector must appear before
the look_at vector.

The sky vector does nothing on its own. It only modifies the way
the look_at vector turns the camera. The default value is
sky<0,1,0>.


4.4.1.3   Angle
The angle keyword followed by a float expression specifies the
(horizontal) viewing angle in degrees of the camera used. Even
though it is possible to use the direction vector to determine
the viewing angle for the perspective camera it is much easier to
use the angle keyword.

When you specify the angle, POV-Ray adjusts the length of the
direction vector accordingly.  The formula used is
direction_length = 0.5 * right_length / tan(angle / 2) where
right_length is the length of the right vector.  You should
therefore specify the direction and right vectors before the
angle keyword.  The right vector is explained in the next
section.

There is no limitation to the viewing angle except for the
perspective projection. If you choose viewing angles larger than
360 degrees you'll see repeated images of the scene (the way the
repetition takes place depends on the camera). This might be
useful for special effects.


4.4.1.4   The Direction Vector
You will probably not need to explicitly specify or change the
camera direction vector but it is described here in case you do.
It tells POV-Ray the initial direction to point the camera before
moving it with the look_at or rotate vectors (the default value
is direction<0,0,1>). It may also be used to control the
(horizontal) field of view with some types of projection. The
length of the vector determines the distance of the viewing plane
from the camera's location.  A shorter direction vector gives a
wider view while a longer vector zooms in for close-ups.  In
early versions of POV-Ray, this was the only way to adjust field
of view.  However zooming should now be done using the easier to
use angle keyword.

If you are using the ultra_wide_angle, panoramic, or cylindrical
projection you should use a unit length direction vector to avoid
strange results.

The length of the direction vector doesn't matter when using the
orthographic, fisheye, or omnimax projection types.


4.4.1.5   Up and Right Vectors
The primary purpose of the up and right vectors is to tell POV-
Ray the relative height and width of the view screen. The default
values are:

 right 4/3*x
 up y
In the default perspective camera, these two vectors also define
the initial plane of the view screen before moving it with the
look_at or rotate vectors.  The length of the right vector
(together with the direction vector) may also be used to control
the (horizontal) field of view with some types of projection.
The look_at modifier changes both up and right so you should
always specify them before look_at.  Also the angle calculation
depends on the right vector so right should precede it.

Most camera types treat the up and right vectors the same as the
perspective type.  However several make special use of them.  In
the orthographic projection: The lengths of the up and right
vectors set the size of the viewing window regardless of the
direction vector length, which is not used by the orthographic
camera.

When using cylindrical projection: types 1 and 3, the axis of the
cylinder lies along the up vector and the width is determined by
the length of right vector or it may be overridden with the angle
vector. In type 3 the up vector determines how many units high
the image is. For example if you have up 4*y on a camera at the
origin. Only points from y=2 to y=-2 are visible. All viewing
rays are perpendicular to the y-axis. For type 2 and 4, the
cylinder lies along the right vector. Viewing rays for type 4 are
perpendicular to the right vector.

Note that the up, right, and direction vectors should always
remain perpendicular to each other or the image will be
distorted. If this is not the case a warning message will be
printed. The vista buffer will not work for non-perpendicular
camera vectors.  If you specify the 3 vectors as initially
perpendicular and do not explicitly re-specify the after any
look_at or rotate vectors, the everything will work fine.


4.4.1.5.1 Aspect Ratio
Together the up and right vectors define the aspect ratio (height
to width ratio) of the resulting image. The default values
up<0,1,0> and right<1.33,0,0> result in an aspect ratio of 4 to
3. This is the aspect ratio of a typical computer monitor. If you
wanted a tall skinny image or a short wide panoramic image or a
perfectly square image you should adjust the up and right vectors
to the appropriate proportions.

Most computer video modes and graphics printers use perfectly
square pixels. For example Macintosh displays and IBM SVGA modes
640x480, 800x600 and 1024x768 all use square pixels. When your
intended viewing method uses square pixels then the width and
height you set with the Width and Height options or +W or +H
switches should also have the same ratio as the up and right
vectors. Note that 640/480 = 4/3 so the ratio is proper for this
square pixel mode.

Not all display modes use square pixels however. For example IBM
VGA mode 320x200 and Amiga 320x400 modes do not use square
pixels. These two modes still produce a 4/3 aspect ratio image.
Therefore images intended to be viewed on such hardware should
still use 4/3 ratio on their up and right vectors but the pixel
settings will not be 4/3.

For example:

 camera {
  location <3,5,-10>
  up    <0,1,0>
  right  <1,0,0>
  look_at <0,2,1>
 }
This specifies a perfectly square image. On a square pixel
display like SVGA you would use pixel settings such as +W480
+H480 or +W600 +H600. However on the non-square pixel Amiga
320x400 mode you would want to use values of +W240 +H400 to
render a square image.

The bottom line issue is this: the up and right vectors should
specify the artist's intended aspect ratio for the image and the
pixel settings should be adjusted to that same ratio for square
pixels and to an adjusted pixel resolution for non-square pixels.
The up and right vectors should not be adjusted based on non-
square pixels.


4.4.1.5.2 Handedness
The right vector also describes the direction to the right of the
camera. It tells POV-Ray where the right side of your screen is.
The sign of the right vector can be used to determine the
handedness of the coordinate system in use. The default value is:
right<1.33,0,0>.  This means that the +x-direction is to the
right. It is called a left-handed system because you can use your
left hand to keep track of the axes. Hold out your left hand with
your palm facing to your right. Stick your thumb up. Point
straight ahead with your index finger. Point your other fingers
to the right. Your bent fingers are pointing to the +x-direction.
Your thumb now points into +y-direction. Your index finger points
into the +z-direction.

To use a right-handed coordinate system, as is popular in some
CAD programs and other ray-tracers, make the same shape using
your right hand. Your thumb still points up in the +y-direction
and your index finger still points forward in the +z-direction
but your other fingers now say the +x-direction is to the left.
That means that the right side of your screen is now in the -x-
direction. To tell POV-Ray to act like this you can use a
negative x value in the right vector such as: right<-1.33,0,0>.
Since having x values increasing to the left doesn't make much
sense on a 2D screen you now rotate the whole thing 180 degrees
around by using a positive z value in your camera's location. You
end up with something like this.

 camera {
  location <0,0,10>
  up    <0,1,0>
  right  <-1.33,0,0>
  look_at <0,0,0>
 }
Now when you do your ray-tracer's aerobics, as explained in the
section "Understanding POV-Ray's Coordinate System", you use your
right hand to determine the direction of rotations.

In a two dimensional grid, x is always to the right and y is up.
The two versions of handedness arise from the question of whether
z points into the screen or out of it and which axis in your
computer model relates to up in the real world.

Architectural CAD systems, like AutoCAD, tend to use the God's
Eye orientation that the z-axis is the elevation and is the
model's up direction. This approach makes sense if you're an
architect looking at a building blueprint on a computer screen. z
means up, and it increases towards you, with x and y still across
and up the screen. This is the basic right handed system.

Stand alone rendering systems, like POV-Ray, tend to consider you
as a participant. You're looking at the screen as if you were a
photographer standing in the scene. The up direction in the model
is now y, the same as up in the real world and x is still to the
right, so z must be depth, which increases away from you into the
screen. This is the basic left handed system.


4.4.1.6   Transforming the Camera
The various transformations such as translate and rotate
modifiers can re-position the camera once you've defined it. For
example:

 camera {
  location < 0, 0, 0>
  direction < 0, 0, 1>
  up    < 0, 1, 0>
  right   < 1, 0, 0>
  rotate  <30, 60, 30>
  translate < 5, 3, 4>
 }
In this example, the camera is created, then rotated by 30
degrees about the x-axis, 60 degrees about the y-axis and 30
degrees about the z-axis, then translated to another point in
space.


4.4.2     Types of Projection
The following list explains the different projection types that
can be used with the camera. The most common types are the
perspective and orthographic projections.  In general the
CAMERA_TYPE should be the first item in a camera statement.  If
none is specified, the perspective camera is the default.

Perspective projection: The perspective specifies the default
perspective camera which simulates the classic pinhole camera.
The (horizontal) viewing angle is either determined by the ratio
between the length of the direction vector and the length of the
right vector or by the optional keyword angle, which is the
preferred way. The viewing angle has to be larger than 0 degrees
and smaller than 180 degrees. See the figure in "Placing the
Camera" for the geometry of the perspective camera.

Orthographic projection: This projection uses parallel camera
rays to create an image of the scene. The size of the image is
determined by the lengths of the right and up vectors.

If you add the orthographic keyword after all other parameters of
a perspective camera you'll get an orthographic view with the
same image area, i.e. the size of the image is the same. In this
case you needn't specify the lengths of the right and up vector
because they'll be calculated automatically. You should be aware
though that the visible parts of the scene change when switching
from perspective to orthographic view. As long as all objects of
interest are near the look_at point they'll be still visible if
the orthographic camera is used. Objects farther away may get out
of view while nearer objects will stay in view.

Fisheye projection: This is a spherical projection. The viewing
angle is specified by the angle keyword. An angle of 180 degrees
creates the "standard" fisheye while an angle of 360 degrees
creates a super-fisheye ("I-see-everything-view"). If you use
this projection you should get a circular image. If this isn't
the case, i.e. you get an elliptical image, you should read
"Aspect Ratio".

Ultra wide angle projection: This projection is somewhat similar
to the fisheye but it projects the image onto a rectangle instead
of a circle. The viewing angle can be specified using the angle
keyword.

Omnimax projection: The omnimax projection is a 180 degrees
fisheye that has a reduced viewing angle in the vertical
direction. In reality this projection is used to make movies that
can be viewed in the dome-like Omnimax theaters. The image will
look somewhat elliptical. The angle keyword isn't used with this
projection.

Panoramic projection: This projection is called "cylindrical
equirectangular projection". It overcomes the degeneration
problem of the perspective projection if the viewing angle
approaches 180 degrees. It uses a type of cylindrical projection
to be able to use viewing angles larger than 180 degrees with a
tolerable lateral-stretching distortion. The angle keyword is
used to determine the viewing angle.

Cylindrical projection: Using this projection the scene is
projected onto a cylinder. There are four different types of
cylindrical projections depending on the orientation of the
cylinder and the position of the viewpoint. A float value in the
range 1 to 4 must follow the cylinder keyword.  The viewing angle
and the length of the up or right vector determine the dimensions
of the camera and the visible image. The camera to use is
specified by a number. The types are:
1 vertical cylinder, fixed viewpoint
2 horizontal cylinder, fixed
  viewpoint
3 vertical cylinder, viewpoint moves
  along the cylinder's axis
4 horizontal cylinder, viewpoint
  moves along the cylinder's axis
You should note that the vista buffer can only be used with the
perspective and orthographic camera.


4.4.3     Focal Blur
POV-Ray can simulate focal depth-of-field by shooting a number of
sample rays from jittered points within each pixel and averaging
the results.

To turn on focal blur, you must specify the aperture keyword
followed by a float value which determines the depth of the
sharpness zone. Large apertures give a lot of blurring, while
narrow apertures will give a wide zone of sharpness. Note that,
while this behaves as a real camera does, the values for aperture
are purely arbitrary and are not related to f-stops.

You must also specify the blur_samples keyword followed by an
integer value specifying the maximum number of rays to use for
each pixel. More rays give a smoother appearance but is slower.
By default no focal blur is used, i. e. the default aperture is 0
and the default number of samples is 0.

The center of the zone of sharpness is specified by the
focal_point vector.  Objects close to this point are in focus and
those farther from that point are more blurred.  The default
value is focal_point<0,0,0>.

Although blur_samples specifies the maximum number of samples,
there is an adaptive mechanism that stops shooting rays when a
certain degree of confidence has been reached.  At that point,
shooting more rays would not result in a significant change.  The
confidence and variance keywords are followed by float values to
control the adaptive function. The confidence value is used to
determine when the samples seem to be close enough to the correct
color. The variance value specifies an acceptable tolerance on
the variance of the samples taken so far. In other words, the
process of shooting sample rays is terminated when the estimated
color value is very likely (as controlled by the confidence
probability) near the real color value.

Since the confidence is a probability its values can range from 0
to 1 (the default is 0.9, i. e. 90%). The value for the variance
should be in the range of the smallest displayable color
difference (the default is 1/128).

Larger confidence values will lead to more samples, slower traces
and better images. The same holds for smaller variance
thresholds.


4.4.4     Camera Ray Perturbation
The optional normal may be used to assign a normal pattern to the
camera.  For example:

 camera{
   location Here
   look_at There
   normal{bumps 0.5}
 }
All camera rays will be perturbed using this pattern. The image
will be distorted as though you were looking through bumpy glass
or seeing a reflection off of a bumpy surface.  This lets you
create special effects. See the animated scene camera2.pov for an
example.  See "Normal" for information on normal patterns.


4.4.5     Camera Identifiers
Camera identifiers may be declared to make scene files more
readable and to parameterize scenes so that changing a single
declaration changes many values. You may declare several camera
identifiers if you wish. This makes it easy to quickly change
cameras. An identifier is declared as follows.

CAMERA_DECLARATION:
  #declare IDENTIFIER = CAMERA  |
  #local IDENTIFIER = CAMERA
Where IDENTIFIER is the name of the identifier up to 40
characters long and CAMERA is any valid camera statement. See
"#declare vs. #local" for information on identifier scope.  Here
is an example...

 #declare Long_Lens =
  camera {
   location -z*100
   angle 3
  }
 #declare Short_Lens =
  camera {
   location -z*50
   angle 15
  }
 camera {
  Long_Lens  // edit this line to change lenses
  look_at Here
 }


4.5  Objects
Objects are the building blocks of your scene. There are a lot of
different types of objects supported by POV-Ray.  In the sections
which follow, we describe "Finite Solid Primitives", "Finite
Patch Primitives", "Infinite Solid Primitives", and "Light
Sources". These primitive shapes may be combined into complex
shapes using "Constructive Solid Geometry" or CSG.

The basic syntax of an object is a keyword describing its type,
some floats, vectors or other parameters which further define its
location and/or shape and some optional object modifiers such as
texture, pigment, normal, finish, interior, bounding, clipping or
transformations.  Specifically the syntax is:

OBJECT:
  FINITE_SOLID_OBJECT   |   FINITE_PATCH_OBJECT   |
  INFINITE_SOLID_OBJECT   |   CSG_OBJECT   |   LIGHT_SOURCE   |
  object { OBJECT_IDENTIFIER  [OBJECT_MODIFIERS...] }
FINITE_SOLID_OBJECT:
  BLOB   |   BOX   |   CONE   |   CYLINDER   |   HEIGHT_FIELD
  |   JULIA_FRACTAL   |
  LATHE   |   PRISM   |   SPHERE   |   SUPERELLIPSOID   |   SOR
  |   TEXT   |   TORUS
FINITE_PATCH_OBJECT:
  BICUBIC_PATCH   |   DISC   |   MESH   |   POLYGON   |
  TRIANGLE   |   SMOOTH_TRIANGLE
INFINITE_SOLID_OBJECT:
  PLANE   |   POLY   |   CUBIC   |   QUARTIC   |   QUADRIC
CSG_OBJECT:
  UNION   |   INTERSECTION   |   DIFFERENCE   |   MERGE
Object identifiers may be declared to make scene files more
readable and to parameterize scenes so that changing a single
declaration changes many values. An identifier is declared as
follows.

OBJECT_DECLARATION:
  #declare IDENTIFIER = OBJECT   |
  #local IDENTIFIER = OBJECT
Where IDENTIFIER is the name of the identifier up to 40
characters long and OBJECT is any valid object.  Note that to
invoke an object identifier, you wrap it in an object{...}
statement.  You use the object statement regardless of what type
of object it originally was.  Although early versions of POV-Ray
required this object wrapper all of the time, now it is only used
with OBJECT_IDENTIFIERS.

Object modifiers are covered in detail later.  However here is a
brief overview.

The texture describes the surface properties of the object.
Complete details are in "Textures".  Textures are combinations of
pigments, normals, and finishes. In the section "Pigment" you'll
learn how to specify the color or pattern of colors inherent in
the. In "Normal" we describe a method of simulating various
patterns of bumps, dents, ripples or waves by modifying the
surface normal vector. The section on "Finish" describes the
reflective properties of the surface.  The "Interior" is a new
feature in POV-Ray 3.1.  It contains information about the
interior of the object which was formerly contained in the finish
and halo parts of a texture.  Interior items are no longer part
of the texture.  Instead, they attach directly to the objects.
The halo feature has been discontinued and replaced with a new
feature called "Media" which replaces both halo and atmosphere.

Bounding shapes are finite, invisible shapes which wrap around
complex, slow rendering shapes in order to speed up rendering
time. Clipping shapes are used to cut away parts of shapes to
expose a hollow interior. Transformations tell the ray-tracer how
to move, size or rotate the shape and/or the texture in the
scene.


4.5.1     Finite Solid Primitives
There are thirteen different solid finite primitive shapes: blob,
box, cone, cylinder, height field, Julia fractal, lathe, prisms,
sphere, superellipsoid, surface of revolution, text object and
torus. These have a well-defined inside and can be used in CSG
(see section "Constructive Solid Geometry"). They are finite and
respond to automatic bounding.  You may specify an interior for
these objects.


4.5.1.1   Blob
Blobs are an interesting and flexible object type. Mathematically
they are iso-surfaces of scalar fields, i.e. their surface is
defined by the strength of the field in each point. If this
strength is equal to a threshold value you're on the surface
otherwise you're not.

Picture each blob component as an object floating in space. This
object is filled with a field that has its maximum at the center
of the object and drops off to zero at the object's surface. The
field strength of all those components are added together to form
the field of the blob. Now POV-Ray looks for points where this
field has a given value, the threshold value. All these points
form the surface of the blob object. Points with a greater field
value than the threshold value are considered to be inside while
points with a smaller field value are outside.

There's another, simpler way of looking at blobs. They can be
seen as a union of flexible components that attract or repel each
other to form a blobby organic looking shape. The components'
surfaces actually stretch out smoothly and connect as if they
were made of honey or something like that.

The syntax for blob is defined as follows:

BLOB:
  blob { BLOB_ITEM... [BLOB_MODIFIERS...]}
BLOB_ITEM:
  sphere{<Center>, Radius, [ strength ] Strength
  [COMPONENT_MODIFIER...] }   |
  cylinder{<End1>, <End2>, Radius, [ strength ] Strength
  [COMPONENT_MODIFIER...] }   |
  component Strength, Radius, <Center>   |
  threshold Amount
COMPONENT_MODIFIER:
  TEXTURE   |   PIGMENT   |   NORMAL   |   FINISH   |
  TRANSFORMATION
BLOB_MODIFIER:
  hierarchy [Boolean]   |
  sturm [Boolean]   |
  OBJECT_MODIFIER
The threshold keyword is followed by a float value which
determines the total field strength value that POV-Ray is looking
for. The default value if none is specified is threshold 1.0.  By
following the ray out into space and looking at how each blob
component affects the ray, POV-Ray will find the points in space
where the field strength is equal to the threshold value. The
following list shows some things you should know about the
threshold value.

1) The threshold value must be positive.
2) A component disappears if the threshold value is greater than
  its strength.
3) As the threshold value gets larger, the surface you see gets
  closer to the centers of the components.
4) As the threshold value gets smaller, the surface you see gets
  closer to the surface of the components.
Cylindrical components are specified by a cylinder statement.
The center of the end-caps of the cylinder is defined by the
vectors <End1> and <End2>.  Next is the float value of the Radius
followed by the float Strength.  These vectors and floats are
required and should be separated by commas.  The keyword strength
may optionally precede the strength value. The cylinder has
hemispherical caps at each end.

Spherical components are specified by a sphere statement.  The
location is defined by the vector <Center>.  Next is the float
value of the Radius followed by the float Strength.  These vector
and float values are required and should be separated by commas.
The keyword strength may optionally precede the strength value.

You usually will apply a single texture to the entire blob
object, and you typically use transformations to change its size,
location, and orientation.  However both the cylinder and sphere
statements may have individual texture, pigment, normal, finish,
and transformations applied to them.  You may not apply separate
interior statements to the components but you may specify one for
the entire blob.  Note that by unevenly scaling a spherical
component you can create ellipsoidal components. The tutorial
section on "Blob Object" illustrates individually textured blob
components and many other blob examples.

The component keyword is an obsolete method for specifying a
spherical component and is only used for compatibility with
earlier POV-Ray versions.  It may not have textures or
transformations individually applied to it.

The strength parameter of either type of blob component is a
float value specifying the field strength at the center of the
object. The strength may be positive or negative. A positive
value will make that component attract other components while a
negative value will make it repel other components. Components in
different, separate blob shapes do not affect each other.

You should keep the following things in mind.

1) The strength value may be positive or negative. Zero is a bad
  value, as the net result is that no field was added --- you
  might just as well have not used this component.
2) If strength is positive, then POV-Ray will add the component's
  field to the space around the center of the component. If this
  adds enough field strength to be greater than the threshold
  value you will see a surface.
3) If the strength value is negative, then POV-Ray will subtract
  the component's field from the space around the center of the
  component. This will only do something if there happen to be
  positive components nearby. What happens is that the surface
  around any nearby positive components will be dented away from
  the center of the negative component.
After all components and the optional threshold value have been
specified you may specify zero or more blob modifiers. A blob
modifier is any regular object modifier or the hierarchy or sturm
keywords.

The components of each blob object are internally bounded by a
spherical bounding hierarchy to speed up blob intersection tests
and other operations. By using the optional keyword hierarchy
followed by an optional boolean float value to turn it off or on.
By default it is on.

The calculations for blobs must be very accurate. If this shape
renders improperly you may add the keyword sturm followed by an
optional boolean float value to turn it off or on POV-Ray's
slower-yet-more-accurate Sturmian root solver. By default it is
off.

An example of a three component blob is:

 blob {
  threshold 0.6
  sphere { <.75, 0, 0>, 1, 1 }
  sphere { <-.375, .64952, 0>, 1, 1 }
  sphere { <-.375, -.64952, 0>, 1, 1 }
  scale 2
 }
If you have a single blob component then the surface you see will
just look like the object used, i.e. a sphere or a cylinder, with
the surface being somewhere inside the surface specified for the
component. The exact surface location can be determined from the
blob equation listed below (you will probably never need to know
this, blobs are more for visual appeal than for exact modeling).

For the more mathematically minded, here's the formula used
internally by POV-Ray to create blobs. You don't need to
understand this to use blobs. The density of the blob field of a
single component is:

                                
                                
where distance is the distance of a given point from the
spherical blob's center or cylinder blob's axis.  This formula
has the nice property that it is exactly equal to the strength
parameter at the center of the component and drops off to exactly
0 at a distance from the center of the component that is equal to
the radius value. The density formula for more than one blob
component is just the sum of the individual component densities.


4.5.1.2   Box
A simple box can be defined by listing two corners of the box
using the following syntax for a box statement:

BOX:
  box { <Corner_1>, <Corner_2> [OBJECT_MODIFIERS...]}
                                
                                
                     The geometry of a box.
                                
Where <Corner_1> and <Corner_2> are vectors defining the x, y, z
coordinates of the opposite corners of the box.

Note that all boxes are defined with their faces parallel to the
coordinate axes. They may later be rotated to any orientation
using the rotate keyword.

Boxes are calculated efficiently and make good bounding shapes
(if manually bounding seems to be necessary).


4.5.1.3   Cone
The cone statement creates a finite length cone or a frustum (a
cone with the point cut off).  The syntax is:

CONE:
  cone { <Base_Point>, Base_Radius, <Cap_Point>, Cap_Radius
     [ open ][OBJECT_MODIFIERS...]
  }
                                
                                
                     The geometry of a cone.
                                
Where <Base_Point> and < Cap_Point> are vectors defining the x,
y, z coordinates of the center of the cone's base and cap and
Base_Radius and Cap_Radius are float values for the corresponding
radii.

Normally the ends of a cone are closed by flat planes which are
parallel to each other and perpendicular to the length of the
cone. Adding the optional keyword open after Cap_Radius will
remove the end caps and results in a tapered hollow tube like a
megaphone or funnel.


4.5.1.4   Cylinder
The cylinder statement creates finite length cylinder with
parallel end caps The syntax is:

CYLINDER:
  cylinder{ <Base_Point>, <Cap_Point>, Radius
     [ open ][OBJECT_MODIFIERS...]
  }
                                
                                
                   The geometry of a cylinder.
                                
Where <Base_Point> and <Cap_Point> are vectors defining the x, y,
z coordinates of the cylinder's base and cap and Radius is a
float value for the radius.

Normally the ends of a cylinder are closed by flat planes which
are parallel to each other and perpendicular to the length of the
cylinder. Adding the optional keyword open after the radius will
remove the end caps and results in a hollow tube.


4.5.1.5   Height Field
Height fields are fast, efficient objects that are generally used
to create mountains or other raised surfaces out of hundreds of
triangles in a mesh. The height_field statement syntax is:

HEIGHT_FIELD:
  height_field{ HF_TYPE "filename" [HF_MODIFIER...] }
HF_TYPE:
  gif   |   tga   |   pot   |   png   |   pgm   |   ppm   |
  sys
HF_MODIFIER:
  hierarchy [Boolean]   |
  smooth [Boolean]   |
  water_level Level   |
  OBJECT_MODIFIER
A height field is essentially a one unit wide by one unit long
square with a mountainous surface on top. The height of the
mountain at each point is taken from the color number or palette
index of the pixels in a graphic image file. The maximum height
is one, which corresponds to the maximum possible color or
palette index value in the image file.

                                
                                
     The size and orientation of an un-scaled height field.
                                
The mesh of triangles corresponds directly to the pixels in the
image file. Each square formed by four neighboring pixels is
divided into two triangles. An image with a resolution of N*M
pixels has (N-1)*(M-1) squares that are divided into 2*(N-1)*(M-
1) triangles.

                                
                                
 Four pixels of an image and the resulting heights and triangles
                      in the height field.
                                
The resolution of the height field is influenced by two factors:
the resolution of the image and the resolution of the color/index
values. The size of the image determines the resolution in the x-
and z-direction. A larger image uses more triangles and looks
smoother. The resolution of the color/index value determines the
resolution along the y-axis. A height field made from an 8 bit
image can have 256 different height levels while one made from a
16 bit image can have up to 65536 different height levels. Thus
the second height field will look much smoother in the y-
direction if the height field is created appropriately.

The size/resolution of the image does not affect the size of the
height field. The un-scaled height field size will always be 1 by
1 by 1. Higher resolution image files will create smaller
triangles, not larger height fields.

There are six or possibly seven types of files which can define a
height field. The image file type used to create a height field
is specified by one of the keywords gif, tga, pot, png, pgm, ppm,
and possibly sys which is a system specific (e. g. Windows BMP or
Macintosh Pict) format file. The GIF, PNG, PGM, and possibly SYS
format files are the only ones that can be created using a
standard paint program. Though there are paint programs for
creating TGA image files they won't be of much use for creating
the special 16 bit TGA files used by POV-Ray (see below and
"HF_Gray_16" for more details).

In an image file like GIF that uses a color palette the color
number is the palette index at a given pixel. Use a paint program
to look at the palette of a GIF image. The first color is palette
index zero, the second is index one, the third is index two and
so on. The last palette entry is index 255. Portions of the image
that use low palette entries will result in lower parts of the
height field. Portions of the image that use higher palette
entries will result in higher parts of the height field.

Height fields created from GIF files can only have 256 different
height levels because the maximum number of colors in a GIF file
is 256.

The color of the palette entry does not affect the height of the
pixel. Color entry 0 could be red, blue, black or orange but the
height of any pixel that uses color entry 0 will always be 0.
Color entry 255 could be indigo, hot pink, white or sky blue but
the height of any pixel that uses color entry 255 will always be
1.

You can create height field GIF images with a paint program or a
fractal program like Fractint. You can usually get Fractint from
most of the same sources as POV-Ray.

A POT file is essentially a GIF file with a 16 bit palette. The
maximum number of colors in a POT file is 65536. This means a POT
height field can have up to 65536 possible height values. This
makes it possible to have much smoother height fields. Note that
the maximum height of the field is still 1 even though more
intermediate values are possible. At the time of this writing the
only program that created POT files was a freeware MS-Dos/Windows
program called Fractint. POT files generated with this fractal
program create fantastic landscapes.

The TGA and PPM file formats may be used as a storage device for
16 bit numbers rather than an image file. These formats use the
red and green bytes of each pixel to store the high and low bytes
of a height value. These files are as smooth as POT files but
they must be generated with special custom-made programs. Several
programs can create TGA heightfields in the format POV uses, such
as Gforge and Terrain Maker.

PNG format heightfields are usually stored in the form of a
grayscale image with black corresponding to lower and white to
higher parts of the height field. Because PNG files can store up
to 16 bits in grayscale images they will be as smooth as TGA and
PPM images. Since they are grayscale images you will be able to
view them with a regular image viewer. gforge can create 16-bit
heightfields in PNG format. Color PNG images will be used in the
same way as TGA and PPM images.

SYS format is a platform specific file format. See your platform
specific documentation for details.

In addition to all the usual object modifiers, there are three
additional height field modifiers available.

The optional water_level parameter may be added after the file
name. It consists of the keyword water_level followed by a float
value telling the program to ignore parts of the height field
below that value. The default value is zero and legal values are
between zero and one. For example water_level 0.5 tells POV-Ray
to only render the top half of the height field. The other half
is below the water and couldn't be seen anyway. Using water_level
renders faster than cutting off the lower part using CSG or
clipping. This term comes from the popular use of height fields
to render landscapes. A height field would be used to create
islands and another shape would be used to simulate water around
the islands. A large portion of the height field would be
obscured by the water so the water_level parameter was introduced
to allow the ray-tracer to ignore the unseen parts of the height
field. water_level is also used to cut away unwanted lower values
in a height field. For example if you have an image of a fractal
on a solid colored background, where the background color is
palette entry 0, you can remove the background in the height
field by specifying, water_level 0.001.

Normally height fields have a rough, jagged look because they are
made of lots of flat triangles. Adding the keyword smooth causes
POV-Ray to modify the surface normal vectors of the triangles in
such a way that the lighting and shading of the triangles will
give a smooth look. This may allow you to use a lower resolution
file for your height field than would otherwise be needed.
However, smooth triangles will take longer to render.  The
default value is off.  You may optionally use a boolean value
such as smooth on or smooth off.

In order to speed up the intersection tests an one-level bounding
hierarchy is available. By default it is always used but it can
be switched off using hierarchy off to improve the rendering
speed for small height fields (i.e. low resolution images).  You
may optionally use a boolean value such as hierarchy on or
hierarchy off.


4.5.1.6   Julia Fractal
A julia fractal object is a 3-D slice of a 4-D object created by
generalizing the process used to create the classic Julia sets.
You can make a wide variety of strange objects using the
julia_fractal statement including some that look like bizarre
blobs of twisted taffy. The julia_fractal syntax is:

JULIA_FRACTAL:
  julia_fractal{ <4D_Julia_Parameter> [JF_ITEM...]
  [OBJECT_MODIFIER...] }
JF_ITEM:
  ALGEBRA_TYPE   |   FUNCTION_TYPE   |
  max_iteration Count   |   precision Amt   |
  slice <4D_Normal>, Distance
ALGEBRA_TYPE:
  quaternion   |   hypercomplex
FUNCTION_TYPE:
  sqr   |   cube   |   exp   |   reciprocal   |   sin   |   asin
  |
  sinh   |   asinh   |   cos   |   acos   |   cosh   |   acosh
  |
  tan   |   atan   |   tanh   |   atanh   |   log   |   pwr(
  X_Val, Y_Val )
The required 4-D vector <4D_Julia_Parameter> is the classic Julia
parameter p in the iterated formula f(h) + p.

The julia fractal object is calculated by using an algorithm that
determines whether an arbitrary point h(0) in 4-D space is inside
or outside the object. The algorithm requires generating the
sequence of vectors h(0), h(1), ... by iterating the formula
h(n+1) = f(h(n)) + p (n = 0, 1, ..., max_iteration-1) where p is
the fixed 4-D vector parameter of the julia fractal and f() is
one of the functions sqr, cube, ... specified by the presence of
the corresponding keyword. The point h(0) that begins the
sequence is considered inside the julia fractal object if none of
the vectors in the sequence escapes a hypersphere of radius 4
about the origin before the iteration number reaches the integer
max_iteration value. As you increase max_iteration, some points
escape that did not previously escape, forming the julia fractal.
Depending on the <4D_Julia_Parameter>, the julia fractal object
is not necessarily connected; it may be scattered fractal dust.
Using a low max_iteration can fuse together the dust to make a
solid object. A high max_iteration is more accurate but slows
rendering. Even though it is not accurate, the solid shapes you
get with a low, max_iteration value can be quite interesting.  If
none is specified, the default is max_iteration 20.

Since the mathematical object described by this algorithm is four-
dimensional and POV-Ray renders three dimensional objects, there
must be a way to reduce the number of dimensions of the object
from four dimensions to three. This is accomplished by
intersecting the 4-D fractal with a 3-D "plane" defined by the
slice modifier and then projecting the intersection to 3-D space.
The keyword is followed by 4D vector and a float separated by a
comma.  The slice plane is the 3-D space that is perpendicular to
<4D_Normal> and is Distance units from the origin. Zero length
<4D_Normal> vectors or a  <4D_Normal> vector with a zero fourth
component are illegal.  If none is specified, the default is
slice <0,0,0,1>,0.

You can get a good feel for the four dimensional nature of a
julia fractal by using POV-Ray's animation feature to vary a
slice's Distance parameter. You can make the julia fractal appear
from nothing, grow, then shrink to nothing as Distancechanges,
much as the cross section of a 3-D object changes as it passes
through a plane.

The precision parameter is a tolerance used in the determination
of whether points are inside or outside the fractal object.
Larger values give more accurate results but slower rendering.
Use as low a value as you can without visibly degrading the
fractal object's appearance but note values less than 1.0 are
clipped at 1.0.  The default if none is specified is precision
20.

The presence of the keywords quaternion or hypercomplex determine
which 4-D algebra is used to calculate the fractal. The default
is quaternion. Both are 4-D generalizations of the complex
numbers but neither satisfies all the field properties (all the
properties of real and complex numbers that many of us slept
through in high school). Quaternions have non-commutative
multiplication and hypercomplex numbers can fail to have a
multiplicative inverse for some non-zero elements (it has been
proved that you cannot successfully generalize complex numbers to
four dimensions with all the field properties intact, so
something has to break). Both of these algebras were discovered
in the 19th century. Of the two, the quaternions are much better
known, but one can argue that hypercomplex numbers are more
useful for our purposes, since complex valued functions such as
sin, cos, etc. can be generalized to work for hypercomplex
numbers in a uniform way.

For the mathematically curious, the algebraic properties of these
two algebras can be derived from the multiplication properties of
the unit basis vectors 1 = <1,0,0,0>, i=< 0,1,0,0>, j=<0,0,1,0>
and k=< 0,0,0,1>. In both algebras 1 x = x 1 = x for any x (1 is
the multiplicative identity). The basis vectors 1 and i behave
exactly like the familiar complex numbers 1 and i in both
algebras.
Quaternion basis vector
multiplication rules:
ij = k           jk = i    ki = j
ji = -k          kj = -i   ik = -j
ii = jj = kk = - ijk = -1  
1

Hypercomplex basis vector
multiplication rules:
ij = k           jk = -i   ki = -j
ji = k           kj = -i   ik = -j
ii = jj = kk = - ijk = 1   
1
A distance estimation calculation is used with the quaternion
calculations to speed them up. The proof that this distance
estimation formula works does not generalize from two to four
dimensions but the formula seems to work well anyway, the absence
of proof notwithstanding!

The presence of one of the function keywords sqr, cube, etc.
determines which function is used for f(h) in the iteration
formula h(n+1) = f(h(n)) + p. The default is sqr. Most of the
function keywords work only if the hypercomplex keyword is
present. Only sqr and cube work with quaternion. The functions
are all familiar complex functions generalized to four
dimensions.


Function Keyword  Maps 4-D
value h to:
sqr       h*h
cube      h*h*h
exp       e raised to the
          power h
reciproca 1/h
l
sin       sine of h
asin      arcsine of h
sinh      hyperbolic sine of h
asinh     inverse hyperbolic
          sine of h
cos       cosine of h
acos      arccosine of h
cosh      hyperbolic cos of h
acosh     inverse hyperbolic
          cosine of h
tan       tangent of h
atan      arctangent of h
tanh      hyperbolic tangent
          of h
atanh     inverse hyperbolic
          tangent of h
log       natural logarithm of
          h
pwr(x,y)  h raised to the
          complex power x+iy
A simple example of a julia fractal object is:

 julia_fractal {
  <-0.083,0.0,-0.83,-0.025>
  quaternion
  sqr
  max_iteration 8
  precision 15
 }
The first renderings of julia fractals using quaternions were
done by Alan Norton and later by John Hart in the '80's. This new
POV-Ray implementation follows Fractint in pushing beyond what is
known in the literature by using hypercomplex numbers and by
generalizing the iterating formula to use a variety of
transcendental functions instead of just the classic Mandelbrot
z2 + c formula. With an extra two dimensions and eighteen
functions to work with, intrepid explorers should be able to
locate some new fractal beasts in hyperspace, so have at it!


4.5.1.7   Lathe
The lathe is an object generated from rotating a two-dimensional
curve about an axis. This curve is defined by a set of points
which are connected by linear, quadratic, cubic or bezier spline
curves. The syntax is:

LATHE:
  lathe {
       [SPLINE_TYPE]  Number_Of_Points, <Point_1> <Point_2>...
  <Point_n>
       [LATHE_MODIFIER...]
  }
SPLINE_TYPE:
  linear_spline   |   quadratic_spline   |   cubic_spline   |
  bezier_spline
LATHE_MODIFIER:
  sturm   |   OBJECT_MODIFIER
The first item is a keyword specifying the type of spline.  The
default if none is specified is linear_spline.  The required
integer value Number_Of_Points specifies how many two-dimensional
points are used to define the curve. The points follow and are
specified by 2-D vectors.  The curve is not automatically closed,
i.e. the first and last points are not automatically connected.
You will have to do this by your own if you want a closed curve.
The curve thus defined is rotated about the y-axis to form the
lathe object which is centered at the origin.

The following examples creates a simple lathe object that looks
like a thick cylinder, i.e. a cylinder with a thick wall:

 lathe {
  linear_spline
  5,
  <2, 0>, <3, 0>, <3, 5>, <2, 5>, <2, 0>
  pigment {Red}
 }
The cylinder has an inner radius of 2 and an outer radius of 3,
giving a wall width of 1. It's height is 5 and it's located at
the origin pointing up, i.e. the rotation axis is the y-axis.
Note that the first and last point are equal to get a closed
curve.

The splines that are used by the lathe and prism objects are a
little bit difficult to understand. The basic concept of splines
is to draw a curve through a given set of points in a determined
way. The default linear_spline is the simplest spline because
it's nothing more than connecting consecutive points with a line.
This means that the curve that is drawn between two points only
depends on those two points. No additional information is taken
into account. The other splines are different in that they do
take other points into account when connecting two points.  This
creates a smooth curve and, in the case of the cubic spline,
produces smoother transitions at each point.

The quadratic_spline keyword creates splines that are made of
quadratic curves. Each of them connects two consecutive points.
Since those two points (call them second and third point) are not
sufficient to describe a quadratic curve the predecessor of the
second point is taken into account when the curve is drawn.
Mathematically the relationship (their location on the 2-D plane)
between the first and second point determines the slope of the
curve at the second point. The slope of the curve at the third
point is out of control. Thus quadratic splines look much
smoother than linear splines but the transitions at each point
are generally not smooth because the slopes on both sides of the
point are different.

The cubic_spline keyword creates splines overcome the transition
problem of quadratic splines because they also take the fourth
point into account when drawing the curve between the second and
third point. The slope at the fourth point is under control now
and allows a smooth transition at each point. Thus cubic splines
produce the most flexible and smooth curves.

The bezier_spline is an alternate kind of cubic spline.  Points 1
and 4 specify the end points of a segment and points 2 and 3 are
control points which specify the slope at the endpoints. Points 2
and 3 do not actually lie on the spline.  They adjust the slope
of the spline.  If you draw an imaginary line between point 1 and
2, it represents the slope at point 1.  It is a line tangent to
the curve at point 1.  The greater the distance between 1 and 2,
the flatter the curve.  With a short tangent the spline can bend
more.  The same holds true for control point 3 and endpoint 4.
If you want the spline to be smooth between segments, point 3 and
4 on one segment and point 1 and 2 on the next segment must form
a straight line and point 4 of one segment must be the same as
point one on the next segment.

You should note that the number of spline segments, i. e. curves
between two points, depends on the spline type used. For linear
splines you get n-1 segments connecting the points P[i],
i=1,...,n. A quadratic spline gives you n-2 segments because the
last point is only used for determining the slope as explained
above (thus you'll need at least three points to define a
quadratic spline). The same holds for cubic splines where you get
n-3 segments with the first and last point used only for slope
calculations (thus needing at least four points).  The bezier
spline requires 4 points per segment.

If you want to get a closed quadratic and cubic spline with
smooth transitions at the end points you have to make sure that
in the cubic case P[n-1] = P[2] (to get a closed curve), P[n] =
P[3] and P[n-2] = P[1] (to smooth the transition). In the
quadratic case P[n-1] = P[1] (to close the curve) and P[n] =
P[2].

The sturm keyword can be used to specify that the slower but more
accurate Sturmian root solver should be used.  Use it with the
quadratic spline lathe if the shape does not render properly.
Since a quadratic polynomial has to be solved for the linear
spline lathe the Sturmian root solver is not needed. In case of
cubic or bezier splines, the Sturmian root solver is always used
because a 6th order polynomial has to be solved.


4.5.1.8   Prism
The prism is an object generated specifying one or more two-
dimensional, closed curves in the x-z plane and sweeping them
along y axis. These curves are defined by a set of points which
are connected by linear, quadratic, cubic or bezier splines.

The syntax for the prism is:

PRISM:
  prism { [PRISM_ITEMS...] Height_1, Height_2, Number_Of_Points,
       <Point_1>, <Point_2>, ... <Point_n>
       [ open ]
       [PRISM_MODIFIERS...]
  }
PRISM_ITEM:
  linear_spline   |   quadratic_spline   |   cubic_spline   |
  bezier_spline   |
  linear_sweep   |   conic_sweep
PRISM_MODIFIER:
  sturm   |   OBJECT_MODIFIER
The first items specify the spline type and sweep type.  The
defaults if none is specified is linear_spline and conic_sweep.
This is followed by two float values Height_1 and Height_2 which
are the y coordinates of the top and bottom of the prism. This is
followed by a float value specifying the number of 2-D points you
will use to define the prism. (This includes all control points
needed for quadratic, cubic and bezier splines). This is followed
by the specified number of 2-D vectors which define the shape in
the x-z plane.

The interpretation of the points depends on the spline type.  The
prism object allows you to use any number of sub-prisms inside
one prism statement (they are of the same spline and sweep type).
Wherever an even number of sub-prisms overlaps a hole appears.
Note you need not have multiple sub-prisms and they need not
overlap as these examples do.

In the linear_spline the first point specified is the start of
the first sub-prism.  The following points are connected by
straight lines.  If you specify a value identical to the first
point, this closes the sub-prism and next point starts a new one.
When you specify the value of that sub-prism's start, then it is
closed.  Each of the sub-prisms has to be closed by repeating the
first point of a sub-prism at the end of the sub-prism's point
sequence. In this example, there are two rectangular sub-prisms
nested inside each other to create a frame.

 prism {
  linear_spline
  0, 1, 10,
  <0,0>, <6,0>, <6,8>, <0,8>, <0,0>,  //outer rim
  <1,1>, <5,1>, <5,7>, <1,7>, <1,1>   //inner rim
 }
The last sub-prism of a linear spline prism is automatically
closed - just like the last sub-polygon in the polygon statement
- if the first and last point of the sub-polygon's point sequence
are not the same. This make it very easy to convert between
polygons and prisms. Quadratic, cubic and bezier splines are
never automatically closed.

In the quadratic_spline, each sub-prism needs an additional
control point at the beginning of each sub-prisms' point sequence
to determine the slope at the start of the curve. The first point
specified is the control point which is not actually part of the
spline.  The second point is the start of the spline.  The sub-
prism ends when this second point is duplicated.  The next point
is the control point of the next sub-prism.  The point after that
is the first point of the second sub-prism.  Here is an example:

 prism {
  quadratic_spline
  0, 1, 12,
  <1,-1>, <0,0>, <6,0>, <6,8>, <0,8>, <0,0>,  //outer rim
      //Control is <1,-1> and <0,0> is first & last point
  <2,0>, <1,1>, <5,1>, <5,7>, <1,7>, <1,1>   //inner rim
      //Control is <2,0> and <1,1> is first & last point
 }
In the cubic_spline, each sub-prism needs two additional control
points -- one at the beginning of each sub-prisms' point sequence
to determine the slope at the start of the curve and one at the
end. The first point specified is the control point which is not
actually part of the spline.  The second point is the start of
the spline.  The sub-prism ends when this second point is
duplicated.  The next point is the control point of the end of
the first sub-prism.  Next is the beginning control point of the
next sub-prism.  The point after that is the first point of the
second sub-prism.  Here is an example:

 prism {
  cubic_spline
  0, 1, 14,
  <1,-1>, <0,0>, <6,0>, <6,8>, <0,8>, <0,0>, <-1,1>, //outer rim
  //First control is <1,-1> and <0,0> is first & last point
  // Last control of first spline is <-1,1>
  <2,0>, <1,1>, <5,1>, <5,7>, <1,7>, <1,1>, <0,2> //inner rim
  //First control is <2,0> and <1,1> is first & last point
  // Last control of first spline is <0,2>
 }
The bezier_spline is an alternate kind of cubic spline.  Points 1
and 4 specify the end points of a segment and points 2 and 3 are
control points which specify the slope at the endpoints. Points 2
and 3 do not actually lie on the spline.  They adjust the slope
of the spline.  If you draw an imaginary line between point 1 and
2, it represents the slope at point 1.  It is a line tangent to
the curve at point 1.  The greater the distance between 1 and 2,
the flatter the curve.  With a short tangent the spline can bend
more.  The same holds true for control point 3 and endpoint 4.
If you want the spline to be smooth between segments, point 3 and
4 on one segment and point 1 and 2 on the next segment must form
a straight line and point 4 of one segment must be the same as
point one on the next segment.

By default linear sweeping is used to create the prism, i.e. the
prism's walls are perpendicular to the x-z-plane (the size of the
curve does not change during the sweep). You can also use
conic_sweep that leads to a prism with cone-like walls by scaling
the curve down during the sweep.

Like cylinders the prism is normally closed. You can remove the
caps on the prism by using the open keyword. If you do so you
shouldn't use it with CSG because the results may get wrong.

For an explanation of the spline concept read the description of
the "Lathe" object.  Also see the tutorials on "Lathe Object" and
"Prism Object".

The sturm keyword specifies the slower but more accurate Sturmian
root solver which may be used with the cubic or bezier spline
prisms if the shape does not render properly. The linear and
quadratic spline prisms do not need the Sturmian root solver.


4.5.1.9   Sphere
The syntax of the sphere object is:

SPHERE:
  sphere { <Center>, Radius [OBJECT_MODIFIERS...] }
                                
                                
                    The geometry of a sphere.
                                
Where <Center> is a vector specifying the x, y, z coordinates of
the center of the sphere and Radius is a float value specifying
the radius. Spheres may be scaled unevenly giving an ellipsoid
shape.

Because spheres are highly optimized they make good bounding
shapes (if manual bounding seems to be necessary).


4.5.1.10  Superquadric Ellipsoid
The superellipsoid object creates a shape known as a superquadric
ellipsoid object.  It is an extension of the quadric ellipsoid.
It can be used to create boxes and cylinders with round edges and
other interesting shapes. Mathematically it is given by the
equation:

                                
                                
The values of e and n, called the east-west and north-south
exponent, determine the shape of the superquadric ellipsoid. Both
have to be greater than zero. The sphere is given by e = 1 and n
= 1.

The syntax of the superquadric ellipsoid is:

SUPERELLIPSOID:
  superellipsoid{ <Value_E, Value_N>  [OBJECT_MODIFIERS...] }
The 2-D vector specifies the e and n values in the equation
above.  The object sits at the origin and occupies a space about
the size of a box{<-1,-1,-1>,<1,1,1>}.

Two useful objects are the rounded box and the rounded cylinder.
These are declared in the following way.

 #declare Rounded_Box = superellipsoid { <Round, Round> }
 #declare Rounded_Cylinder = superellipsoid { <1, Round> }
The roundedness value Round determines the roundedness of the
edges and has to be greater than zero and smaller than one. The
smaller you choose the values, the smaller and sharper the edges
will get.

Very small values of e and n might cause problems with the root
solver (the Sturmian root solver cannot be used).


4.5.1.11  Surface of Revolution
The sor object is a surface of revolution generated by rotating
the graph of a function about the y-axis. This function describes
the dependence of the radius from the position on the rotation
axis. The syntax is:

SOR:
  sor { Number_Of_Points,
       <Point_1>, <Point_2>, ... <Point_n>
       [ open ]
       [SOR_MODIFIERS...]
   }
SOR_MODIFIER:
  sturm   |   OBJECT_MODIFIER
The float value Number_Of_Points specifies the number of 2-D
vectors which follow. The points <Point_1> through <Point_n> are
two-dimensional vectors consisting of the radius and the
corresponding height, i.e. the position on the rotation axis.
These points are smoothly connected (the curve is passing through
the specified points) and rotated about the y-axis to form the
SOR object. The first and last points are only used to determine
the slopes of the function at the start and end point. They do
not actually lie on the curve.  The function used for the SOR
object is similar to the splines used for the lathe object. The
difference is that the SOR object is less flexible because it
underlies the restrictions of any mathematical function, i.e. to
any given point y on the rotation axis belongs at most one
function value, i.e. one radius value. You can't rotate closed
curves with the SOR object.

The optional keyword open allows you to remove the caps on the
SOR object. If you do this you shouldn't use it with CSG anymore
because the results may be wrong.

The SOR object is useful for creating bottles, vases, and things
like that. A simple vase could look like this:

 #declare Vase = sor {
  7,
  <0.000000, 0.000000>
  <0.118143, 0.000000>
  <0.620253, 0.540084>
  <0.210970, 0.827004>
  <0.194093, 0.962025>
  <0.286920, 1.000000>
  <0.468354, 1.033755>
  open
 }
One might ask why there is any need for a SOR object if there is
already a lathe object which is much more flexible. The reason is
quite simple. The intersection test with a SOR object involves
solving a cubic polynomial while the test with a lathe object
requires to solve of a 6th order polynomial (you need a cubic
spline for the same smoothness). Since most SOR and lathe objects
will have several segments this will make a great difference in
speed. The roots of the 3rd order polynomial will also be more
accurate and easier to find.

The sturm keyword may be added to specify the slower but more
accurate Sturmian root solver.  It may be used with the surface
of revolution object if the shape does not render properly.

The following explanations are for the mathematically interested
reader who wants to know how the surface of revolution is
calculated. Though it is not necessary to read on it might help
in understanding the SOR object.

The function that is rotated about the y-axis to get the final
SOR object is given by

                                
                                
with radius r and height h. Since this is a cubic function in h
it has enough flexibility to allow smooth curves.

The curve itself is defined by a set of n points P(i), i=0...n-1,
which are interpolated using one function for every segment of
the curve. A segment j, j=1...n-3, goes from point P(j) to point
P(j+1) and uses points P(j-1) and P(j+2) to determine the slopes
at the endpoints. If there are n points we will have n-3
segments. This means that we need at least four points to get a
proper curve.

The coefficients A(j), B(j), C(j) and D(j) are calculated for
every segment using the equation

                                
                                
where r(j) is the radius and h(j) is the height of point P(j).

The figure below shows the configuration of the points P(i), the
location of segment j, and the curve that is defined by this
segment.

                                
                                
 Segment j of n-3 segments in a point configuration of n points.
                                
   The points describe the curve of a surface of revolution.'
                                

4.5.1.12  Text
A text object creates 3-D text as an extruded block letter.
Currently only TrueType fonts are supported but the syntax allows
for other font types to be added in the future. The syntax is:

TEXT_OBECT:
  text { ttf "fontname.ttf" "String_of_Text" Thickness, <Offset>
  [OBJECT_MODIFIERS...] }
Where fontname.ttf is the name of the TrueType font file.  It is
a quoted string literal or string expression. The string
expression which follows is the actual text of the string object.
It too may be a quoted string literal or string expression. See
section "Strings" for more on string expressions.

The text will start with the origin at the lower left, front of
the first character and will extend in the +x-direction. The
baseline of the text follows the x-axis and decenders drop into
the -y-direction.  The front of the character sits in the x-y-
plane and the text is extruded in the +z-direction. The front-to-
back thickness is specified by the required value Thickness.

Characters are generally sized so that 1 unit of vertical spacing
is correct. The characters are about 0.5 to 0.75 units tall.

The horizontal spacing is handled by POV-Ray internally including
any kerning information stored in the font. The required vector
<Offset> defines any extra translation between each character.
Normally you should specify a zero for this value. Specifying
0.1*x would put additional 0.1 units of space between each
character.  Here is an example:

  text { ttf "timrom.ttf" "POV-Ray 3.1" 1, 0
    pigment { Red }
  }
Only printable characters are allowed in text objects. Characters
such as return, line feed, tabs, backspace etc. are not
supported.


4.5.1.13  Torus
A torus is a 4th order quartic polynomial shape that looks like a
donut or inner tube. Because this shape is so useful and quartics
are difficult to define, POV-Ray lets you take a short-cut and
define a torus by:

TORUS:
  torus { Major, Minor [TORUS_MODIFIER...] }
TORUS_MODIFIER:
  sturm   |   OBJECT_MODIFIER
where Major is a float value giving the major radius and Minor is
a float specifying the minor radius. The major radius extends
from the center of the hole to the mid-line of the rim while the
minor radius is the radius of the cross-section of the rim. The
torus is centered at the origin and lies in the x-z-plane with
the y-axis sticking through the hole.

                                
                                
               Major and minor radius of a torus.
                                
The torus is internally bounded by two cylinders and two rings
forming a thick cylinder. With this bounding cylinder the
performance of the torus intersection test is vastly increased.
The test for a valid torus intersection, i.e. solving a 4th order
polynomial, is only performed if the bounding cylinder is hit.
Thus a lot of slow root solving calculations are avoided.

Calculations for all higher order polynomials must be very
accurate. If the torus renders improperly you may add the keyword
sturm to use POV-Ray's slower-yet-more-accurate Sturmian root
solver.


4.5.2     Finite Patch Primitives
There are six totally thin, finite objects which have no well-
defined inside. They are bicubic patch, disc, smooth triangle,
triangle, polygon and mesh. They may be combined in CSG union but
cannot be use in other types of CSG (or inside a clipped_by
statement). Because these types are finite POV-Ray can use
automatic bounding on them to speed up rendering time. As with
all shapes they can be translated, rotated and scaled.


4.5.2.1   Bicubic Patch
A bicubic_patch is a 3D curved surface created from a mesh of
triangles. POV-Ray supports a type of bicubic patch called a
Bezier patch. A bicubic patch is defined as follows:

BICUBIC_PATCH:
  bicubic_patch {
       PATCH_ITEMS...
       <Point_1>,<Point_2>,<Point_3>,<Point_4>,
       <Point_5>,<Point_6>,<Point_7>,<Point_8>,
       <Point_9>,<Point_10>,<Point_11>,<Point_12>,
       <Point_13>,<Point_14>,<Point_15>,<Point_16>
       [OBJECT_MODIFIERS...]
  }
PATCH_ITEMS:
  type Patch_Type   |   u_steps Num_U_Steps   |   v_steps
  Num_V_Steps   |   flatness Flatness
The keyword type is followed by a float Patch_Type which
currently must be either 0 or 1. For type 0 only the control
points are retained within POV-Ray. This means that a minimal
amount of memory is needed but POV-Ray will need to perform many
extra calculations when trying to render the patch. Type 1
preprocesses the patch into many subpatches. This results in a
significant speedup in rendering at the cost of memory.

The four parameters type, flatness, u_steps and v_steps may
appear in any order. All but flatness are required.  They are
followed by 16 vectors (4 rows of 4) that define the x, y, z
coordinates of the 16 control points which define the patch. The
patch touches the four corner points <Point_1>, <Point_4>,
<Point_13> and <Point_16> while the other 12 points pull and
stretch the patch into shape. The Bezier surface is enclosed by
the convex hull formed by the 16 control points, this is known as
the convex hull property.

The keywords u_steps and v_steps are each followed by integer
values which tell how many rows and columns of triangles are the
minimum to use to create the surface. The maximum number of
individual pieces of the patch that are tested by POV-Ray can be
calculated from the following: pieces = 2^u_steps * 2^v_steps.

This means that you really should keep u_steps and v_steps under
4. Most patches look just fine with u_steps 3 and v_steps 3,
which translates to 64 subpatches (128 smooth triangles).

As POV-Ray processes the Bezier patch it makes a test of the
current piece of the patch to see if it is flat enough to just
pretend it is a rectangle. The statement that controls this test
is specified with the flatness keyword followed by a float.
Typical flatness values range from 0 to 1 (the lower the slower).
The default if none is specified is 0.0.

If the value for flatness is 0 POV-Ray will always subdivide the
patch to the extend specified by u_steps and v_steps. If flatness
is greater than 0 then every time the patch is split, POV-Ray
will check to see if there is any need to split further.

There are both advantages and disadvantages to using a non-zero
flatness. The advantages include:

  -  If the patch isn't very curved, then this will be detected
  and POV-Ray won't waste a lot of time looking at the wrong
  pieces.
  -  If the patch is only highly curved in a couple of places,
  POV-Ray will keep subdividing there and concentrate it's
  efforts on the hard part.
The biggest disadvantage is that if POV-Ray stops subdividing at
a particular level on one part of the patch and at a different
level on an adjacent part of the patch there is the potential for
cracking. This is typically visible as spots within the patch
where you can see through. How bad this appears depends very
highly on the angle at which you are viewing the patch.

Like triangles, the bicubic patch is not meant to be generated by
hand. These shapes should be created by a special utility. You
may be able to acquire utilities to generate these shapes from
the same source from which you obtained POV-Ray.  Here is an
example:

  bicubic_patch {
    type 0
    flatness 0.01
    u_steps 4
    v_steps 4
    <0, 0, 2>, <1, 0, 0>, <2, 0, 0>, <3, 0,-2>,
    <0, 1  0>, <1, 1, 0>, <2, 1, 0>, <3, 1, 0>,
    <0, 2, 0>, <1, 2, 0>, <2, 2, 0>, <3, 2, 0>,
    <0, 3, 2>, <1, 3, 0>, <2, 3, 0>, <3, 3, -2>
  }
The triangles in a POV-Ray bicubic_patch are automatically
smoothed using normal interpolation but it is up to the user (or
the user's utility program) to create control points which
smoothly stitch together groups of patches.


4.5.2.2   Disc
Another flat, finite object available with POV-Ray is the disc.
The disc is infinitely thin, it has no thickness. If you want a
disc with true thickness you should use a very short cylinder. A
disc shape may be defined by:

DISC:
  disc { <Center>, <Normal>, Radius [, Hole_Radius]
  [OBJECT_MODIFIERS...] }
The vector <Center> defines the x, y, z coordinates of the center
of the disc. The <Normal> vector describes its orientation by
describing its surface normal vector. This is followed by a float
specifying the Radius. This may be optionally followed by another
float specifying the radius of a hole to be cut from the center
of the disc.


4.5.2.3   Mesh
The mesh object can be used to efficiently store large numbers of
triangles. Its syntax is:

MESH:
  mesh { MESH_TRIANGLE... [MESH_MODIFIER...] }
MESH_TRIANGLE:
  triangle { <Corner_1>, <Corner_2>, <Corner_3> [MESH_TEXTURE] }
  |
  smooth_triangle {
       <Corner_1>, <Normal_1>,
       <Corner_2>, <Normal_2>,
       <Corner_3>, <Normal_3>
       [MESH_TEXTURE]
  }
MESH_TEXTURE:
  texture { TEXTURE_IDENTIFIER }
MESH_MODIFIER:
  hierarchy [ Boolean ]   |   OBJECT_MODIFIER
Any number of triangle and/or smooth_triangle statements can be
used and each of those triangles can be individually textured by
assigning a texture identifier to it. The texture has to be
declared before the mesh is parsed. It is not possible to use
texture definitions inside the triangle or smooth triangle
statements. This is a restriction that is necessary for an
efficient storage of the assigned textures.  See "Triangle and
Smooth Triangle" for more information on triangles.

The mesh's components are internally bounded by a bounding box
hierarchy to speed up intersection testing. The bounding
hierarchy can be turned off with the hierarchy off keyword. This
should only be done if memory is short or the mesh consists of
only a few triangles.  The default is hierarchy on.

Copies of a mesh object refer to the same triangle data and thus
consume very little memory. You can easily trace hundred copies
of an 10000 triangle mesh without running out of memory (assuming
the first mesh fits into memory).

The mesh object has two advantages over a union of triangles: it
needs less memory and it is transformed faster. The memory
requirements are reduced by efficiently storing the triangles
vertices and normals. The parsing time for transformed meshes is
reduced because only the mesh object has to be transformed and
not every single triangle as it is necessary for unions.

The mesh object can currently only include triangle and smooth
triangle components. That restriction may change, allowing
polygonal components, at some point in the future.


4.5.2.4   Polygon
The polygon object is useful for creating rectangles, squares and
other planar shapes with more than three edges. Their syntax is:

POLYGON:
  polygon { Number_Of_Points, <Point_1> <Point_2>... <Point_n>
  [OBJECT_MODIFIER...]}
The float Number_Of_Points tells how many points are used to
define the polygon.  The points <Point_1> through <Point_n>
describe the polygon or polygons.  A polygon can contain any
number of sub-polygons, either overlapping or not. In places
where an even number of polygons overlaps a hole appears. When
you repeat the first point of a sub-polygon, it closes it and
starts a new sub-polygon's point sequence. This means that all
points of a sub-polygon are different.

If the last sub-polygon is not closed a warning is issued and the
program automatically closes the polygon. This is useful because
polygons imported from other programs may not be closed, i.e.
their first and last point are not the same.

All points of a polygon are three-dimensional vectors that have
to lay on the same plane. If this is not the case an error
occurs. It is common to use two-dimensional vectors to describe
the polygon. POV-Ray assumes that the z value is zero in this
case.

A square polygon that matches the default planar image map is
simply:

  polygon {
    4,
    <0, 0>, <0, 1>, <1, 1>, <1, 0>
    texture {
      finish { ambient 1 diffuse 0 }
      pigment { image_map { gif "test.gif"  } }
    }
    //scale and rotate as needed here
  }
The sub-polygon feature can be used to generate complex shapes
like the letter "P", where a hole is cut into another polygon:

  #declare P = polygon {
    12,
    <0, 0>, <0, 6>, <4, 6>, <4, 3>, <1, 3>, <1, 0>, <0, 0>,
    <1, 4>, <1, 5>, <3, 5>, <3, 4>, <1, 4>
  }
The first sub-polygon (on the first line) describes the outer
shape of the letter "P". The second sub-polygon (on the second
line) describes the rectangular hole that is cut in the top of
the letter "P". Both rectangles are closed, i.e. their first and
last points are the same.

The feature of cutting holes into a polygon is based on the
polygon inside/outside test used. A point is considered to be
inside a polygon if a straight line drawn from this point in an
arbitrary direction crosses an odd number of edges (this is known
as Jordan's curve theorem).

Another very complex example showing one large triangle with
three small holes and three separate, small triangles is given
below:

  polygon {
    28,
    <0, 0> <1, 0> <0, 1> <0, 0>          // large outer triangle
    <.3, .7> <.4, .7> <.3, .8> <.3, .7>  // small outer triangle
#1
    <.5, .5> <.6, .5> <.5, .6> <.5, .5>  // small outer triangle
#2
    <.7, .3> <.8, .3> <.7, .4> <.7, .3>  // small outer triangle
#3
    <.5, .2> <.6, .2> <.5, .3> <.5, .2>  // inner triangle #1
    <.2, .5> <.3, .5> <.2, .6> <.2, .5>  // inner triangle #2
    <.1, .1> <.2, .1> <.1, .2> <.1, .1>  // inner triangle #3
  }

4.5.2.5   Triangle and Smooth Triangle
The triangle primitive is available in order to make more complex
objects than the built-in shapes will permit. Triangles are
usually not created by hand but are converted from other files or
generated by utilities. A triangle is defined by

TRIANGLE:
  triangle { <Corner_1>, <Corner_2>, <Corner_3>
  [OBJECT_MODIFIER...] }
where <Corner_n> is a vector defining the x, y, z coordinates of
each corner of the triangle.

Because triangles are perfectly flat surfaces it would require
extremely large numbers of very small triangles to approximate a
smooth, curved surface. However much of our perception of smooth
surfaces is dependent upon the way light and shading is done. By
artificially modifying the surface normals we can simulate a
smooth surface and hide the sharp-edged seams between individual
triangles.

The smooth_triangle primitive is used for just such purposes. The
smooth triangles use a formula called Phong normal interpolation
to calculate the surface normal for any point on the triangle
based on normal vectors which you define for the three corners.
This makes the triangle appear to be a smooth curved surface. A
smooth triangle is defined by

SMOOTH_TRIANGLE:
  smooth_triangle {
       <Corner_1>, <Normal_1>,
       <Corner_2>, <Normal_2>,
       <Corner_3>, <Normal_3>
       [OBJECT_MODIFIER...]
  }
where the corners are defined as in regular triangles and
<Normal_n> is a vector describing the direction of the surface
normal at each corner.

These normal vectors are prohibitively difficult to compute by
hand. Therefore smooth triangles are almost always generated by
utility programs. To achieve smooth results, any triangles which
share a common vertex should have the same normal vector at that
vertex. Generally the smoothed normal should be the average of
all the actual normals of the triangles which share that point.

The mesh object is a way to combine many triangle and
smooth_triangle objects together in a very efficient way.  See
"Mesh" for details.


4.5.3     Infinite Solid Primitives
There are five polynomial primitive shapes that are possibly
infinite and do not respond to automatic bounding. They are
plane, cubic, poly, quadric and quartic. They do have a well
defined inside and may be used in CSG and inside a clipped_by
statement. As with all shapes they can be translated, rotated and
scaled.


4.5.3.1   Plane
The plane primitive is a simple way to define an infinite flat
surface. The plane is specified as follows:

PLANE:
  plane { <Normal>, Distance [OBJECT_MODIFIERS...] }
The <Normal> vector defines the surface normal of the plane. A
surface normal is a vector which points up from the surface at a
90 degree angle. This is followed by a float value that gives the
distance along the normal that the plane is from the origin (that
is only true if the normal vector has unit length; see below).
For example:

  plane { <0, 1, 0>, 4 }
This is a plane where straight up is defined in the positive y-
direction. The plane is 4 units in that direction away from the
origin. Because most planes are defined with surface normals in
the direction of an axis you will often see planes defined using
the x, y or z built-in vector identifiers. The example above
could be specified as:

  plane { y, 4 }
The plane extends infinitely in the x- and z-directions. It
effectively divides the world into two pieces. By definition the
normal vector points to the outside of the plane while any points
away from the vector are defined as inside. This inside/outside
distinction is important when using planes in CSG and clipped_by.
It is also important when using fog or atmospheric media.  If you
place a camera on the "inside" half of the world, then the fog or
media will not appear.  Such issues arise in any solid object but
it is more common with planes.  Users typically know when they've
accidentally placed a camera inside a sphere or box but "inside a
plane" is an unusual concept.  You can reverse the inside/outside
properties of an object by adding the object modifier inverse.
See "Inverse" and "Empty and Solid Objects" for details.

A plane is called a polynomial shape because it is defined by a
first order polynomial equation. Given a plane:

  plane { <A, B, C>, D }
it can be represented by the equation  A*x + B*y + C*z -
D*sqrt(A2 + B2 + C2) = 0.

Therefore our example plane{y,4} is actually the polynomial
equation y=4. You can think of this as a set of all x, y, z
points where all have y values equal to 4, regardless of the x or
z values.

This equation is a first order polynomial because each term
contains only single powers of x, y or z. A second order equation
has terms like x2, y2, z2, xy, xz and yz. Another name for a 2nd
order equation is a quadric equation. Third order polys are
called cubics. A 4th order equation is a quartic. Such shapes are
described in the sections below.


4.5.3.2   Poly, Cubic and Quartic
Higher order polynomial surfaces may be defined by the use of a
poly shape. The syntax is

POLY:
  poly { Order, <A1, A2, A3,... An> [POLY_MODIFIERS...] }
POLY_MODIFIERS:
  sturm   |   OBJECT_MODIFIER
where Order is an integer number from 2 to 7 inclusively that
specifies the order of the equation. A1, A2, ... An are float
values for the coefficients of the equation. There are m such
terms where

  n = ((Order+1)*(Order+2)*(Order+3))/6.

The cubic object is an alternate way to specify 3rd order polys.
Its syntax is:

CUBIC:
  cubic { <A1, A2, A3,... A20> [POLY_MODIFIERS...] }
Also 4th order equations may be specified with the quartic
object.  Its syntax is:

QUARTIC:
  quartic { <A1, A2, A3,... A35> [POLY_MODIFIERS...] }
The following table shows which polynomial terms correspond to
which x,y,z factors.  Remember cubic is actually a 3rd order
polynomial and quartic is 4th order.
   2n  3r 4th 5th 6th  7th         5t  6th  7th         6t 7t
  d   d                         h                 h  h
A1 x2  x3 x4  x5  x6   x7       A4 y3  xy3  x2y3    A8  z3 xz
                             1                 1      3
A2 xy  x2 x3y x4y x5y  x6y      A4 y2  xy2  x2y2    A8  z2 xz
      y                      2  z3  z3   z3      2      2
A3 xz  x2 x3z x4z x5z  x5z      A4 y2  xy2  x2y2    A8  z  xz
      z                      3  z2  z2   z2      3
A4 x   x2 x3  x4  x5   x5       A4 y2  xy2  x2y2    A8  1  x
                             4  z   z    z       4
A5 y2  xy x2y x3y x4y2 x5y2     A4 y2  xy2  x2y2    A8     y7
      2  2   2               5                 5
A6 yz  xy x2y x3y x4yz x5yz     A4 yz  xyz  x2yz    A8     y6
      z  z   z               6  4   4    4       6      z
A7 y   xy x2y x3y x4y  x5y      A4 yz  xyz  x2yz    A8     y6
                             7  3   3    3       7
A8 z2  xz x2z x3z x4z2 x5z2     A4 yz  xyz  x2yz    A8     y5
      2  2   2               8  2   2    2       8      z2
A9 z   xz x2z x3z x4z  x5z      A4 yz  xyz  x2yz    A8     y5
                             9                 9      z
A1 1   x  x2  x3  x4   x5       A5 y   xy   x2y     A9     y5
0                            0                 0
A1     y3 xy3 x2y x3y3 x4y3     A5 z5  xz5  x2z5    A9     y4
1            3               1                 1      z3
A1     y2 xy2 x2y x3y2 x4y2     A5 z4  xz4  x2z4    A9     y4
2     z  z   2z  z    z       2                 2      z2
A1     y2 xy2 x2y x3y2 x4y2     A5 z3  xz3  x2z3    A9     y4
3            2               3                 3      z
A1     yz xyz x2y x3yz x4yz     A5 z2  xz2  x2z2    A9     y4
4     2  2   z2  2    2       4                 4
A1     yz xyz x2y x3yz x4yz     A5 z   xz   x2z     A9     y3
5            z               5                 5      z4
A1     y  xy  x2y x3y  x4y      A5 1   x    x2      A9     y3
6                            6                 6      z3
A1     z3 xz3 x2z x3z3 x4z3     A5     y6   xy6     A9     y3
7            3               7                 7      z2
A1     z2 xz2 x2z x3z2 x4z2     A5     y5z  xy5z    A9     y3
8            2               8                 8      z
A1     z  xz  x2z x3z  x4z      A5     y5   xy5     A9     y3
9                            9                 9
A2     1  x   x2  x3   x4       A6     y4z  xy4z    A1     y2
0                            0      2    2       00     z5
A2        y4  xy4 x2y4 x3y4     A6     y4z  xy4z    A1     y2
1                            1                 01     z4
A2        y3z xy3 x2y3 x3y3     A6     y4   xy4     A1     y2
2            z   z    z       2                 02     z3
A2        y3  xy3 x2y3 x3y3     A6     y3z  xy3z    A1     y2
3                            3      3    3       03     z2
A2        y2z xy2 x2y2 x3y2     A6     y3z  xy3z    A1     y2
4        2   z2  z2   z2      4      2    2       04     z
A2        y2z xy2 x2y2 x3y2     A6     y3z  xy3z    A1     y2
5            z   z    z       5                 05
A2        y2  xy2 x2y2 x3y2     A6     y3   xy3     A1     yz
6                            6                 06     6
A2        yz3 xyz x2yz x3yz     A6     y2z  xy2z    A1     yz
7            3   3    3       7      4    4       07     5
A2        yz2 xyz x2yz x3yz     A6     y2z  xy2z    A1     yz
8            2   2    2       8      3    3       08     4
A2        yz  xyz x2yz x3yz     A6     y2z  xy2z    A1     yz
9                            9      2    2       09     3
A3        y   xy  x2y  x3y      A7     y2z  xy2z    A1     yz
0                            0                 10     2
A3        z4  xz4 x2z4 x3z4     A7     y2   xy2     A1     yz
1                            1                 11
A3        z3  xz3 x2z3 x3z3     A7     yz5  xyz5    A1     y
2                            2                 12
A3        z2  xz2 x2z2 x3z2     A7     yz4  xyz4    A1     z7
3                            3                 13
A3        z   xz  x2z  x3z      A7     yz3  xyz3    A1     z6
4                            4                 14
A3        1   x   x2   x3       A7     yz2  xyz2    A1     z5
5                            5                 15
A3            y5  xy5  x2y5     A7     yz   xyz     A1     z4
6                            6                 16
A3            y4z xy4z x2y4     A7     y    xy      A1     z3
7                     z       7                 17
A3            y4  xy4  x2y4     A7     z6   xz6     A1     z2
8                            8                 18
A3            y3z xy3z x2y3     A7     z5   xz5     A1     z
9            2   2    z2      9                 19
A4            y3z xy3z x2y3     A8     z4   xz4     A1     1
0                     z       0                 20
Polynomial shapes can be used to describe a large class of shapes
including the torus, the lemniscate, etc. For example, to declare
a quartic surface requires that each of the coefficients (A1 ...
A35) be placed in order into a single long vector of 35 terms.

As an example let's define a torus the hard way. A Torus can be
represented by the equation:

 x4 + y4 + z4 + 2 x2 y2 + 2 x2 z2 + 2 y2 z2 -
 2 (r_02 + r_12) x2 + 2 (r_02 - r_12) y2 -
 2 (r_02 + r_12) z2 + (r_02 - r_12)2 = 0
Where r_0 is the major radius of the torus, the distance from the
hole of the donut to the middle of the ring of the donut, and r_1
is the minor radius of the torus, the distance from the middle of
the ring of the donut to the outer surface. The following object
declaration is for a torus having major radius 6.3 minor radius
3.5 (Making the maximum width just under 20).

  // Torus having major radius sqrt(40), minor radius sqrt(12)
  quartic {
    < 1,   0,   0,   0,   2,   0,   0,   2,   0,
   -104,   0,   0,   0,   0,   0,   0,   0,   0,
      0,   0,   1,   0,   0,   2,   0,  56,   0,
      0,   0,   0,   1,   0, -104,  0, 784 >
    sturm
  }
Poly, cubic and quartics are just like quadrics in that you don't
have to understand what one is to use one. The file shapesq.inc
has plenty of pre-defined quartics for you to play with.

Polys use highly complex computations and will not always render
perfectly. If the surface is not smooth, has dropouts, or extra
random pixels, try using the optional keyword sturm in the
definition. This will cause a slower but more accurate
calculation method to be used. Usually, but not always, this will
solve the problem. If sturm doesn't work, try rotating or
translating the shape by some small amount.

There are really so many different polynomial shapes, we can't
even begin to list or describe them all. If you are interested
and mathematically inclined, an excellent reference book for
curves and surfaces where you'll find more polynomial shape
formulas is:

  "The CRC Handbook of Mathematical Curves and Surfaces"
  David von Seggern
  CRC Press, 1990

4.5.3.3   Quadric
The quadric object can produce shapes like paraboloids (dish
shapes) and hyperboloids (saddle or hourglass shapes). It can
also produce ellipsoids, spheres, cones, and cylinders but you
should use the sphere, cone, and cylinder objects built into POV-
Ray because they are faster than the quadric version.  Note that
you do not confuse "quaDRic" with "quaRTic". A quadric is a 2nd
order polynomial while a quartic is 4th order. Quadrics render
much faster and are less error-prone but produce less complex
objects.  The syntax is:

QUADRIC:
  quadric { <A,B,C>,<D,E,F>,<G,H,I>,J  [OBJECT_MODIFIERS...] }
Although the syntax actually will parse 3 vector expressions
followed by a float, we traditionally have written the syntax as
above where A through J are float expressions.  These 10 float
that define a surface of x, y, z points which satisfy the
equation

 A x2 + B y2 + C z2 + D xy + E xz + F yz + G x + H y + I z + J =
0
Different values of A, B, C, ... J will give different shapes. If
you take any three dimensional point and use its x, y and z
coordinates in the above equation the answer will be 0 if the
point is on the surface of the object. The answer will be
negative if the point is inside the object and positive if the
point is outside the object.  Here are some examples:
X2 + Y2 + Z2 -  Sphere
1 = 0
X2 + Y2 - 1 = 0 Infinite cylinder
                along the Z axis
X2 + Y2 - Z2 =  Infinite cone
0               along the Z axis
The easiest way to use these shapes is to include the standard
file shapes.inc into your program. It contains several pre-
defined quadrics and you can transform these pre-defined shapes
(using translate, rotate and scale) into the ones you want. For a
complete list, see the file shapes.inc.


4.5.4     Constructive Solid Geometry
In addition to all of the primitive shapes POV-Ray supports, you
can also combine multiple simple shapes into complex shapes using
Constructive Solid Geometry (CSG).  There are four basic types of
CSG operations: union, intersection, difference, and merge.  CSG
objects can be composed of primitives or other CSG objects to
create more, and more complex shapes.


4.5.4.1   Inside and Outside
Most shape primitives, like spheres, boxes and blobs divide the
world into two regions. One region is inside the object and one
is outside. Given any point in space you can say it's either
inside or outside any particular primitive object. Well, it could
be exactly on the surface but this case is rather hard to
determine due to numerical problems.

Even planes have an inside and an outside. By definition, the
surface normal of the plane points towards the outside of the
plane. You should note that triangles and triangle-based shapes
cannot be used as solid objects in CSG since they have no well
defined inside and outside.

CSG uses the concepts of inside and outside to combine shapes
together as explained in the following sections.

Imagine you have two objects that partially overlap like shown in
the figure below. Four different areas of points can be
distinguished: points that are neither in object A nor in object
B, points that are in object A but not in object B, points that
are not in object A but in object B and last not least points
that are in object A and object B.

                                
                                
                    Two overlapping objects.
                                
Keeping this in mind it will be quite easy to understand how the
CSG operations work.

When using CSG it is often useful to invert an object so that
it'll be inside-out. The appearance of the object is not changed,
just the way that POV-Ray perceives it. When the inverse keyword
is used the inside of the shape is flipped to become the outside
and vice versa.

The inside/outside distinction is not important for a union, but
is important for intersection, difference, and merge.Therefore
any objects may be combined using union but only solid objects,
i.e. objects that have a well-defined interior can be used in the
other kinds of CSG. The objects described in "Finite Patch
Primitives" have no well defined inside/outside.  All objects
described in the sections "Finite Solid Primitives" and "Infinite
Solid Primitives".


4.5.4.2   Union
                                
                                
                    The union of two objects.
                                
The simplest kind of CSG is the union. The syntax is:

UNION:
  union { OBJECTS...  [OBJECT_MODIFIERS...] }
Unions are simply glue used to bind two or more shapes into a
single entity that can be manipulated as a single object. The
image above shows the union of A and B. The new object created by
the union operation can be scaled, translated and rotated as a
single shape. The entire union can share a single texture but
each object contained in the union may also have its own texture,
which will override any texture statements in the parent object.

You should be aware that the surfaces inside the union will not
be removed. As you can see from the figure this may be a problem
for transparent unions. If you want those surfaces to be removed
you'll have to use the merge operations explained in a later
section.

The following union will contain a box and a sphere.

  union {
    box { <-1.5, -1, -1>, <0.5, 1, 1> }
    cylinder { <0.5, 0, -1>, <0.5, 0, 1>, 1 }
  }
Earlier versions of POV-Ray placed restrictions on unions so you
often had to combine objects with composite statements.  Those
earlier restrictions have been lifted so composite is no longer
needed. It is still supported for backwards compatibility.


4.5.4.3   Intersection
The intersection object creates a shape containing only those
areas where all components overlap.  A point is part an
intersection if it is inside both objects, A and B, as show in
the figure below.

                                
                                
                The intersection of two objects.
                                
The syntax is:

INTERSECTION:
  intersection { SOLID_OBJECTS...  [OBJECT_MODIFIERS...] }
The component objects must have well defined inside/outside
properties.  Patch objects are not allowed.  Note that if all
components do not overlap, the intersection object disappears.

Here is an example that overlaps:

  intersection {
    box { <-1.5, -1, -1>, <0.5, 1, 1> }
    cylinder { <0.5, 0, -1>, <0.5, 0, 1>, 1 }
  }

4.5.4.4   Difference
The CSG difference operation takes the intersection between the
first object and the inverse of all subsequent objects. Thus only
points inside object A and outside object B belong to the
difference of both objects.

The results is a subtraction of the 2nd shape from the first
shape as shown in the figure below.

                                
                                
               The difference between two objects.
                                
The syntax is:

DIFFERENCE:
  difference { SOLID_OBJECTS...  [OBJECT_MODIFIERS...] }
The component objects must have well defined inside/outside
properties.  Patch objects are not allowed.  Note that if the
first object is entirely inside the subtracted objects, the
difference object disappears.

Here is an example of a properly formed difference:

  difference {
    box { <-1.5, -1, -1>, <0.5, 1, 1> }
    cylinder { <0.5, 0, -1>, <0.5, 0, 1>, 1 }
  }
Note that internally, POV-Ray simply adds the inverse keyword to
the second (and subsequent) objects and then performs an
intersection.  The example above is equivalent to:

  intersection {
    box { <-1.5, -1, -1>, <0.5, 1, 1> }
    cylinder { <0.5, 0, -1>, <0.5, 0, 1>, 1 inverse }
  }

4.5.4.5   Merge
The union operation just glues objects together, it does not
remove the objects' surfaces inside the union.  Under most
circumstances this doesn't matter.  However if a transparent
union is used, those interior surfaces will be visible.  The
merge operations can be used to avoid this problem. It works just
like union but it eliminates the inner surfaces like shown in the
figure below.

                                
                                
                  Merge removes inner surfaces.
                                
The syntax is:

MERGE:
  merge { SOLID_OBJECTS...  [OBJECT_MODIFIERS...] }
The component objects must have well defined inside/outside
properties.  Patch objects are not allowed.  Note that merge is
slower rendering than union so it should only be used when it is
really necessary.


4.5.5     Light Sources
The light_source is not really an object. Light sources have no
visible shape of their own.  They are just points or areas which
emit light. They are categorized as objects so that they can be
combined with regular objects using union.  Their full syntax is:

LIGHT_SOURCE:
  light_source { <Location>, COLOR [LIGHT_MODIFIERS...] }
LIGHT_MODIFIER:
  LIGHT_TYPE   |   SPOTLIGHT_ITEM   |
  AREA_LIGHT_ITEMS   |   GENERAL_LIGHT_MODIFIERS
LIGHT_TYPE:
  spotlight   |   shadowless   |   cylinder
SPOTLIGHT_ITEM:
  radius Radius   |   falloff Falloff   |   tightness Tightness
  |   point_at <Spot>
AREA_LIGHT_ITEM:
  area_light <Axis_1>, <Axis_2>, Size_1, Size_2   |
  adaptive Adaptive   |   jitter Jitter
GENERAL_LIGHT_MODIFIERS:
  looks_like { OBJECT }   |   TRANSFORMATION
  fade_distance Fade_Distance   |   fade_power Fade_Power   |
  media_attenuation [Bool]   |   media_interaction [Bool]
The different types of light sources and the optional modifiers
are described in the following sections.

The first two items are common to all light sources.  The
<Location> vector gives the location of the light.  The COLOR
gives the color of the light.  Only the red, green, and blue
components are significant.  Any transmit or filter values are
ignored.  Note that you vary the intensity of the light as well
as the color using this parameter.  A color such as rgb
<0.5,0.5,0.5> gives a white light that is half the normal
intensity.

All of the keywords or items in the syntax specification above
may appear in any order.  Some keywords only have effect if
specified with other keywords.  The keywords are grouped into
functional categories to make it clear which keywords work
together.  The GENERAL_LIGHT_MODIFIERS work with all types of
lights and all options.  Note that TRANSFORMATIONS such as
translate, rotate etc. may be applied but no other
OBJECT_MODIFIERS may be used.

There are four mutually exclusive light types.  If no LIGHT_TYPE
is specified it is a point light.  The other choices are
spotlight, shadowless, and cylinder.


4.5.5.1   Point Lights
The simplest kid of light is a point light. A point light source
sends light of the specified color uniformly in all directions.
The default light type is a point source.  The <Location> and
COLOR is all that is required.  For example:

  light_source {
    <1000,1000,-1000>, rgb <1,0.75,0> //an orange light
  }

4.5.5.2   Spotlights
Normally light radiates outward equally in all directions from
the source.  However the spotlight keyword can be used to create
a cone of light that is bright in the center and falls of to
darkness in a soft fringe effect at the edge.  Although the cone
of light fades to soft edges, objects illuminated by spotlights
still cast hard shadows.  The syntax is:

SPOTLIGHT_SOURCE:
  light_source { <Location>, COLOR spotlight
  [LIGHT_MODIFIERS...] }
LIGHT_MODIFIER:
  SPOTLIGHT_ITEM   |   AREA_LIGHT_ITEMS   |
  GENERAL_LIGHT_MODIFIERS
SPOTLIGHT_ITEM:
  radius Radius   |   falloff Falloff   |   tightness Tightness
  |   point_at <Spot>
The point_at keyword tells the spotlight to point at a particular
3D coordinate.  A line from the location of the spotlight to the
point_at coordinate forms the center line of the cone of light.
The following illustration will be helpful in understanding how
these values relate to each other.

                                
                                
                  The geometry of a spotlight.
                                
The falloff, radius, and tightness keywords control the way that
light tapers off at the edges of the cone.  These four keywords
apply only when the spotlight or cylinder keywords are used.

The falloff keyword specifies the overall size of the cone of
light.  This is the point where the light falls off to zero
intensity.  The float value you specify is the angle, in degrees,
between the edge of the cone and center line.  The radius keyword
specifies the size of the "hot-spot" at the center of the cone of
light.  The "hot-spot" is a brighter cone of light inside the
spotlight cone and has the same center line.  The radius value
specifies the angle, in degrees, between the edge of this bright,
inner cone and the center line.  The light inside the inner cone
is of uniform intensity.  The light between the inner and outer
cones tapers off to zero.

For example with radius 10 and falloff 20 the light from the
center line out to 10 degrees is full intensity.  From 10 to 20
degrees from the center line the light falls off to zero
intensity.  At 20 degrees or greater there is no light.  Note
that if the radius and falloff values are close or equal the
light intensity drops rapidly and the spotlight has a sharp edge.
The default values for both radius and falloff is 70.

The values for these two parameters are half the opening angles
of the corresponding cones, both angles have to be smaller than
90 degrees. The light smoothly falls off between the radius and
the falloff angle like shown in the figures below (as long as the
radius angle is not negative).

                                
                                
   Intensity multiplier curve with a fixed falloff angle of 45
                            degrees.
                                
                                
                                
   Intensity multiplier curve with a fixed radius angle of 45
                            degrees.
                                
The tightness keyword is used to specify an additional
exponential softening of the edges.  The intensity of light at an
angle from the center line is given by: intensity *
cos(angle)tightness.  The default value for tightness is 10.
Lower tightness values will make the spotlight brighter, making
the spot wider and the edges sharper. Higher values will dim the
spotlight, making the spot tighter and the edges softer. Values
from 1 to 100 are acceptable.

                                
                                
 Intensity multiplier curve with fixed angle and falloff angles
                                
of 30 and 60 degrees respectively and different tightness values.
                                
You should note from the figures that the radius and falloff
angles interact with the tightness parameter. Only negative
radius angles will give the tightness value full control over the
spotlight's appearance as you can see from the figure below. In
that case the falloff angle has no effect and the lit area is
only determined by the tightness parameter.

                                
                                
   Intensity multiplier curve with a negative radius angle and
                   different tightness values.
                                
Spotlights may be used anyplace that a normal light source is
used. Like any light sources, they are invisible. They may also
be used in conjunction with area lights.


4.5.5.3   Cylindrical Lights
The cylinder keyword specifies a cylindrical light source that is
great for simulating laser beams.  Cylindrical light sources work
pretty much like spotlights except that the light rays are
constrained by a cylinder and not a cone. The syntax is:

CYLINDER_LIGHT_SOURCE:
  light_source { <Location>, COLOR cylinder [LIGHT_MODIFIERS...]
  }
LIGHT_MODIFIER:
  SPOTLIGHT_ITEM   |   AREA_LIGHT_ITEMS   |
  GENERAL_LIGHT_MODIFIERS
SPOTLIGHT_ITEM:
  radius Radius   |   falloff Falloff   |   tightness Tightness
  |   point_at <Spot>
The point_at, radius, falloff and tightness keywords control the
same features as with the spotlight.  See "Spotlights" for
details.

You should keep in mind that the cylindrical light source is
still a point light source. The rays are emitted from one point
and are only constraint by a cylinder. The light rays are not
parallel.


4.5.5.4   Area Lights
Area light sources occupy a finite, one- or two-dimensional area
of space. They can cast soft shadows because an object can
partially block their light.  Point sources are either totally
blocked or not blocked.

The area_light keyword in POV-Ray creates sources that are
rectangular in shape, sort of like a flat panel light. Rather
than performing the complex calculations that would be required
to model a true area light, it is approximated as an array of
point light sources spread out over the area occupied by the
light. The array-effect applies to shadows only.  The object's
illumination is still that of a point source.  The intensity of
each individual point light in the array is dimmed so that the
total amount of light emitted by the light is equal to the light
color specified in the declaration. The syntax is:
AREA_LIGHT_SOURCE:
  light_source { <Location>, COLOR area_light <Axis_1>,
  <Axis_2>, Size_1, Size_2
     [adaptive Adaptive] [ jitter Jitter ]
     [LIGHT_MODIFIERS...]
  }
The light's location and color are specified in the same way as a
for a regular light source.  Any type of light source may be an
area light.

The area_light command defines the size and orientation of the
area light as well as the number of lights in the light source
array. The vectors <Axis_1> and <Axis_2> specify the lengths and
directions of the edges of the light. Since the area lights are
rectangular in shape these vectors should be perpendicular to
each other. The larger the size of the light the thicker the soft
part of shadows will be. The integers Size_1 and Size_2 specify
the number of rows and columns of point sources of the. The more
lights you use the smoother your shadows will be but the longer
they will take to render.

Note that it is possible to specify spotlight parameters along
with the area light parameters to create area spotlights. Using
area spotlights is a good way to speed up scenes that use area
lights since you can confine the lengthy soft shadow calculations
to only the parts of your scene that need them.

An interesting effect can be created using a linear light source.
Rather than having a rectangular shape, a linear light stretches
along a line sort of like a thin fluorescent tube. To create a
linear light just create an area light with one of the array
dimensions set to 1.

The jitter command is optional. When used it causes the positions
of the point lights in the array to be randomly jittered to
eliminate any shadow banding that may occur. The jittering is
completely random from render to render and should not be used
when generating animations.

The adaptive command is used to enable adaptive sampling of the
light source. By default POV-Ray calculates the amount of light
that reaches a surface from an area light by shooting a test ray
at every point light within the array. As you can imagine this is
very slow. Adaptive sampling on the other hand attempts to
approximate the same calculation by using a minimum number of
test rays. The number specified after the keyword controls how
much adaptive sampling is used. The higher the number the more
accurate your shadows will be but the longer they will take to
render. If you're not sure what value to use a good starting
point is adaptive 1. The adaptive keyword only accepts integer
values and cannot be set lower than 0.

When performing adaptive sampling POV-Ray starts by shooting a
test ray at each of the four corners of the area light. If the
amount of light received from all four corners is approximately
the same then the area light is assumed to be either fully in
view or fully blocked. The light intensity is then calculated as
the average intensity of the light received from the four
corners. However, if the light intensity from the four corners
differs significantly then the area light is partially blocked.
The area light is split into four quarters and each section is
sampled as described above. This allows POV-Ray to rapidly
approximate how much of the area light is in view without having
to shoot a test ray at every light in the array. Visually the
sampling goes like shown below.

                                
                                
                  Area light adaptive samples.
                                
While the adaptive sampling method is fast (relatively speaking)
it can sometimes produces inaccurate shadows. The solution is to
reduce the amount of adaptive sampling without completely turning
it off. The number after the adaptive keyword adjusts the number
of times that the area light will be split before the adaptive
phase begins.  For example if you use adaptive 0 a minimum of 4
rays will be shot at the light. If you use adaptive 1 a minimum
of 9 rays will be shot (adaptive 2 gives 25 rays, adaptive 3
gives 81 rays, etc). Obviously the more shadow rays you shoot the
slower the rendering will be so you should use the lowest value
that gives acceptable results.

The number of rays never exceeds the values you specify for rows
and columns of points. For example area_light x,y,4,4 specifies a
4 by 4 array of lights. If you specify adaptive 3 it would mean
that you should start with a 9 by 9 array. In this case no
adaptive sampling is done. The 4 by 4 array is used.


4.5.5.5   Shadowless Lights
Using the shadowless keyword you can stop a light source from
casting shadows.  These lights are sometimes called "fill
lights".  They are another way to simulate ambient light however
shadowless lights have a definite source.  The syntax is:

SHADOWLESS_LIGHT_SOURCE:
  light_source { <Location>, COLOR  shadowless
  [LIGHT_MODIFIERS...] }
LIGHT_MODIFIER:
  AREA_LIGHT_ITEMS   |   GENERAL_LIGHT_MODIFIERS
Shadowless may be used with area_light but not spotlight or
cylinder.


4.5.5.6   Looks_like
Normally the light source itself has no visible shape. The light
simply radiates from an invisible point or area. You may give a
light source any shape by adding a looks_like { OBJECT }
statement.

There is an implied no_shadow attached to the looks_like object
so that light is not blocked by the object. Without the automatic
no_shadow the light inside the object would not escape. The
object would, in effect, cast a shadow over everything.

If you want the attached object to block light then you should
attach it with a union and not a looks_like as follows:

  union {
    light_source { <100, 200, -300> color White }
    object { My_Lamp_Shape }
  }
Presumably parts of the lamp shade are transparent to let some
light out.


4.5.5.7   Light Fading
By default POV-Ray does not diminish light from any light source
as it travels through space. In order to get a more realistic
effect fade_distance and fade_power keywords followed by float
values can be used to model the distance based falloff in light
intensity.

The fade_distance Fade_Distance is used to specify the distance
at which the full light intensity arrives, i. e. the intensity
which was given by the COLOR specification. The actual
attenuation is described by the fade_power Fade_Power, which
determines the falloff rate. For example linear or quadratic
falloff can be used by setting fade_power to 1 or 2 respectively.
The complete formula to calculate the factor by which the light
is attenuated is

                                
                                
with d being the distance the light has traveled.

                                
                                
       Light fading functions for different fading powers.
                                
You should note two important facts: First, for Fade_Distance
larger than one the light intensity at distances smaller than
Fade_Distance actually increases. This is necessary to get the
light source color if the distance traveled equals the
Fade_Distance. Second, only light coming directly from light
sources is attenuated. Reflected or refracted light is not
attenuated by distance.


4.5.5.8   Atmospheric Media Interaction
By default light sources will interact with an atmosphere added
to the scene. This behaviour can be switched off by using
media_interaction off keyword inside the light source statement.
Note in POV-Ray 3.0 this feature was turned off and on with the
atmosphere keyword.

4.5.5.9   Atmospheric Attenuation
Normally light coming from light sources is not influenced by fog
or atmospheric media. This can be changed by turning the
media_attenuation on for a given light source on. All light
coming from this light source will now be diminished as it
travels through the fog or media.  This results in an distance-
based, exponential intensity falloff ruled by the used fog or
media. If there is no fog or media no change will be seen. Note
in POV-Ray 3.0 this feature was turned off and on with the
atmospheric_attenuation keyword.

4.5.6     Object Modifiers
A variety of modifiers may be attached to objects. The following
items may be applied to any object:

OBJECT_MODIFIER:
  clipped_by { UNTEXTURED_SOLID_OBJECT... }   |   clipped_by {
  bounded_by }   |
  bounded_by { UNTEXTURED_SOLID_OBJECT... }   |   bounded_by {
  clipped_by }   |
  no_shadow   |   inverse   |   sturm [ Bool ]   |   hierarchy [
  Bool ]   |
  interior { INTERIOR_ITEMS... }   |
  material { [MATERIAL_IDENTIFIER][MATERIAL_ITEMS...] }   |
  texture { TEXTURE_BODY }   |   pigment { PIGMENT_BODY }   |
  normal { NORMAL_BODY }   |   finish { FINISH_ITEMS... }   |
  TRANSFORMATION
Transformations such as translate, rotate and scale have already
been discussed. The modifiers "Textures" and its parts "Pigment",
"Normal", and "Finish" as well as "Interior", and "Media" (which
is part of interior) are each in major chapters of their own
below. In the sub-sections below we cover several other important
modifiers: clipped_by, bounded_by, material, no_shadow, hollow,
inverse, sturm, and hierarchy. Although the examples below use
object statements and object identifiers, these modifiers may be
used on any type of object such as sphere, box etc.


4.5.6.1   Clipped_By
The clipped_by statement is technically an object modifier but it
provides a type of CSG similar to CSG intersection. The syntax
is:

CLIPPED_BY:
  clipped_by { UNTEXTURED_SOLID_OBJECT... }   |   clipped_by {
  bounded_by }
Where UNTEXTURED_SOLID_OBJECT is one or more solid objects which
have had no texture applied.  For example:

  object {
    My_Thing
    clipped_by{plane{y,0}}
  }
Every part of the object My_Thing that is inside the plane is
retained while the remaining part is clipped off and discarded.
In an intersection object the hole is closed off. With clipped_by
it leaves an opening. For example the following figure shows
object A being clipped by object B.

                                
                                
              An object clipped by another object.
                                
You may use clipped_by to slice off portions of any shape. In
many cases it will also result in faster rendering times than
other methods of altering a shape.  Occasionally you will want to
use the clipped_by and bounded_by options with the same object.
The following shortcut saves typing and uses less memory.

  object {
    My_Thing
    bounded_by { box { <0,0,0>, <1,1,1> } }
    clipped_by { bounded_by }
  }
This tells POV-Ray to use the same box as a clip that was used as
a bounds.


4.5.6.2   Bounded_By
The calculations necessary to test if a ray hits an object can be
quite time consuming. Each ray has to be tested against every
object in the scene. POV-Ray attempts to speed up the process by
building a set of invisible boxes, called bounding boxes, which
cluster the objects together. This way a ray that travels in one
part of the scene doesn't have to be tested against objects in
another, far away part of the scene. When large a number of
objects are present the boxes are nested inside each other. POV-
Ray can use bounding boxes on any finite object and even some
clipped or bounded quadrics. However infinite objects (such as a
planes, quartic, cubic and poly) cannot be automatically bound.
CSG objects are automatically bound if they contain finite (and
in some cases even infinite) objects. This works by applying the
CSG set operations to the bounding boxes of all objects used
inside the CSG object. For difference and intersection operations
this will hardly ever lead to an optimal bounding box. It's
sometimes better (depending on the complexity of the CSG object)
to have you place a bounding shape yourself using a bounded_by
statement.

Normally bounding shapes are not necessary but there are cases
where they can be used to speed up the rendering of complex
objects. Bounding shapes tell the ray-tracer that the object is
totally enclosed by a simple shape. When tracing rays, the ray is
first tested against the simple bounding shape. If it strikes the
bounding shape the ray is further tested against the more
complicated object inside. Otherwise the entire complex shape is
skipped, which greatly speeds rendering.  The syntax is:

BOUNDED_BY:
  bounded_by { UNTEXTURED_SOLID_OBJECT... }   |   bounded_by {
  clipped_by }
Where UNTEXTURED_SOLID_OBJECT is one or more solid objects which
have had no texture applied.  For example:

  intersection {
    sphere { <0,0,0>, 2 }
    plane  { <0,1,0>, 0 }
    plane  { <1,0,0>, 0 }
    bounded_by { sphere { <0,0,0>, 2 } }
  }
The best bounding shape is a sphere or a box since these shapes
are highly optimized, although, any shape may be used. If the
bounding shape is itself a finite shape which responds to
bounding slabs then the object which it encloses will also be
used in the slab system.

While it may a good idea to manually add a bounded_by to
intersection, difference and merge, it is best to never bound a
union. If a union has no bounded_by POV-Ray can internally split
apart the components of a union and apply automatic bounding
slabs to any of its finite parts. Note that some utilities such
as raw2pov may be able to generate bounds more efficiently than
POV-Ray's current system. However most unions you create yourself
can be easily bounded by the automatic system. For technical
reasons POV-Ray cannot split a merge object. It is may be best to
hand bound a merge, especially if it is very complex.

Note that if bounding shape is too small or positioned
incorrectly it may clip the object in undefined ways or the
object may not appear at all. To do true clipping, use clipped_by
as explained in the previous section. Occasionally you will want
to use the clipped_by and bounded_by options with the same
object. The following shortcut saves typing and uses less memory.

  object {
    My_Thing
    clipped_by{ box { <0,0,0>,<1,1,1 > }}
    bounded_by{ clipped_by }
  }
This tells POV-Ray to use the same box as a bounds that was used
as a clip.


4.5.6.3   Material
One of the changes in POV-Ray 3.1 was remove several items from
texture{finish{...}} and to move them to the new interior
statement.  The halo statement, formerly part of texture, are now
renamed media and made a part of the interior.  This split was
deliberate and purposeful (see "Why are Interior and Media
Necessary?") however beta testers have pointed out that it makes
it difficult to entirely describe the surface properties and
interior of an object in one statement that can be referenced by
a single identifier in a texture library.

The result is that we created a "wrapper" around texture and
interior which we call material.  The syntax is:

MATERIAL:
  material { [MATERIAL_IDENTIFIER][MATERIAL_ITEMS...] }
MATERIAL_ITEMS:
  TEXTURE   |   INTERIOR   |   TRANSFORMATIONS
For example:

  #declare MyGlass=material{texture{Glass_T} interior{Glass_I}}
  object{MyObject material{MyGlass}}
Internally, the "material" isn't attached to the object.  The
material is just a container that brings the texture and interior
to the object.  It is the texture and interior itself that is
attached to the object.  Users should still consider texture and
interior as separate items attached to the object.  The material
is just a "bucket" to carry them.

If the object already has a texture, the material texture is
layered over it.  If the object already has an interior, the
material interior fully replaces it and the old interior is
destroyed.

Transformations inside the material affect only the textures and
interiors which are inside the material{} wrapper and only those
textures or interiors specifed are affected.  For example:

  object{MyObject
    material{
      texture{MyTexture}
      scale 4         //affects texture but not object or
interior
      interior{MyInterior}
      translate 5*x   //affects texture and interior, not object
    }
  }
Note: The material statement has nothing to do with the
material_map statement.  A material_map is not a way to create
patterned material.  See "Material Maps" for explanation of this
unrelated, yet similarly named, older feature.


4.5.6.4   Inverse
When using CSG it is often useful to invert an object so that
it'll be inside-out. The appearance of the object is not changed,
just the way that POV-Ray perceives it. When the inverse keyword
is used the inside of the shape is flipped to become the outside
and vice versa.  For example:

  object { MyObject inverse }
The inside/outside distinction is also important when attaching
interior to an object especially if media is also used.
Atmospheric media and fog also do not work as expected if your
camera is inside an object.  Using inverse is useful to correct
that problem.

Finally the internal_reflections and internal_highlights keywords
depend upon the inside/outside status of an object.


4.5.6.5   Hollow
POV-Ray by default assumes that objects are made of a solid
material that completely fills the interior of an object. By
adding the hollow keyword to the object you can make it hollow.
That is very useful if you want atmospheric effects to exist
inside an object. It is even required for objects containing an
interior media.  The keyword may optionally be followed by a
float expression which is interpreted as a boolean value.  For
example hollow off may be used to force it off.  When the keyword
is specified alone, it is the same as hollow on.  The default no
hollow is specified is off.

In order to get a hollow CSG object you just have to make the top
level object hollow. All children will assume the same hollow
state except their state is explicitly set. The following example
will set both spheres inside the union hollow

  union {
    sphere { -0.5*x, 1 }
    sphere {  0.5*x, 1 }
    hollow
  }
while the next example will only set the second sphere hollow
because the first sphere was explicitly set to be not hollow.

  union {
    sphere { -0.5*x, 1 hollow off }
    sphere {  0.5*x, 1 }
    hollow on
  }

4.5.6.6   No_Shadow
You may specify the no_shadow keyword in an object to make that
object cast no shadow. This is useful for special effects and for
creating the illusion that a light source actually is visible.
This keyword was necessary in earlier versions of POV-Ray which
did not have the looks_like statement. Now it is useful for
creating things like laser beams or other unreal effects.  During
test rendering it speeds things up if no_shadow is applied.

Simply attach the keyword as follows:

  object {
    My_Thing
    no_shadow
  }

4.5.6.7   Sturm
Some of POV-Ray's objects allow you to choose between a fast but
sometimes inaccurate root solver and a slower but more accurate
one. This is the case for all objects that involve the solution
of a cubic or quartic polynomial. There are analytic mathematical
solutions for those polynomials that can be used.

Lower order polynomials are trivial to solve while higher order
polynomials require iterative algorithms to solve them. One of
those algorithms is the Sturmian root solver.  For example:

  blob {
    threshold .65
    sphere { <.5,0,0>, .8, 1 }
    sphere { <-.5,0,0>,.8, 1 }
    sturm
  }

The keyword may optionally be followed by a float expression
which is interpreted as a boolean value.  For example sturm off
may be used to force it off.  When the keyword is specified
alone, it is the same as sturm on.  The default no sturm is
specified is off.

The following list shows all objects for which the Sturmian root
solver can be used.

    blob
    cubic
    lathe    (only with quadratic splines)
    poly
    prism    (only with cubic splines)
    quartic
    sor


4.6  Interior
New with POV-Ray 3.1 is an object modifier statement called
interior.  The syntax is:

INTERIOR:
  interior { [INTERIOR_IDENTIFIER] [INTERIOR_ITEMS...] }
INTERIOR_ITEM:
  ior Value   |   caustics Value   |
  fade_distance Distance   |   fade_power Power
  MEDIA...
The interior contains items which describe the properties of the
interior of the object.  This is in contrast to the texture which
describes the surface properties only.  The interior of an object
is only of interest if it has a transparent texture which allows
you to see inside the object.  It also applies only to solid
objects which have a well-defined inside/outside distinction.
Note that the open keyword, or clipped_by modifier also allows
you to see inside but interior features may not render properly.
They should be avoided if accurate interiors are required.

Interior identifiers may be declared to make scene files more
readable and to parameterize scenes so that changing a single
declaration changes many values. An identifier is declared as
follows.

INTERIOR_DECLARATION:
  #declare IDENTIFIER = INTERIOR     |
  #local IDENTIFIER = INTERIOR
Where IDENTIFIER is the name of the identifier up to 40
characters long and INTERIOR is any valid interior statement.
See "#declare vs. #local" for information on identifier scope.


4.6.1     Why are Interior and Media Necessary?
In previous versions of POV-Ray, most of the items in the
interior statement were previously part of the finish statement.
Also the halo statement which was once part of the texture
statement has been discontinued and has been replaced by the
media statement which is part of interior.

You are probably asking WHY?  As explained earlier, the interior
contains items which describe the properties of the interior of
the object.  This is in contrast to the texture which describes
the surface properties only.  However this is not just a
philosophical change.  There were serious inconsistencies in the
old model.

The main problem arises when a texture_map or other patterned
texture is used.  These features allow you to create textures
that are a blend of two textures and which vary the entire
texture from one point to another.  It does its blending by fully
evaluating the apparent color as though only one texture was
applied and then fully reevaluating it with the other texture.
The two final results are blended.

It is totally illogical to have a ray enter an object with one
index or refraction and then recalculate with another index.  The
result is not an average of the two ior values.  Similarly it
makes no sense to have a ray enter at one ior and exit at a
different ior without transitioning between them along the way.
POV-Ray only calculates refraction as the ray enters or leaves.
It cannot incrementally compute a changing ior through the
interior of an object.  Real world objects such as optical fibers
or no-line bifocal eyeglasses can have variable iors but POV-Ray
cannot simulate them.

Similarly the halo calculations were not performed as the syntax
implied.  Using a halo in such multi-textured objects did not
vary the halo through the interior of the object.  Rather, it
computed two separate halos through the whole object and averaged
the results.  The new design for media which replaces halo makes
it possible to have media that varies throughout the interior of
the object according to a pattern but it does so independently of
the surface texture.  Because there are other changes in the
design of this feature which make it significantly different, it
was not only moved to the interior but the name was changed.

During our development, someone asked if we will create patterned
interiors or a hypothetical interior_map feature.  We will not.
That would defeat the whole purpose of moving these features in
the first place.  They cannot be patterned and have logical or
self-consistent results.


4.6.2     Empty and Solid Objects
It is very important that you know the basic concept behind empty
and solid objects in POV-Ray to fully understand how features
like interior and translucency are used.  Objects in POV-Ray can
either be solid, empty or filled with (small) particles.

A solid object is made from the material specified by its pigment
and finish statements (and to some degree its normal statement).
By default all objects are assumed to be solid. If you assign a
stone texture to a sphere you'll get a ball made completely of
stone. It's like you had cut this ball from a block of stone. A
glass ball is a massive sphere made of glass.  You should be
aware that solid objects are conceptual things. If you clip away
parts of the sphere you'll clearly see that the interior is empty
and it just has a very thin surface.

This is not contrary to the concept of a solid object used in POV-
Ray. It is assumed that all space inside the sphere is covered by
the sphere's interior. Light passing through the object is
affected by attenuation and refraction properties.  However there
is no room for any other particles like those used by fog or
interior media.

Empty objects are created by adding the hollow keyword (see
"Hollow") to the object statement. An empty (or hollow) object is
assumed to be made of a very thin surface which is of the
material specified by the pigment, finish and normal statements.
The object's interior is empty, it normally contains air
molecules.

An empty object can be filled with particles by adding fog or
atmospheric media to the scene or by adding an interior media to
the object.  It is very important to understand that in order to
fill an object with  any kind of particles it first has to be
made hollow.

There is a pitfall in the empty/solid object implementation that
you have to be aware of.

In order to be able to put solid objects inside a media or fog, a
test has to be made for every ray that passes through the media.
If this ray travels through a solid object the media will not be
calculated. This is what anyone will expect. A solid glass sphere
in a fog bank does not contain fog.

The problem arises when the camera ray is inside any non-hollow
object. In this case the ray is already traveling through a solid
object and even if the media's container object is hit and it is
hollow, the media will not be calculated. There is no way of
telling between these two cases.

POV-Ray has to determine whether the camera is inside any object
prior to tracing a camera ray in order to be able to correctly
render medias when the camera is inside the container object.
There's no way around doing this.

The solution to this problem (that will often happen with
infinite objects like planes) is to make those objects hollow
too. Thus the ray will travel through a hollow object, will hit
the container object and the media will be calculated.


4.6.3     Refraction
When light passes through a surface either into or out of a dense
medium the path of the ray of light is bent. Such bending is
called refraction.  The amount of bending or refracting of light
depends upon the density of the material. Air, water, crystal and
diamonds all have different densities and thus refract
differently. The index of refraction or ior value is used by
scientists to describe the relative density of substances. The
ior keyword is used in POV-Ray in the interior to turn on
refraction and to specify the ior value. For example:

  object{ MyObject pigment{Clear} interior{ior 1.5}}
The default ior value of 1.0 will give no refraction. The index
of refraction for air is 1.0, water is 1.33, glass is 1.5 and
diamond is 2.4.

Normally transparent or semi-transparent surfaces in POV-Ray do
not refract light. Earlier versions of POV-Ray required you to
use the refraction keyword in the finish statement to turn on
refraction.  This is no longer necessary.  Any non-zero ior value
now turns refraction on.

In addition to turning refraction on or off, the old refraction
keyword was followed by a float value from 0.0 to 1.0.  Values in
between 0.0 and 1.0 would darken the refracted light in ways that
do not correspond to any physical property. Many POV-Ray scenes
were created with intermediate refraction values before this bug
was discovered so the feature has been maintained. A more
appropriate way to reduce the brightness of refracted light is to
change the filter or transmit value in the colors specified in
the pigment statement or to use the fade_power and fade_distance
keywords.  See "Attenuation". Note also that neither the ior nor
refraction keywords cause the object to be transparent.
Transparency only occurs if there is a non-zero filter or
transmit value in the color.

The refraction and ior keywords were original specified in finish
but are now properly specified in interior.  They are accepted in
finish for backward compatibility and generate a warning message.


4.6.4     Attenuation
Light attenuation is used to model the decrease in light
intensity as the light travels through a transparent object.  The
keywords fade_power Fade_Power and fade_distance Fade_Distance
keywords are specified in the interior statement.

The fade_distance value determines the distance the light has to
travel to reach half intensity while the fade_power value
determines how fast the light will fall off. For realistic
effects a fade power of 1 to 2 should be used.  Default values
for both keywords is 0.0 which turns this feature off.

The attenuation is calculated by a formula similar to that used
for light source attenuation.



The fade_power and fade_distance keywords were original specified
in finish but are now properly specified in interior.  They are
accepted in finish for backward compatibility and generate a
warning message.


4.6.5     Faked Caustics
Caustics are light effects that occur if light is reflected or
refracted by specular reflective or refractive surfaces. Imagine
a glass of water standing on a table. If sunlight falls onto the
glass you will see spots of light on the table. Some of the spots
are caused by light being reflected by the glass while some of
them are caused by light being refracted by the water in the
glass.

Since it is a very difficult and time-consuming process to
actually calculate those effects (though it is not impossible)
POV-Ray uses a quite simple method to simulate caustics caused by
refraction. The method calculates the angle between the incoming
light ray and the surface normal.  Where they are nearly parallel
it makes the shadow brighter.  Where the angle is greater, the
effect is diminished.  Unlike real-world caustics, the effect
does not vary based on distance.  This caustic effect is limited
to areas that are shaded by the transparent object. You'll get no
caustic effects from reflective surfaces nor in parts that are
not shaded by the object.

The caustics Power keyword controls the effect.  Values typically
range from 0.0 to 1.0 or higher.  Zero is the default which is no
caustics.  Low, non-zero values give broad hot-spots while higher
values give tighter, smaller simulated focal points.

The caustics keyword was originally specified in finish but is
now properly specified in interior.  It is accepted in finish for
backward compatibility and generates a warning message.


4.6.6     Object Media
The interiorstatement may contain one or more media statements.
Media is used to simulate suspended particles such as smoke,
haze, or dust.  Or visible gasses such as steam or fire and
explosions.  When used with an object interior, the effect is
constrained by the object's shape.  The calculations begin when
the ray enters an object and ends when it leaves the object.
This section only discusses media when used with object interior.
The complete syntax and an explanation of all of the parameters
and options for media is given in the section "Media".

Typically the object itself is given a fully transparent texture
however media also works in partially transparent objects.  The
texture pattern itself does not effect the interior media except
perhaps to create shadows on it.  The texture pattern of an
object applies only to the surface shell.  Any interior media
patterns are totally independent of the texture.

In previous versions of POV-Ray, this feature was called halo and
was part of the texture specification along with pigment, normal,
and finish.  See "Why are Interior and Media Necessary?" for an
explanation of the reasons for the change.

Note a strange design side-effect was discovered during testing
and it was too difficult to fix.  If the enclosing object uses
transmit rather than filter for transparency, then the media
casts no shadows.  For example:

 object{MyObject pigment{rgbt 1.0} interior{media{MyMedia}}} //no
shadows
 object{MyObject pigment{rgbf 1.0} interior{media{MyMedia}}}
//shadows
Media may also be specified outside an object to simulate
atmospheric media.  There is no constraining object in this case.
If you only want media effects in a particular area, you should
use object media rather than only relying upon the media pattern.
In general it will be faster and more accurate because it only
calculates inside the constraining object.  See "Atmospheric
Media" for details on unconstrained uses of media.

You may specify more than one media statement per interior
statement.  In that case, all of the media participate and where
they overlap, they add together.

Any object which is supposed to have media effects inside it,
whether those effects are object media or atmospheric media, must
have the hollow on keyword applied.  Otherwise the media is
blocked.  See "Empty and Solid Objects" for details.


4.7  Textures
The texture statement is an object modifier which describes what
the surface of an object looks like, i.e. its material. Textures
are combinations of pigments, normals, and finishes. Pigment is
the color or pattern of colors inherent in the material. Normal
is a method of simulating various patterns of bumps, dents,
ripples or waves by modifying the surface normal vector. Finish
describes the reflective properties of a material.

Note that in previous versions of POV-Ray, the texture also
contained information about the interior of an object.  This
information has been moved to a separate object modifier called
interior.  See "Interior" for details.

There are three basic kinds of textures: plain, patterned, and
layered. A plain texture consists of a single pigment, an
optional normal, and a single finish. A patterned texture
combines two or more textures using a block pattern or blending
function pattern.  Patterned textures may be made quite complex
by nesting patterns within patterns. At the innermost levels
however, they are made up from plain textures. A layered texture
consists of two or more semi-transparent textures layered on top
of one another. Note that although we call a plain texture plain
it may be a very complex texture with patterned pigments and
normals. The term plain only means that it has a single pigment,
normal, and finish.

The syntax for texture is as follows:

TEXTURE:
  PLAIN_TEXTURE   |   PATTERNED_TEXTURE   |   LAYERED_TEXTURE
PLAIN_TEXTURE:
  texture { [TEXTURE_IDENTIFIER] [PNF_IDENTIFIER...]
  [PNF_ITEMS...] }
PNF_IDENTIFIER:
  PIGMENT_IDENTIFIER   |   NORMAL_IDENTIFIER   |
  FINISH_IDENTIFIER
PNF_ITEMS:
  PIGMENT   |   NORMAL   |   FINISH   |   TRANSFORMATION
LAYERED_TEXTURE:
  NON_PATTERNED_TEXTURE...
PATTERNED_TEXTURE:
  texture { [PATTERNED_TEXTURE_ID] [TRANSFORMATIONS...] }   |
  texture { PATTERN_TYPE [TEXTURE_PATTERN_MODIFIERS...] }   |
  texture { tiles TEXTURE  tile2 TEXTURE [TRANSFORMATIONS...] }
  |
  texture {
     material_map{
       BITMAP_TYPE "bitmap.ext" [MATERIAL_MODS...] TEXTURE...
     [TRANSFORMATIONS...]
     }
  }
TEXTURE_PATTERN_MODIFIER:
  PATTERN_MODIFIER   |   TEXTURE_LIST   |
  texture_map{ TEXTURE_MAP_BODY }
In the PLAIN_TEXTURE, each of the items are optional but if they
are present the TEXTURE_IDENTIFIER must be first. If no texture
identifier is given, then POV-Ray creates a copy of the default
texture.  See "The #default Directive" for details.

Next are optional pigment, normal, and/or finish identifiers
which fully override the any pigment, normal and finish already
specified in the previous texture identifier or default texture.
Typically this is used for backward compatibility to allow things
like: texture{MyPigment} where MyPigment is a pigment identifier.

Finally we have optional pigment, normal or finish statements
which modify any pigment, normal and finish already specified in
the identifier. If no texture identifier is specified the
pigment, normal and finish statements modify the current default
values. This is the typical plain texture:

  texture{
    pigment{MyPigment}
    normal{MyNormal}
    finish{MyFinish}
    scale SoBig
    rotate SoMuch
    translate SoFar
}
The TRANSFORMATIONS may be interspersed between the pigment,
normal and finish statements but are generally specified last.
If they are interspersed, then they modify only those parts of
the texture already specified.  For example:

  texture{
    pigment{MyPigment}
    scale SoBig        //affects pigment only
    normal{MyNormal}
    rotate SoMuch      //affects pigment and normal
    finish{MyFinish}
    translate SoFar    //finish is never transformable no matter
what.
                       //Therefore affects pigment and normal
only
}
Texture identifiers may be declared to make scene files more
readable and to parameterize scenes so that changing a single
declaration changes many values. An identifier is declared as
follows.

TEXTURE_DECLARATION:
  #declare IDENTIFIER = TEXTURE    |
  #local IDENTIFIER = TEXTURE
Where IDENTIFIER is the name of the identifier up to 40
characters long and TEXTURE is any valid texture statement.  See
"#declare vs. #local" for information on identifier scope.

The sections below describe all of the options available in
"Pigment", "Normal", and "Finish" which are the main part of
plain textures.. There are also separate sections for "Patterned
Textures" and "Layered Textures" which are made up of plain
textures.  Note that the tiles and material_map versions of
patterned textures are obsolete and are only supported for
backwards compatibility.


4.7.1     Pigment
The color or pattern of colors for an object is defined by a
pigment statement. All plain textures must have a pigment. If you
do not specify one the default pigment is used.  The color you
define is the way you want the object to look if fully
illuminated. You pick the basic color inherent in the object and
POV-Ray brightens or darkens it depending on the lighting in the
scene. The parameter is called pigment because we are defining
the basic color the object actually is rather than how it looks.

The syntax for pigment is:

PIGMENT:
  pigment{ [PIGMENT_IDENTIFIER] [PIGMENT_TYPE]
  [PIGMENT_MODIFIER...] }
PIGMENT_TYPE:
  PATTERN_TYPE   |
  COLOR   |
  image_map{ BITMAP_TYPE "bitmap.ext" [IMAGE_MAP_MODS...] }
PIGMENT_MODIFIER:
  PATTERN_MODIFIER   |   COLOR_LIST   |   PIGMENT_LIST   |
  color_map{ COLOR_MAP_BODY }   |   colour_map{ COLOR_MAP_BODY }
  |
  pigment_map{ PIGMENT_MAP_BODY }   |
  quick_color COLOR   |   quick_colour COLOR
Each of the items in a pigment are optional but if they are
present, they must be in the order shown. Any items after the
PIGMENT_IDENTIFIER modify or override settings given in the
identifier. If no identifier is specified then the items modify
the pigment values in the current default texture. The
PIGMENT_TYPE  fall into roughly four categories. Each category is
discussed the sub-sections which follow. The four categories are
solid color and image map patterns which are specific to pigment
statements or color list patterns, color mapped patterns which
use POV-Ray's wide selection of general patterns.  See "Patterns"
for details about specific patterns.

The pattern type is optionally followed by one or more pigment
modifiers.  In addition to general pattern modifiers such as
transformations, turbulence, and warp modifiers, pigments may
also have a COLOR_LIST, PIGMENT_LIST, color_map, pigment_map, and
quick_color which are specific to pigments.  See "Pattern
Modifiers" for information on general modifiers.  The pigment-
specific modifiers are described in sub-sections which follow.
Pigment modifiers of any kind apply only to the pigment and not
to other parts of the texture. Modifiers must be specified last.

A pigment statement is part of a texture specification.  However
it can be tedious to use a texture statement just to add a color
to an object. Therefore you may attach a pigment directly to an
object without explicitly specifying that it as part of a
texture. For example instead of this:

  object {My_Object texture{pigment{color Red}}}
you may shorten it to:

  object {My_Object pigment{color Red}}
Note however that doing so creates an entire texture structure
with default normal and finish statements just as if you had
explicitly typed the full texture{...} around it.

Pigment identifiers may be declared to make scene files more
readable and to parameterize scenes so that changing a single
declaration changes many values. An identifier is declared as
follows.

PIGMENT_DECLARATION:
  #declare IDENTIFIER = PIGMENT   |
  #local IDENTIFIER = PIGMENT
Where IDENTIFIER is the name of the identifier up to 40
characters long and PIGMENT is any valid pigment statement.  See
"#declare vs. #local" for information on identifier scope.


4.7.1.1   Solid Color Pigments
The simplest type of pigment is a solid color. To specify a solid
color you simply put a color specification inside a pigment
statement. For example:

  pigment {color Orange}
A color specification consists of the optional keyword color
followed by a color identifier or by a specification of the
amount of red, green, blue, filtered and unfiltered transparency
in the surface. See section "Specifying Colors" for more details
about colors. Any pattern modifiers used with a solid color are
ignored because there is no pattern to modify.


4.7.1.2   Color List Pigments
There are three color list patterns: checker, hexagon and brick.
The result is a pattern of solid colors with distinct edges
rather than a blending of colors as with color mapped patterns.
Each of these patterns is covered in more detail in a later
section. The syntax is:

COLOR_LIST_PIGMENT:
  pigment{brick [COLOR_1, [COLOR_2]] [PIGMENT_MODIFIERS...] }
  |
  pigment{checker [COLOR_1, [COLOR_2]] [PIGMENT_MODIFIERS...] }
  |
  pigment{hexagon [COLOR_1, [COLOR_2, [COLOR_3]]]
  [PIGMENT_MODIFIERS...] }
Each COLOR_n is any valid color specification. There should be a
comma between each color or the color keyword should be used as a
separator so that POV-Ray can determine where each color
specification starts and ends. The brick and checker pattern
expects two colors and hexagon expects three.  If an insufficient
number of colors is specified then default colors are used.


4.7.1.3   Color Maps
Most of the color patterns do not use abrupt color changes of
just two or three colors like those in the brick, checker or
hexagon patterns.  They instead use smooth transitions of many
colors that gradually change from one point to the next. The
colors are defined in a pigment modifier called a color_map that
describes how the pattern blends from one color to the next.

Each of the various pattern types available is in fact a
mathematical function that takes any x, y, z location and turns
it into a number between 0.0 and 1.0 inclusive. That number is
used to specify what mix of colors to use from the color map.

The syntax for color_map is as follows:

COLOR_MAP:
  color_map{ COLOR_MAP_BODY }   |   colour_map{ COLOR_MAP_BODY }
COLOR_MAP_BODY:
  COLOR_MAP_IDENTIFIER   |   COLOR_MAP_ENTRY...
COLOR_MAP_ENTRY:
  [ Value  COLOR ]   |   [ Value_1, Value_2 color COLOR_1 color
  COLOR_2 ]
Where each Value_n is a float values between 0.0 and 1.0
inclusive and each COLOR_n, is color specifications. Note that
the [] brackets are part of the actual COLOR_MAP_ENTRY. They are
not notational symbols denoting optional parts. The brackets
surround each entry in the color map. There may be from 2 to 256
entries in the map. The alternate spelling colour_map may be
used.

Here is an example:

  sphere {
    <0,1,2>, 2
    pigment {
      gradient x       //this is the PATTERN_TYPE
      color_map {
        [0.1  color Red]
        [0.3  color Yellow]
        [0.6  color Blue]
        [0.6  color Green]
        [0.8  color Cyan]
      }
    }
  }
The pattern function gradient x is evaluated and the result is a
value from 0.0 to 1.0. If the value is less than the first entry
(in this case 0.1) then the first color (red) is used. Values
from 0.1 to 0.3 use a blend of red and yellow using linear
interpolation of the two colors. Similarly values from 0.3 to 0.6
blend from yellow to blue. Note that the 3rd and 4th entries both
have values of 0.6. This causes an immediate abrupt shift of
color from blue to green. Specifically a value that is less than
0.6 will be blue but exactly equal to 0.6 will be green. Moving
along, values from 0.6 to 0.8 will be a blend of green and cyan.
Finally any value greater than or equal to 0.8 will be cyan.

If you want areas of unchanging color you simply specify the same
color for two adjacent entries. For example:

  color_map {
    [0.1  color Red]
    [0.3  color Yellow]
    [0.6  color Yellow]
    [0.8  color Green]
  }
In this case any value from 0.3 to 0.6 will be pure yellow.

The first syntax version of COLOR_MAP_ENTRY with one float and
one color is the current standard.  The other double entry
version is obsolete and should be avoided.  The previous example
would look as follows using the old syntax.

  color_map {
    [0.0 0.1  color Red color Red]
    [0.1 0.3  color Red color Yellow]
    [0.3 0.6  color Yellow color Yellow]
    [0.6.0.8  color Yellow color Green]
    [0.8 1.0  color Green color Green]
  }
You may use color_map with any patterns except brick, checker,
hexagon and image_map. You may declare and use color_map
identifiers. For example:

  #declare Rainbow_Colors=
    color_map {
      [0.0   color Magenta]
      [0.33  color Yellow]
      [0.67  color Cyan]
      [1.0   color Magenta]
    }
  object{My_Object
    pigment{
      gradient x
      color_map{Rainbow_Colors}
    }
  }

4.7.1.4   Pigment Maps and Pigment Lists
In addition to specifying blended colors with a color map you may
create a blend of pigments using a pigment_map. The syntax for a
pigment map is identical to a color map except you specify a
pigment in each map entry (and not a color).

The syntax for pigment_map is as follows:

PIGMENT_MAP:
  pigment_map{ PIGMENT_MAP_BODY }
PIGMENT_MAP_BODY:
  PIGMENT_MAP_IDENTIFIER   |   PIGMENT_MAP_ENTRY...
PIGMENT_MAP_ENTRY:
  [ Value  PIGMENT_BODY ]
Where Value is a float value between 0.0 and 1.0 inclusive and
each PIGMENT_BODY is anything which can be inside a pigment{...}
statement.  The pigment keyword and {} braces need not be
specified.

Note that the [] brackets are part of the actual
PIGMENT_MAP_ENTRY. They are not notational symbols denoting
optional parts. The brackets surround each entry in the pigment
map. There may be from 2 to 256 entries in the map.

For example

  sphere {
    <0,1,2>, 2
    pigment {
      gradient x       //this is the PATTERN_TYPE
      pigment_map {
        [0.3 wood scale 0.2]
        [0.3 Jade]    //this is a pigment identifier
        [0.6 Jade]
        [0.9 marble turbulence 1]
      }
    }
  }
When the gradient x function returns values from 0.0 to 0.3 the
scaled wood pigment is used. From 0.3 to 0.6 the pigment
identifier Jade is used. From 0.6 up to 0.9 a blend of Jade and a
turbulent marble is used. From 0.9 on up only the turbulent
marble is used.

Pigment maps may be nested to any level of complexity you desire.
The pigments in a map may have color maps or pigment maps or any
type of pigment you want. Any entry of a pigment map may be a
solid color however if all entries are solid colors you should
use a color_map which will render slightly faster.

Entire pigments may also be used with the block patterns such as
checker, hexagon and brick. For example...

  pigment {
    checker
    pigment { Jade scale .8 }
    pigment { White_Marble scale .5 }
  }
Note that in the case of block patterns the pigment wrapping is
required around the pigment information.

A pigment map is also used with the average pigment type. See
"Average" for details.

You may not use pigment_map or individual pigments with an
image_map. See section "Texture Maps" for an alternative way to
do this.

You may declare and use pigment map identifiers but the only way
to declare a pigment block pattern list is to declare a pigment
identifier for the entire pigment.


4.7.1.5   Image Maps
When all else fails and none of the above pigment pattern types
meets your needs you can use an image_map to wrap a 2-D bit-
mapped image around your 3-D objects.


4.7.1.5.1 Specifying an Image Map
The syntax for an image_map is:

IMAGE_MAP:
  pigment{
     image_map{ BITMAP_TYPE "bitmap.ext" [IMAGE_MAP_MODS...] }
     [PIGMENT_MODFIERS...]
  }
BITMAP_TYPE:
  gif   |   tga   |   iff   |   ppm   |   pgm   |   png   |
  sys
IMAGE_MAP_MOD:
  map_type  Type   |   once   |   interpolate  Type   |
  filter Palette, Amount   |   filter all Amount   |
  transmit Palette, Amount   |   transmit all Amount
After the required BITMAP_TYPE keyword is a string expression
containing the name of a bitmapped image file of the specified
type.  Several optional modifiers may follow the file
specification. The modifiers are described below. Note that
earlier versions of POV-Ray allowed some modifiers before the
BITMAP_TYPE but that syntax is being phased out in favor of the
syntax described here.  Note sys format is a system-specific
format such as BMP for Windows or Pict for Macintosh.

Filenames specified in the image_map statements will be searched
for in the home (current) directory first and, if not found, will
then be searched for in directories specified by any +L or
Library_Path options active. This would facilitate keeping all
your image maps files in a separate subdirectory and giving a
Library_Path option to specify where your library of image maps
are.  See "Library Paths" for details.

By default, the image is mapped onto the x-y-plane. The image is
projected onto the object as though there were a slide projector
somewhere in the -z-direction. The image exactly fills the square
area from (x,y) coordinates (0,0) to (1,1) regardless of the
image's original size in pixels. If you would like to change this
default you may translate, rotate or scale the pigment or texture
to map it onto the object's surface as desired.

In the section "Checker", the checker pigment pattern is
explained. The checks are described as solid cubes of colored
clay from which objects are carved. With image maps you should
imagine that each pixel is a long, thin, square, colored rod that
extends parallel to the z-axis. The image is made from rows and
columns of these rods bundled together and the object is then
carved from the bundle.

If you would like to change this default orientation you may
translate, rotate or scale the pigment or texture to map it onto
the object's surface as desired.

The file name is optionally followed by one or more
BITMAP_MODIFIERS.  The filter, filter all, transmit, and transmit
all modifiers are specific to image maps and are discussed in the
following sections.  An image_map may also use generic bitmap
modifiers map_type, once and interpolate described in "Bitmap
Modifiers"


4.7.1.5.2 The Filter and Transmit Bitmap Modifiers
To make all or part of an image map transparent you can specify
filter and/or transmit values for the color palette/registers of
PNG, GIF or IFF pictures (at least for the modes that use
palettes). You can do this by adding the keyword filter or
transmit following the filename. The keyword is followed by two
numbers. The first number is the palette number value and the
second is the amount of transparency. The values should be
separated by a comma. For example:

  image_map {
    gif "mypic.gif"
    filter   0, 0.5 // Make color 0 50% filtered transparent
    filter   5, 1.0 // Make color 5 100% filtered transparent
    transmit 8, 0.3 // Make color 8 30% non-filtered transparent
  }
You can give the entire image a filter or transmit value using
filter all Amount or transmit all Amount. For example:

  image_map {
    gif "stnglass.gif"
    filter all 0.9
  }
Note that early versions of POV-Ray used the keyword alpha to
specify filtered transparency however that word is often used to
describe non-filtered transparency. For this reason alpha is no
longer used.

See section "Specifying Colors" for details on the differences
between filtered and non-filtered transparency.


4.7.1.5.3 Using the Alpha Channel
Another way to specify non-filtered transmit transparency in an
image map is by using the alpha channel.  PNG file format allows
you to store a different transparency for each color index in the
PNG file, if desired. If your paint programs support this feature
of PNG you can do the transparency editing within your paint
program rather than specifying transmit values for each color in
the POV file. Since PNG and TGA image formats can also store full
alpha channel (transparency) information you can generate image
maps that have transparency which isn't dependent on the color of
a pixel but rather its location in the image.

Although POV uses transmit 0.0 to specify no transparency and 1.0
to specify full transparency, the alpha data ranges from 0 to 255
in the opposite direction. Alpha data 0 means the same as
transmit 1.0 and alpha data 255 produces transmit 0.0.


4.7.1.6   Quick Color
When developing POV-Ray scenes its often useful to do low quality
test runs that render faster. The +Q command line switch or
Quality INI option can be used to turn off some time consuming
color pattern and lighting calculations to speed things up. See
"Quality Settings" for details.  However all settings of +Q5 or
Quality=5 or lower turns off pigment calculations and creates
gray objects.

By adding a quick_color to a pigment you tell POV-Ray what solid
color to use for quick renders instead of a patterned pigment.
For example:

  pigment {
    gradient x
    color_map{
      [0.0 color Yellow]
      [0.3 color Cyan]
      [0.6 color Magenta]
      [1.0 color Cyan]
    }
    turbulence 0.5
    lambda 1.5
    omega 0.75
    octaves 8
    quick_color Neon_Pink
  }
This tells POV-Ray to use solid Neon_Pink for test runs at
quality +Q5 or lower but to use the turbulent gradient pattern
for rendering at +Q6 and higher.

Note that solid color pigments such as

  pigment {color Magenta}
automatically set the quick_color to that value. You may override
this if you want. Suppose you have 10 spheres on the screen and
all are yellow. If you want to identify them individually you
could give each a different quick_color like this:

  sphere {
    <1,2,3>,4
    pigment { color Yellow  quick_color Red }
  }
  sphere {
    <-1,-2,-3>,4
    pigment { color Yellow  quick_color Blue }
  }
and so on. At +Q6 or higher they will all be yellow but at +Q5 or
lower each would be different colors so you could identify them.

The alternate spelling quick_colour is also supported.


4.7.2     Normal
Ray-tracing is known for the dramatic way it depicts reflection,
refraction and lighting effects. Much of our perception depends
on the reflective properties of an object. Ray tracing can
exploit this by playing tricks on our perception to make us see
complex details that aren't really there.

Suppose you wanted a very bumpy surface on the object. It would
be very difficult to mathematically model lots of bumps. We can
however simulate the way bumps look by altering the way light
reflects off of the surface. Reflection calculations depend on a
vector called a surface normal vector. This is a vector which
points away from the surface and is perpendicular to it. By
artificially modifying (or perturbing) this normal vector you can
simulate bumps.  This is done by adding an optional normal
statement.

Note that attaching a normal pattern does not really modify the
surface. It only affects the way light reflects or refracts at
the surface so that it looks bumpy.  The syntax is:

NORMAL:
  normal{ [NORMAL_IDENTIFIER] [NORMAL_TYPE] [NORMAL_MODIFIER...]
  }
NORMAL_TYPE:
  PATTERN_TYPE Amount   |
  bump_map{ BITMAP_TYPE "bitmap.ext" [BUMP_MAP_MODS...] }
NORMAL_MODIFIER:
  PATTERN_MODIFIER   |   NORMAL_LIST   |
  normal_map{ NORMAL_MAP_BODY }   |
  slope_map{ SLOPE_MAP_BODY }   |
  bump_size Amount
Each of the items in a normal are optional but if they are
present, they must be in the order shown. Any items after the
NORMAL_IDENTIFIER modify or override settings given in the
identifier. If no identifier is specified then the items modify
the normal values in the current default texture. The
PATTERN_TYPE may optionally be followed by a float value that
controls the apparent depth of the bumps. Typical values range
from 0.0 to 1.0 but any value may be used. Negative values invert
the pattern. The default value if none is specified is 0.5.

There are four basic types of NORMAL_TYPEs. They are block
pattern normals, continuous pattern normals, specialized normals
and bump maps. They differ in the types of modifiers you may use
with them. The pattern type is optionally followed by one or more
normal modifiers.  In addition to general pattern modifiers such
as transformations, turbulence, and warp modifiers, normals may
also have a NORMAL_LIST, slope_map, normal_map, and
bump_sizewhich are specific to normals.  See "Pattern Modifiers"
for information on general modifiers.  The normal-specific
modifiers are described in sub-sections which follow.  Normal
modifiers of any kind apply only to the normal and not to other
parts of the texture. Modifiers must be specified last.

Originally POV-Ray had some patterns which were exclusively used
for pigments while others were exclusively used for normals.
Since POV-Ray 3.0 you can use any pattern for either pigments or
normals. For example it is now valid to use ripples as a pigment
or wood as a normal type. The patterns bumps, dents, ripples,
waves, wrinkles, and bump_map were once exclusively normal
patterns which could not be used as pigments. Because these six
types use specialized normal modification calculations they
cannot have slope_map, normal_map or wave shape modifiers. All
other normal pattern types may use them.  Because block patterns
checker, hexagon, and brick do not return a continuous series of
values, they cannot use these modifiers either.  See "Patterns"
for details about specific patterns.

A normal statement is part of a texture specification.  However
it can be tedious to use a texture statement just to add a bumps
to an object. Therefore you may attach a normal directly to an
object without explicitly specifying that it as part of a
texture. For example instead of this:

  object {My_Object texture{normal{bumps 0.5}}}
you may shorten it to:

  object {My_Object normal{bumps 0.5}}
Note however that doing so creates an entire texture structure
with default pigment and finish statements just as if you had
explicitly typed the full texture{...} around it.

Normal identifiers may be declared to make scene files more
readable and to parameterize scenes so that changing a single
declaration changes many values. An identifier is declared as
follows.

NORMAL_DECLARATION:
  #declare IDENTIFIER = NORMAL   |
  #local IDENTIFIER = NORMAL
Where IDENTIFIER is the name of the identifier up to 40
characters long and NORMAL is any valid normal statement.  See
"#declare vs. #local" for information on identifier scope.


4.7.2.1   Slope Maps
A slope_map is a normal pattern modifier which gives the user a
great deal of control over the exact shape of the bumpy features.
Each of the various pattern types available is in fact a
mathematical function that takes any x, y, z location and turns
it into a number between 0.0 and 1.0 inclusive. That number is
used to specify where the various high and low spots are.  The
slope_map lets you further shape the contours. It is best
illustrated with a gradient normal pattern. Suppose you have...

  plane{ z, 0
    pigment{ White }
    normal { gradient x }
  }
This gives a ramp wave pattern that looks like small linear ramps
that climb from the points at x=0 to x=1 and then abruptly drops
to 0 again to repeat the ramp from x=1 to x=2. A slope map turns
this simple linear ramp into almost any wave shape you want. The
syntax is as follows...

The syntax for slope_map is as follows:

SLOPE_MAP:
  slope_map{ SLOPE_MAP_BODY }
SLOPE_MAP_BODY:
  SLOPE_MAP_IDENTIFIER   |   SLOPE_MAP_ENTRY...
SLOPE_MAP_ENTRY:
  [ Value, <Height, Slope> ]
Note that the [] brackets are part of the actual SLOPE_MAP_ENTRY.
They are not notational symbols denoting optional parts. The
brackets surround each entry in the slope map. There may be from
2 to 256 entries in the map.

Each Value is a float value between 0.0 and 1.0 inclusive and
each <Height, Slope> is a 2 component vectors such as <0,1> where
the first value represents the apparent height of the wave and
the second value represents the slope of the wave at that point.
The height should range between 0.0 and 1.0 but any value could
be used.

The slope value is the change in height per unit of distance. For
example a slope of zero means flat, a slope of 1.0 means slope
upwards at a 45 degree angle and a slope of -1 means slope down
at 45 degrees. Theoretically a slope straight up would have
infinite slope. In practice, slope values should be kept in the
range -3.0 to +3.0. Keep in mind that this is only the visually
apparent slope. A normal does not actually change the surface.

For example here is how to make the ramp slope up for the first
half and back down on the second half creating a triangle wave
with a sharp peak in the center.

  normal {
    gradient x       // this is the PATTERN_TYPE
    slope_map {
      [0   <0, 1>]   // start at bottom and slope up
      [0.5 <1, 1>]   // halfway through reach top still climbing
      [0.5 <1,-1>]   // abruptly slope down
      [1   <0,-1>]   // finish on down slope at bottom
    }
  }
The pattern function is evaluated and the result is a value from
0.0 to 1.0. The first entry says that at x=0 the apparent height
is 0 and the slope is 1. At x=0.5 we are at height 1 and slope is
still up at 1. The third entry also specifies that at x=0.5
(actually at some tiny fraction above 0.5) we have height 1 but
slope -1 which is downwards. Finally at x=1 we are at height 0
again and still sloping down with slope -1.

Although this example connects the points using straight lines
the shape is actually a cubic spline. This example creates a
smooth sine wave.

  normal {
    gradient x          // this is the PATTERN_TYPE
    slope_map {
      [0    <0.5, 1>]   // start in middle and slope up
      [0.25 <1.0, 0>]   // flat slope at top of wave
      [0.5  <0.5,-1>]   // slope down at mid point
      [0.75 <0.0, 0>]   // flat slope at bottom
      [1    <0.5, 1>]   // finish in middle and slope up
    }
  }
This example starts at height 0.5 sloping up at slope 1. At a
fourth of the way through we are at the top of the curve at
height 1 with slope 0 which is flat. The space between these two
is a gentle curve because the start and end slopes are different.
At half way we are at half height sloping down to bottom out at
3/4ths. By the end we are climbing at slope 1 again to complete
the cycle. There are more examples in slopemap.pov in the sample
scenes.

A slope_map may be used with any pattern except brick, checker,
hexagon, bumps, dents, ripples, waves, wrinkles and bump_map.

You may declare and use slope map identifiers. For example:

  #declare Fancy_Wave =
    slope_map {       // Now let's get fancy
      [0.0  <0, 1>]   // Do tiny triangle here
      [0.2  <1, 1>]   //  down
      [0.2  <1,-1>]   //     to
      [0.4  <0,-1>]   //       here.
      [0.4  <0, 0>]   // Flat area
      [0.5  <0, 0>]   //   through here.
      [0.5  <1, 0>]   // Square wave leading edge
      [0.6  <1, 0>]   //   trailing edge
      [0.6  <0, 0>]   // Flat again
      [0.7  <0, 0>]   //   through here.
      [0.7  <0, 3>]   // Start scallop
      [0.8  <1, 0>]   //   flat on top
      [0.9  <0,-3>]   //     finish here.
      [0.9  <0, 0>]   // Flat remaining through 1.0
    }
  object{ My_Object
    pigment { White }
    normal {
      wood
      slope_map { Fancy_Wave }
    }
  }

4.7.2.2   Normal Maps and Normal Lists
Most of the time you will apply single normal pattern to an
entire surface but you may also create a pattern or blend of
normals using a normal_map. The syntax for a normal_map is
identical to a pigment_map except you specify a normal in each
map entry.

The syntax for normal_map is as follows:

NORMAL_MAP:
  normal_map{ NORMAL_MAP_BODY }
NORMAL_MAP_BODY:
  NORMAL_MAP_IDENTIFIER   |   NORMAL_MAP_ENTRY...
NORMAL_MAP_ENTRY:
  [ Value  NORMAL_BODY ]
Where Value is a float value between 0.0 and 1.0 inclusive and
each NORMAL_BODY is anything which can be inside a normal{...}
statement.  The normal keyword and {} braces need not be
specified.

Note that the [] brackets are part of the actual
NORMAL_MAP_ENTRY. They are not notational symbols denoting
optional parts. The brackets surround each entry in the normal
map. There may be from 2 to 256 entries in the map.

For example

  normal {
    gradient x       //this is the PATTERN_TYPE
    normal_map {
      [0.3  bumps scale 2]
      [0.3  dents]
      [0.6  dents]
      [0.9  marble turbulence 1]
    }
  }
When the gradient x function returns values from 0.0 to 0.3 then
the scaled bumps normal is used. From 0.3 to 0.6 dents are From
0.6 up to 0.9 a blend of dents and a turbulent marble is used.
From 0.9 on up only the turbulent marble is used.

Normal maps may be nested to any level of complexity you desire.
The normals in a map may have slope maps or normal maps or any
type of normal you want.

A normal map is also used with the average normal type. See
"Average" for details.

Entire normals in a normal list may also be used with the block
patterns such as checker, hexagon and brick. For example...

  normal {
    checker
      normal { gradient x scale .2 }
      normal { gradient y scale .2 }
    }
  }
Note that in the case of block patterns the normal wrapping is
required around the normal information.

You may not use normal_map or individual normals with a bump_map.
See section "Texture Maps" for an alternative way to do this.

You may declare and use normal map identifiers but the only way
to declare a normal block pattern list is to declare a normal
identifier for the entire normal.


4.7.2.3   Bump Maps
When all else fails and none of the above normal pattern types
meets your needs you can use a bump_map to wrap a 2-D bit-mapped
bump pattern around your 3-D objects.

Instead of placing the color of the image on the shape like an
image_map a bump_map perturbs the surface normal based on the
color of the image at that point. The result looks like the image
has been embossed into the surface. By default, a bump map uses
the brightness of the actual color of the pixel. Colors are
converted to gray scale internally before calculating height.
Black is a low spot, white is a high spot. The image's index
values may be used instead (see section "Use_Index and Use_Color"
below).


4.7.2.3.1 Specifying a Bump Map
The syntax for an bump_map is:

BUMP_MAP:
  normal{
     bump_map{ BITMAP_TYPE "bitmap.ext" [BUMP_MAP_MODS...] }
     [NORMAL_MODFIERS...]
  }
BITMAP_TYPE:
  gif   |   tga   |   iff   |   ppm   |   pgm   |   png   |
  sys
BUMP_MAP_MOD:
  map_type  Type   |   once   |   interpolate  Type   |
  use_color   |   use_colour   |   bump_size  Value
After the required BITMAP_TYPE keyword is a string expression
containing the name of a bitmapped bump file of the specified
type.  Several optional modifiers may follow the file
specification. The modifiers are described below. Note that
earlier versions of POV-Ray allowed some modifiers before the
BITMAP_TYPE but that syntax is being phased out in favor of the
syntax described here.  Note sys format is a system-specific
format such as BMP for Windows or Pict for Macintosh.

Filenames specified in the bump_map statements will be searched
for in the home (current) directory first and, if not found, will
then be searched for in directories specified by any +L or
Library_Path options active. This would facilitate keeping all
your bump maps files in a separate subdirectory and giving a
Library_Path option to specify where your library of bump maps
are.  See "Library Paths" for details.

By default, the bump pattern is mapped onto the x-y-plane. The
bump pattern is projected onto the object as though there were a
slide projector somewhere in the -z-direction. The pattern
exactly fills the square area from (x,y) coordinates (0,0) to
(1,1) regardless of the pattern's original size in pixels. If you
would like to change this default you may translate, rotate or
scale the pigment or texture to map it onto the object's surface
as desired.  If you would like to change this default orientation
you may translate, rotate or scale the pigment or texture to map
it onto the object's surface as desired.

The file name is optionally followed by one or more
BITMAP_MODIFIERS. The bump_size, use_color and use_index
modifiers are specific to bump maps and are discussed in the
following sections. See section "Bitmap Modifiers" for the
generic bitmap modifiers map_type, once and interpolate described
in "Bitmap Modifiers"


4.7.2.3.2 Bump_Size
The relative bump size can be scaled using the bump_size
modifier.  The bump size number can be any number other than 0
but typical values are from about 0.1 to as high as 4.0 or 5.0.

  normal {
    bump_map {
      gif "stuff.gif"
      bump_size 5.0
    }
  }
Originally bump_size could only be used inside a bump map but it
can now be used with any normal. Typically it is used to override
a previously defined size. For example:

  normal {
    My_Normal   //this is a previously defined normal identifier
    bump_size 2.0
  }

4.7.2.3.3 Use_Index and Use_Color
Usually the bump map converts the color of the pixel in the map
to a gray scale intensity value in the range 0.0 to 1.0 and
calculates the bumps based on that value. If you specify
use_index, the bump map uses the color's palette number to
compute as the height of the bump at that point. So, color number
0 would be low and color number 255 would be high (if the image
has 256 palette entries). The actual color of the pixels doesn't
matter when using the index. This option is only available on
palette based formats. The use_color keyword may be specified to
explicitly note that the color methods should be used instead.
The alternate spelling use_colour is also valid. These modifiers
may only be used inside the bump_map statement.


4.7.3     Finish
The finish properties of a surface can greatly affect its
appearance. How does light reflect? What happens in shadows? What
kind of highlights are visible. To answer these questions you
need a finish.

The syntax for finish is as follows:

FINISH:
  finish { [FINISH_IDENTIFIER] [FINISH_ITEMS...] }
FINISH_ITEMS:
  ambient COLOR   |   diffuse Amount   |   brilliance Amount   |
  phong Amount   |   phong_size Amount   |
  specular Amount   |   roughness Amount   |
  metallic [Amount]   |   reflection COLOR   |
  reflection_exponent Amount   |
  irid { Irid_Amount [IRID_ITEMS...] }   |   crand Amount
IRID_ITEMS:
  thickness Amount   |   turbulence Amount
The FINISH_IDENTIFIER is optional but should proceed all other
items. Any items after the FINISH_IDENTIFIER modify or override
settings given in the FINISH_IDENTIFIER. If no identifier is
specified then the items modify the finish values in the current
default texture.  Note that transformations are not allowed
inside a finish because finish items cover the entire surface
uniformly.  Each of the FINISH_ITEMS listed above is described in
sub-sections below.

In earlier versions of POV-Ray, the refraction, ior, and caustics
keywords were part of the finish statement but they are now part
of the interior statement.  They are still supported under finish
for backward compatibility but the results may not be 100%
identical to previous versions. See "Why are Interior and Media
Necessary?" for details.

A finish statement is part of a texture specification.  However
it can be tedious to use a texture statement just to add a
highlights or other lighting properties to an object. Therefore
you may attach a finish directly to an object without explicitly
specifying that it as part of a texture. For example instead of
this:

  object {My_Object texture{finish{phong 0.5}}}
you may shorten it to:

  object {My_Object finish{phong 0.5}}
Note however that doing so creates an entire texture structure
with default pigment and normal statements just as if you had
explicitly typed the full texture{...} around it.

Finish identifiers may be declared to make scene files more
readable and to parameterize scenes so that changing a single
declaration changes many values. An identifier is declared as
follows.

FINISH_DECLARATION:
  #declare IDENTIFIER = FINISH   |
  #local IDENTIFIER = FINISH
Where IDENTIFIER is the name of the identifier up to 40
characters long and FINISH is any valid finish statement.  See
"#declare vs. #local" for information on identifier scope.


4.7.3.1   Ambient
The light you see in dark shadowed areas comes from diffuse
reflection off of other objects. This light cannot be directly
modeled using ray-tracing. However we can use a trick called
ambient lighting to simulate the light inside a shadowed area.

Ambient light is light that is scattered everywhere in the room.
It bounces all over the place and manages to light objects up a
bit even where no light is directly shining. Computing real
ambient light would take far too much time, so we simulate
ambient light by adding a small amount of white light to each
texture whether or not a light is actually shining on that
texture.

This means that the portions of a shape that are completely in
shadow will still have a little bit of their surface color. It's
almost as if the texture glows, though the ambient light in a
texture only affects the shape it is used on.

The ambient keyword controls the amount of ambient light. Usually
a single float value is specified even though the syntax calls
for a color. For example a float value of 0.3 gets promoted to
the full color vector <0.3,0.3,0.3,0.3,0.3> which is acceptable
because only the red, green and blue parts are used.

The default value is 0.1 which gives very little ambient light.
The value can range from 0.0 to 1.0. Ambient light affects both
shadowed and non-shadowed areas so if you turn up the ambient
value you may want to turn down the diffuse and reflection
values.

Note that this method doesn't account for the color of
surrounding objects. If you walk into a room that has red walls,
floor and ceiling then your white clothing will look pink from
the reflected light. POV-Ray's ambient shortcut doesn't account
for this. There is also no way to model specular reflected
indirect illumination such as the flashlight shining in a mirror.

You may color the ambient light using one of two methods. You may
specify a color rather than a float after the ambient keyword in
each finish statement. For example

   finish { ambient rgb <0.3,0.1,0.1> } //a pink ambient
You may also specify the overall ambient light source used when
calculating the ambient lighting of an object using the global
ambient_light setting. The formula is given by

   Ambient = Finish_Ambient * Global_Ambient_Light_Source

See section "Ambient Light" for details.


4.7.3.2   Diffuse Reflection Items
When light reflects off of a surface the laws of physics say that
it should leave the surface at the exact same angle it came in.
This is similar to the way a billiard ball bounces off a bumper
of a pool table. This perfect reflection is called specular
reflection. However only very smooth polished surfaces reflect
light in this way. Most of the time, light reflects and is
scattered in all directions by the roughness of the surface. This
scattering is called diffuse reflection because the light
diffuses or spreads in a variety of directions. It accounts for
the majority of the reflected light we see.

POV-Ray and most other ray-tracers can only simulate directly
light which comes directly from actual light sources.  Light
coming from other objects such as mirrors via specular reflection
(such as shining a flashlight onto a mirror for example) cannot
be simulated.  Neither can we simulate light coming from other
objects via diffuse reflections.  For example look at some dark
area under a desk or in a corner: even though a lamp may not
directly illuminate that spot, you can still see a little bit
because light comes from diffuse reflection off of nearby
objects.


4.7.3.2.1 Diffuse
The keyword diffuse is used in a finish statement to control how
much of the light coming directly from any light sources is
reflected via diffuse reflection. For example

  finish {diffuse 0.7}
means that 70% of the light seen comes from direct illumination
from light sources. The default value is diffuse 0.6.


4.7.3.2.2 Brilliance
The amount of direct light that diffuses from an object depends
upon the angle at which it hits the surface. When light hits at a
shallow angle it illuminates less. When it is directly above a
surface it illuminates more. The brilliance keyword can be used
in a finish statement to vary the way light falls off depending
upon the angle of incidence.  This controls the tightness of the
basic diffuse illumination on objects and slightly adjusts the
appearance of surface shininess.  Objects may appear more
metallic by increasing their brilliance. The default value is
1.0.  Higher values from 5.0 to about 10.0 cause the light to
fall off less at medium to low angles. There are no limits to the
brilliance value.  Experiment to see what works best for a
particular situation. This is best used in concert with
highlighting.


4.7.3.2.3 Crand Graininess
Very rough surfaces, such as concrete or sand, exhibit a dark
graininess in their apparent color. This is caused by the shadows
of the pits or holes in the surface. The crand keyword can be
added to a finish cause a minor random darkening in the diffuse
reflection of direct illumination. Typical values range from
crand 0.01 to crand 0.5 or higher. The default value is 0. For
example:

  finish { crand 0.05 }
This feature is carried over from the earliest versions of POV-
Ray and is considered obsolete. This is because the grain or
noise introduced by this feature is applied on a pixel-by-pixel
basis. This means that it will look the same on far away objects
as on close objects. The effect also looks different depending
upon the resolution you are using for the rendering. Note that
this should not be used when rendering animations. This is the
one of a few truly random features in POV-Ray and will produce an
annoying flicker of flying pixels on any textures animated with a
crand value.  For these reasons it is not a very accurate way to
model the rough surface effect.


4.7.3.3   Highlights
Highlights are the bright spots that appear when a light source
reflects off of a smooth object. They are a blend of specular
reflection and diffuse reflection. They are specular-like because
they depend upon viewing angle and illumination angle. However
they are diffuse-like because some scattering occurs. In order to
exactly model a highlight you would have to calculate specular
reflection off of thousands of microscopic bumps called micro
facets. The more that micro facets are facing the viewer the
shinier the object appears and the tighter the highlights become.
POV-Ray uses two different models to simulate highlights without
calculating micro facets. They are the specular and Phong models.

Note that specular and Phong highlights are not mutually
exclusive. It is possible to specify both and they will both take
effect. Normally, however, you will only specify one or the
other.


4.7.3.3.1 Phong Highlights
The phong keyword in the finish statement controls the amount of
Phong highlighting on the object. It causes bright shiny spots on
the object that are the color of the light source being
reflected.

The Phong method measures the average of the facets facing in the
mirror direction from the light sources to the viewer.

Phong's value is typically from 0.0 to 1.0, where 1.0 causes
complete saturation to the light source's color at the brightest
area (center) of the highlight. The default phong 0.0 gives no
highlight.

The size of the highlight spot is defined by the phong_size
value. The larger the phong size the tighter, or smaller, the
highlight and the shinier the appearance.  The smaller the phong
size the looser, or larger, the highlight and the less glossy the
appearance.

Typical values range from 1.0 (very dull) to 250 (highly
polished) though any values may be used. Default phong size is 40
(plastic) if phong_size is not specified. For example:

  finish { phong 0.9 phong_size 60 }
If phong is not specified phong_size has no effect.


4.7.3.3.2 Specular Highlight
The specular keyword in a finish statement produces a highlight
which is very similar to Phong highlighting but it uses slightly
different model. The specular model more closely resembles real
specular reflection and provides a more credible spreading of the
highlights occurring near the object horizons.

The specular value is typically from 0.0 to 1.0, where 1.0 causes
complete saturation to the light source's color at the brightest
area (center) of the highlight. The default specular 0.0 gives no
highlight.

The size of the spot is defined by the value given the roughness
keyword. Typical values range from 1.0 (very rough - large
highlight) to 0.0005 (very smooth - small highlight). The default
value, if roughness is not specified, is 0.05 (plastic).

It is possible to specify wrong values for roughness that will
generate an error when you try to render the file. Don't use 0
and if you get errors check to see if you are using a very, very
small roughness value that may be causing the error. For example:

  finish {specular 0.9  roughness 0.02}
If specular is not specified roughness has no effect.

Note that when light reflects perfectly of a smooth surface such
as a mirror, it is called specular reflection however such
reflection is not controlled by the specular keyword. The
reflection keyword controls mirror-like specular reflection.


4.7.3.3.3 Metallic Highlight Modifier
The keyword metallic may be used with Phong or specular
highlights. This keyword indicates that the color of the
highlights will be calculated by an empirical function that
models the reflectivity of metallic surfaces.

Normally highlights are the color of the light source.  Adding
this keyword filters the highlight so that white light reflected
from a metallic surface takes the color of the surface.

The metallic keyword may optionally be follow by a numeric value
to specify the influence the amount of the effect.  If no keyword
is specified, the default value is zero.  If the keyword is
specified without a value, the default value is one. For example:

  finish {
    phong 0.9
    phong_size 60
    metallic
  }
If phong or specular keywords are not specified then metallic has
no effect.


4.7.3.4   Specular Reflection
When light does not diffuse and it does reflect at the same angle
as it hits an object, it is called specular reflection. Such
mirror-like reflection is controlled by the reflection keyword in
a finish statement. For example:

  finish { reflection 1.0 ambient 0 diffuse 0 }
This gives the object a mirrored finish. It will reflect all
other elements in the scene. Usually a single float value is
specified after the keyword even though the syntax calls for a
color. For example a float value of 0.3 gets promoted to the full
color vector < 0.3,0.3,0.3,0.3,0.3> which is acceptable because
only the red, green and blue parts are used.

The value can range from 0.0 to 1.0. By default there is no
reflection.

Adding reflection to a texture makes it take longer to render
because an additional ray must be traced. The reflected light may
be tinted by specifying a color rather than a float. For example

   finish { reflection rgb <1,0,0> }
gives a red mirror that only reflects red light.

POV-Ray uses a limited light model that cannot distinguish
between objects which are simply brightly colored and objects
which are extremely bright.  A white piece of paper, a light
bulb, the sun, and a supernova, all would be modeled as
rgb<1,1,1> and slightly off-white objects would be only slightly
darker.  It is especially difficult to model partially reflective
surfaces in a realistic way.  Middle and lower brightness objects
typically look too bright when reflected.  If you reduce the
reflection value, it tends to darken the bright objects too much.
Therefore the reflection_exponent keyword has been added.  It
produces non-linear reflection intensities.  The default value of
1.0 produces a linear curve.  Lower values darken middle and low
intensities and keeps high intensity reflections bright.  This is
a somewhat experimental feature designed for artistic use.  It
does not directly correspond to any real world reflective
properties.  We are researching ways to deal with this issue in a
more scientific model.  The reflection_exponent has no effect
unless reflection is used.

Note that although such reflection is called specular it is not
controlled by the specular keyword. That keyword controls a
specular highlight.


4.7.3.5   Iridescence
Iridescence, or Newton's thin film interference, simulates the
effect of light on surfaces with a microscopic transparent film
overlay. The effect is like an oil slick on a puddle of water or
the rainbow hues of a soap bubble.  This effect is controlled by
the irid statement specified inside a finish statement.

This parameter modifies the surface color as a function of the
angle between the light source and the surface. Since the effect
works in conjunction with the position and angle of the light
sources to the surface it does not behave in the same ways as a
procedural pigment pattern.

The syntax is:

IRID:
  irid { Irid_Amount [IRID_ITEMS...] }
IRID_ITEMS:
  thickness Amount   |   turbulence Amount
The required Irid_Amount parameter is the contribution of the
iridescence effect to the overall surface color. As a rule of
thumb keep to around 0.25 (25% contribution) or less, but
experiment. If the surface is coming out too white, try lowering
the diffuse and possibly the ambient values of the surface.

The thickness keyword represents the film's thickness. This is an
awkward parameter to set, since the thickness value has no
relationship to the object's scale.  Changing it affects the
scale or busy-ness of the effect. A very thin film will have a
high frequency of color changes while a thick film will have
large areas of color.  The default value is zero.

The thickness of the film can be varied with the turbulence
keyword. You can only specify the amount of turbulence with
iridescence.  The octaves, lambda, and omega values are
internally set and are not adjustable by the user at this time.
This parameter varies only a single value: the thickness.
Therefore the value must be a single float value.  It cannot be a
vector as in other uses of the turbulence keyword.

In addition, perturbing the object's surface normal through the
use of bump patterns will affect iridescence.

For the curious, thin film interference occurs because, when the
ray hits the surface of the film, part of the light is reflected
from that surface, while a portion is transmitted into the film.
This subsurface ray travels through the film and eventually
reflects off the opaque substrate. The light emerges from the
film slightly out of phase with the ray that was reflected from
the surface.

This phase shift creates interference, which varies with the
wavelength of the component colors, resulting in some wavelengths
being reinforced, while others are cancelled out. When these
components are recombined, the result is iridescence.  See also
the global setting "Irid_Wavelength".

The concept used for this feature came from the book Fundamentals
of Three-Dimensional Computer Graphics by Alan Watt (Addison-
Wesley).


4.7.4     Halo
Earlier versions of POV-Ray used a feature called halo to
simulate fine particles such as smoke, steam, fog, or flames.
The halo statement was part of the texture statement.  This
feature has been discontinued and replaced by the interior and
media statements which are object modifiers outside the texture
statement.

See "Why are Interior and Media Necessary?" for a detailed
explanation on the reasons for the change.  See "Media" for
details on media.


4.7.5     Patterned Textures
Patterned textures are complex textures made up of multiple
textures.  The component textures may be plain textures or may be
made up of patterned textures. A plain texture has just one
pigment, normal and finish statement. Even a pigment with a
pigment map is still one pigment and thus considered a plain
texture as are normals with normal map statements.

Patterned textures use either a texture_map statement to specify
a blend or pattern of textures or they use block textures such as
checker with a texture list or a bitmap similar to an image map
called a material map specified with a material_map statement.

The syntax is...

PATTERNED_TEXTURE:
  texture { [PATTERNED_TEXTURE_ID] [TRANSFORMATIONS...] }   |
  texture { PATTERN_TYPE [TEXTURE_PATTERN_MODIFIERS...] }   |
  texture { tiles TEXTURE  tile2 TEXTURE [TRANSFORMATIONS...] }
  |
  texture {
     material_map{
       BITMAP_TYPE "bitmap.ext" [BITMAP_MODS...] TEXTURE...
     [TRANSFORMATIONS...]
     }
  }
TEXTURE_PATTERN_MODIFIER:
  PATTERN_MODIFIER   |   TEXTURE_LIST   |
  texture_map{ TEXTURE_MAP_BODY }
There are restrictions on using patterned textures. A patterned
texture may not be used as a default texture (see section "The
#default Directive"). A patterned texture cannot be used as a
layer in a layered texture however you may use layered textures
as any of the textures contained within a patterned texture.


4.7.5.1   Texture Maps
In addition to specifying blended color with a color map or a
pigment map you may create a blend of textures using texture_map.
The syntax for a texture map is identical to the pigment map
except you specify a texture in each map entry.

The syntax for texture_map is as follows:

TEXTURE_MAP:
  texture_map{ TEXTURE_MAP_BODY }
TEXTURE_MAP_BODY:
  TEXTURE_MAP_IDENTIFIER   |   TEXTURE_MAP_ENTRY...
TEXTURE_MAP_ENTRY:
  [ Value  TEXTURE_BODY ]
Where Value is a float value between 0.0 and 1.0 inclusive and
each TEXTURE_BODY is anything which can be inside a texture{...}
statement.  The texture keyword and {} braces need not be
specified.

Note that the [] brackets are part of the actual
TEXTURE_MAP_ENTRY. They are not notational symbols denoting
optional parts. The brackets surround each entry in the texture
map. There may be from 2 to 256 entries in the map.

For example:

  texture {
    gradient x       //this is the PATTERN_TYPE
    texture_map {
      [0.3  pigment{Red} finish{phong 1}]
      [0.3  T_Wood11]    //this is a texture identifier
      [0.6  T_Wood11]
      [0.9  pigment{DMFWood4} finish{Shiny}]
    }
  }
When the gradient x function returns values from 0.0 to 0.3 the
red highlighted texture is used. From 0.3 to 0.6 the texture
identifier T_Wood11 is used. From 0.6 up to 0.9 a blend of
T_Wood11 and a shiny DMFWood4 is used. From 0.9 on up only the
shiny wood is used.

Texture maps may be nested to any level of complexity you desire.
The textures in a map may have color maps or texture maps or any
type of texture you want.

The blended area of a texture map works by fully calculating both
contributing textures in their entirety and then linearly
interpolating the apparent colors. This means that reflection,
refraction and lighting calculations are done twice for every
point.  This is in contrast to using a pigment map and a normal
map in a plain texture, where the pigment is computed, then the
normal, then reflection, refraction and lighting are calculated
once for that point.

Entire textures may also be used with the block patterns such as
checker, hexagon and brick. For example...

  texture {
    checker
      texture { T_Wood12 scale .8 }
      texture {
        pigment { White_Marble }
        finish { Shiny }
        scale .5
      }
    }
  }
Note that in the case of block patterns the texture wrapping is
required around the texture information. Also note that this
syntax prohibits the use of a layered texture however you can
work around this by declaring a texture identifier for the
layered texture and referencing the identifier.

A texture map is also used with the average texture type. See
"Average" for details.

You may declare and use texture map identifiers but the only way
to declare a texture block pattern list is to declare a texture
identifier for the entire texture.


4.7.5.2   Tiles
Earlier versions of POV-Ray had a patterned texture called a
tiles texture.  It used the tiles and tile2 keywords to create a
checkered pattern of textures.

TILES_TEXTURE:
  texture { tiles TEXTURE  tile2 TEXTURE [TRANSFORMATIONS...] }
Although it is still supported for backwards compatibility you
should use a checker block texture pattern described in section
"Texture Maps" rather than tiles textures.


4.7.5.3   Material Maps
The material_map patterned texture extends the concept of image
maps to apply to entire textures rather than solid colors. A
material map allows you to wrap a 2-D bit-mapped texture pattern
around your 3-D objects.

Instead of placing a solid color of the image on the shape like
an image map, an entire texture is specified based on the index
or color of the image at that point. You must specify a list of
textures to be used like a texture palette rather than the usual
color palette.

When used with mapped file types such as GIF, and some PNG and
TGA images, the index of the pixel is used as an index into the
list of textures you supply. For unmapped file types such as some
PNG and TGA images the 8 bit value of the red component in the
range 0-255 is used as an index.

If the index of a pixel is greater than the number of textures in
your list then the index is taken modulo N where N is the length
of your list of textures.

Note: The material_map statement has nothing to do with the
material statement.  A material_map is not a way to create
patterned material.  See "Material" for explanation of this
unrelated, yet similarly named, older feature.


4.7.5.3.1 Specifying a Material Map
The syntax for an material_map is:

MATERIAL_MAP:
  texture {
     material_map{
       BITMAP_TYPE "bitmap.ext" [BITMAP_MODS...] TEXTURE...
     [TRANSFORMATIONS...]
     }
  }
BITMAP_TYPE:
  gif   |   tga   |   iff   |   ppm   |   pgm   |   png   |
  sys
BITMAP_MOD:
  map_type  Type   |   once   |   interpolate  Type
After the required BITMAP_TYPE keyword is a string expression
containing the name of a bitmapped material file of the specified
type.  Several optional modifiers may follow the file
specification. The modifiers are described below. Note that
earlier versions of POV-Ray allowed some modifiers before the
BITMAP_TYPE but that syntax is being phased out in favor of the
syntax described here.  Note sys format is a system-specific
format such as BMP for Windows or Pict for Macintosh.

Filenames specified in the material_map statements will be
searched for in the home (current) directory first and, if not
found, will then be searched for in directories specified by any
+L or Library_Path options active. This would facilitate keeping
all your material maps files in a separate subdirectory and
giving a Library_Path option to specify where your library of
material maps are.  See "Library Paths" for details.

By default, the material is mapped onto the x-y-plane. The
material is projected onto the object as though there were a
slide projector somewhere in the -z-direction. The material
exactly fills the square area from (x,y) coordinates (0,0) to
(1,1) regardless of the material's original size in pixels. If
you would like to change this default you may translate, rotate
or scale the texture or texture to map it onto the object's
surface as desired.

The file name is optionally followed by one or more
BITMAP_MODIFIERS.  There are no modifiers which are unique to a
material_map.  It only uses the generic bitmap modifiers
map_type, once and interpolate described in "Bitmap Modifiers".

Although interpolate is legal in material maps, the color index
is interpolated before the texture is chosen. It does not
interpolate the final color as you might hope it would. In
general, interpolation of material maps serves no useful purpose
but this may be fixed in future versions.

Next is one or more texture statements.  Each texture in the list
corresponds to an index in the bitmap file.  For example:

   texture {
      material_map {
         png "povmap.png"
         texture {  //used with index 0
            pigment {color red 0.3 green 0.1 blue 1}
            normal  {ripples 0.85 frequency 10 }
            finish  {specular 0.75}
            scale 5
         }
         texture {  //used with index 1
            pigment {White}
            finish {ambient 0 diffuse 0 reflection 0.9 specular
0.75}
         }
         // used with index 2
         texture {pigment{NeonPink} finish{Luminous}}
         texture {  //used with index 3
            pigment {
               gradient y
               color_map {
                  [0.00 rgb < 1 , 0 , 0>]
                  [0.33 rgb < 0 , 0 , 1>]
                  [0.66 rgb < 0 , 1 , 0>]
                  [1.00 rgb < 1 , 0 , 0>]
               }
            }
            finish{specular 0.75}
            scale 8
         }
      }
      scale 30
      translate <-15, -15, 0>
   }
After a material_map statement but still inside the texture
statement you may apply any legal texture modifiers. Note that no
other pigment, normal, or finish statements may be added to the
texture outside the material map. The following is illegal:

  texture {
    material_map {
      gif "matmap.gif"
      texture {T1}
      texture {T2}
      texture {T3}
    }
    finish {phong 1.0}
  }
The finish must be individually added to each texture.  Note that
earlier versions of POV-Ray allowed such specifications but they
were ignored. The above restrictions on syntax were necessary for
various bug fixes. This means some POV-Ray 1.0 scenes using
material maps many need minor modifications that cannot be done
automatically with the version compatibility mode.

If particular index values are not used in an image then it may
be necessary to supply dummy textures. It may be necessary to use
a paint program or other utility to examine the map file's
palette to determine how to arrange the texture list.

The textures within a material map texture may be layered but
material map textures do not work as part of a layered texture.
To use a layered texture inside a material map you must declare
it as a texture identifier and invoke it in the texture list.


4.7.6     Layered Textures
It is possible to create a variety of special effects using
layered textures. A layered texture consists of several textures
that are partially transparent and are laid one on top of the
other to create a more complex texture. The different texture
layers show through the transparent portions to create the
appearance of one texture that is a combination of several
textures.

You create layered textures by listing two or more textures one
right after the other. The last texture listed will be the top
layer, the first one listed will be the bottom layer. All
textures in a layered texture other than the bottom layer should
have some transparency.  For example:

  object {
    My_Object
    texture {T1}  // the bottom layer
    texture {T2}  // a semi-transparent layer
    texture {T3}  // the top semi-transparent layer
  }
In this example T2 shows only where T3 is transparent and T1
shows only where T2 and T3 are transparent.

The color of underlying layers is filtered by upper layers but
the results do not look exactly like a series of transparent
surfaces. If you had a stack of surfaces with the textures
applied to each, the light would be filtered twice: once on the
way in as the lower layers are illuminated by filtered light and
once on the way out. Layered textures do not filter the
illumination on the way in. Other parts of the lighting
calculations work differently as well. The results look great and
allow for fantastic looking textures but they are simply
different from multiple surfaces. See stones.inc in the standard
include files directory for some magnificent layered textures.

Note layered textures must use the texture wrapped around any
pigment, normal or finish statements. Do not use multiple
pigment, normal or finish statements without putting them inside
the texture statement.

Layered textures may be declared. For example

  #declare Layered_Examp =
    texture {T1}
    texture {T2}
    texture {T3}
may be invoked as follows:

  object {
    My_Object
    texture {
      Layer_Examp
      // Any pigment, normal or finish here
      // modifies the bottom layer only.
    }
  }
If you wish to use a layered texture in a block pattern, such as
checker, hexagon, or brick, or in a material_map, you must
declare it first and then reference it inside a single texture
statement. A patterned texture cannot be used as a layer in a
layered texture however you may use layered textures as any of
the textures contained within a patterned texture.


4.7.7     Patterns
POV-Ray uses a method called three-dimensional solid texturing to
define the color, bumpiness and other properties of an object.
You specify the way that the texture varies over a surface by
specifying a pattern.  Patterns are used in pigments, normals and
texture maps as well as media density.

All patterns in POV-Ray are three dimensional. For every point in
space, each pattern has a unique value. Patterns do not wrap
around a surface like putting wallpaper on an object. The
patterns exist in 3d and the objects are carved from them like
carving an object from a solid block of wood or stone.

Consider a block of wood. It contains light and dark bands that
are concentric cylinders being the growth rings of the wood. On
the end of the block you see these concentric circles. Along its
length you see lines that are the veins. However the pattern
exists throughout the entire block. If you cut or carve the wood
it reveals the pattern inside. Similarly an onion consists of
concentric spheres that are visible only when you slice it.
Marble stone consists of wavy layers of colored sediments that
harden into rock.

These solid patterns can be simulated using mathematical
functions. Other random patterns such as granite or bumps and
dents can be generated using a random number system and a noise
function.

In each case, the x, y, z coordinate of a point on a surface is
used to compute some mathematical function that returns a float
value. When used with color maps or pigment maps, that value
looks up the color of the pigment to be used. In normal
statements the pattern function result modifies or perturbs the
surface normal vector to give a bumpy appearance. Used with a
texture map, the function result determines which combinations of
entire textures to be used.  When used with media density it
specifies the density of the particles or gasses.

The following sections describe each pattern. See the sections
"Pigment", "Normal", "Patterned Textures" and "Density" for more
details on how to use patterns. Unless mentioned otherwise, all
patterns use the ramp_wave wave type by default but may use any
wave type and may be used with color_map, pigment_map,
normal_map, slope_map, texture_map, density, and density_map.


4.7.7.1   Agate
The agate pattern is a banded pattern similar to marble but it
uses a specialized built-in turbulence function that is different
from the traditional turbulence. The traditional turbulence can
be used as well but it is generally not necessary because agate
is already very turbulent. You may control the amount of the
built-in turbulence by adding the optional agate_turb keyword
followed by a float value. For example:

  pigment {
    agate
    agate_turb 0.5
    color_map {MyMap}
  }

4.7.7.2   Average
Technically average is not a pattern type but it is listed here
because the syntax is similar to other patterns. Typically a
pattern type specifies how colors or normals are chosen from a
pigment_map¸ texture_map, density_map, or normal_map, however
average tells POV-Ray to average together all of the patterns you
specify.  Average was originally designed to be used in a normal
statement with a normal_map as a method of specifying more than
one normal pattern on the same surface. However average may be
used in a pigment statement with a pigment_map or in a texture
statement with a texture_map or media density with density_map to
average colors too.

When used with pigments, the syntax is:

AVERAGED_PIGMENT:
  pigment {
    pigment_map{ PIGMENT_MAP_ENTRY... }
  }
PIGMENT_MAP_ENTRY:
  [ [Weight]  PIGMENT_BODY ]
Where Weight is an optional float value that defaults to 1.0 if
not specified.  This weight value is the relative weight applied
to that pigment.  Each PIGMENT_BODY is anything which can be
inside a pigment{...} statement.  The pigment keyword and {}
braces need not be specified.

Note that the [] brackets are part of the actual
PIGMENT_MAP_ENTRY. They are not notational symbols denoting
optional parts. The brackets surround each entry in the
pigment_map. There may be from 2 to 256 entries in the map.

For example

    pigment {
      average
      pigment_map {
        [1.0  Pigment_1]
        [2.0  Pigment_2]
        [0.5  Pigment_3]
      }
    }
All three pigments are evaluated.  The weight values are
multiplied by the resulting color.  It is then divided by the
total of the weights which, in this example is 3.5.  When used
with texture_map or density_map it works the same way.

When used with a normal_map in a normal statement, multiple
copies of the original surface normal are created and are
perturbed by each pattern. The perturbed normals are then
weighted, added and normalized.

See the sections "Pigment Maps and Pigment Lists", "Normal Maps
and Normal Lists", "Texture Maps", and "Density Maps and Density
Lists" for more information.


4.7.7.3   Boxed
The boxed pattern creates a 2x2x2 unit cube centered at the
origin.  It is computed by:

  value =1.0- min(1, max(abs(X), abs(Y), abs(Z)))

It starts at 1.0 at the origin and increases to a minimum value
of 0.0 as it approaches any plane which is one unit from the
origin.  It remains at 0.0 for all areas beyond that distance.
This pattern was originally created for use with halo or media
but it may be used anywhere any pattern may be used.


4.7.7.4   Bozo
The bozo pattern is a very smooth, random noise function that is
traditionally used with some turbulence to create clouds. The
spotted pattern is identical to bozo but in early versions of POV-
Ray spotted did not allow turbulence to be added. Turbulence can
now be added to any pattern so these are redundant but both are
retained for backwards compatibility. The bumps pattern is also
identical to bozo when used anywhere except in a normal
statement. When used as a normal pattern, bumps uses a slightly
different method to perturb the normal with a similar noise
function.

The bozo noise function has the following properties:

  1.  It's defined over 3D space i.e., it takes x, y, and z and
  returns the noise value there.
  2.  If two points are far apart, the noise values at those
  points are relatively random.
  3.  If two points are close together, the noise values at those
  points are close to each other.
You can visualize this as having a large room and a thermometer
that ranges from 0.0 to 1.0. Each point in the room has a
temperature. Points that are far apart have relatively random
temperatures. Points that are close together have close
temperatures. The temperature changes smoothly but randomly as we
move through the room.

Now let's place an object into this room along with an artist.
The artist measures the temperature at each point on the object
and paints that point a different color depending on the
temperature.  What do we get? A POV-Ray bozo texture!


4.7.7.5   Brick
The brick pattern generates a pattern of bricks. The bricks are
offset by half a brick length on every other row in the x- and z-
directions. A layer of mortar surrounds each brick. The syntax is
given by

    pigment {
      brick COLOR_1, COLOR_2
      [brick_size <Size>]
      [mortar Size]
    }
where COLOR_1 is the color of the mortar and COLOR_2 is the color
of the brick itself. If no colors are specified a default deep
red and dark gray are used. The default size of the brick and
mortar together is <8, 3, 4.5> units. The default thickness of
the mortar is 0.5 units. These values may be changed using the
optional brick_size and mortar pattern modifiers. You may also
use pigment statements in place of the colors. For example:

  pigment {
    brick pigment{Jade}, pigment{Black_Marble}
  }
This example uses normals:

  normal { brick 0.5 }
The float value is an optional bump size. You may also use full
normal statements. For example:

  normal {
    brick normal{bumps 0.2}, normal{granite 0.3}
  }
When used with textures, the syntax is

  texture {
    brick texture{T_Gold_1A}, texture{Stone12}
  }
This is a block pattern which cannot use wave types, color_map,
or slope_map modifiers.


4.7.7.6   Bumps
The bumps pattern was originally designed only to be used as a
normal pattern. It uses a very smooth, random noise function that
creates the look of rolling hills when scaled large or a bumpy
orange peal when scaled small. Usually the bumps are about 1 unit
apart.

When used as a normal pattern, this pattern uses a specialized
normal perturbation function. This means that the pattern cannot
be used with normal_map, slope_map or wave type modifiers in a
normal statement.

When used as a pigment pattern or texture pattern, the bumps
pattern is identical to bozo or spotted and is similar to normal
bumps but is not identical as are most normals when compared to
pigments.


4.7.7.7   Checker
The checker pattern produces a checkered pattern consisting of
alternating squares of two colors.  The syntax is:

  pigment { checker [COLOR_1 [, COLOR_2]] [PATTERN_MODIFIERS...]
  }
If no colors are specified then default blue and green colors are
used.

The checker pattern is actually a series of cubes that are one
unit in size. Imagine a bunch of 1 inch cubes made from two
different colors of modeling clay. Now imagine arranging the
cubes in an alternating check pattern and stacking them in layer
after layer so that the colors still alternate in every
direction. Eventually you would have a larger cube. The pattern
of checks on each side is what the POV-Ray checker pattern
produces when applied to a box object.  Finally imagine cutting
away at the cube until it is carved into a smooth sphere or any
other shape. This is what the checker pattern would look like on
an object of any kind.

You may also use pigment statements in place of the colors. For
example:

  pigment { checker pigment{Jade}, pigment{Black_Marble} }
This example uses normals:

  normal { checker 0.5 }
The float value is an optional bump size. You may also use full
normal statements. For example:

  normal {
    checker normal{gradient x scale .2},
            normal{gradient y scale .2}
  }
When used with textures, the syntax is

  texture { checker texture{T_Wood_3A},texture{Stone12} }
This use of checker as a texture pattern replaces the special
tiles texture in previous versions of POV-Ray. You may still use
tiles but it may be phased out in future versions so checker
textures are best.

This is a block pattern which cannot use wave types, color_map,
or slope_map modifiers.


4.7.7.8   Crackle
The crackle pattern is a set of random tiled polygons. With a
large scale and no turbulence it makes a pretty good stone wall
or floor. With a small scale and no turbulence it makes a pretty
good crackle ceramic glaze. Using high turbulence it makes a good
marble that avoids the problem of apparent parallel layers in
traditional marble.

Mathematically, the set crackle(p)=0 is a 3D Voronoi diagram of a
field of semi random points and crackle(p) < 0 is the distance
from the set along the shortest path (a Voronoi diagram is the
locus of points equidistant from their two nearest neighbors from
a set of disjoint points, like the membranes in suds are to the
centers of the bubbles).


4.7.7.9   Cylindrical
The cylindrical pattern creates a one unit radius cylinder along
the Y axis.  It is computed by:

  value = 1.0-min(1, sqrt(X^2 + Z^2))

It starts at 1.0 at the origin and increases to a minimum value
of 0.0 as it approaches a distance of 1 unit from the Y axis.  It
remains at 0.0 for all areas beyond that distance.  This pattern
was originally created for use with halo or media but it may be
used anywhere any pattern may be used.


4.7.7.10  Density_File
The density_file pattern is a 3-D bitmap pattern that occupies a
unit cube from location <0,0,0> to <1,1,1>.  The data file is a
raw binary file format created for POV-Ray called df3 format.
The syntax provides for the possibility of implementing other
formats in the future.  This pattern was originally created for
use with halo or media but it may be used anywhere any pattern
may be used.  The syntax is:

  pigment {density_file df3 "filename.df3" [interpolate Type]
  [PIGMENT_MODIFIERS...] }
where "filename.df3" is a file name of the data file.

As a normal pattern, the syntax is

  normal {density_file df3 "filename.df3"  [, Bump_Size]
     [interpolate Type] [NORMAL_MODIFIERS...]
  }
The optional float Bump_Size should follow the file name and any
other modifiers follow that.

The df3 format consists of a 6 byte header of three 16-bit
integers with high order byte first.  These three values give the
x,y,z size of the data in pixels (or more appropriately called
voxels).  This is followed by x*y*z unsigned integer bytes of
data.  The data in the range of 0 to 255 is scaled into a float
value in the range 0.0 to 1.0.  It remains at 0.0 for all areas
beyond the unit cube.  The pattern occupies the unit cube
regardless of the dimensions in voxels.

The interpolate keyword may be specified to add interpolation of
the data.  The default value of zero specifies no interpolation.
A value of one specifies tri-linear interpolation.

See the sample scenes for data file include\spiral.df3,and the
scenes which use it: scenes\textures\surfaces\densfile.pov,
scenes\interior\media\galaxy.pov for examples.


4.7.7.11  Dents
The dents pattern was originally designed only to be used as a
normal pattern. It is especially interesting when used with
metallic textures. It gives impressions into the metal surface
that look like dents have been beaten into the surface with a
hammer. Usually the dents are about 1 unit apart.

When used as a normal pattern, this pattern uses a specialized
normal perturbation function. This means that the pattern cannot
be used with normal_map, slope_map or wave type modifiers in a
normal statement.

When used as a pigment pattern or texture pattern, the dents
pattern is similar to normal dents but is not identical as are
most normals when compared to pigments.


4.7.7.12  Gradient
One of the simplest patterns is the gradient pattern. It is
specified as

  pigment {gradient <Orientation> [PIGMENT_MODIFIERS...] }
where <Orientation> is a vector pointing in the direction that
the colors blend. For example

   pigment { gradient x } // bands of color vary as you move
                          // along the "x" direction.
produces a series of smooth bands of color that look like layers
of colors next to each other. Points at x=0 are the first color
in the color map. As the x location increases it smoothly turns
to the last color at x=1. Then it starts over with the first
again and gradually turns into the last color at x=2. The pattern
reverses for negative values of x. Using gradient y or gradient z
makes the colors blend along the y- or z-axis. Any vector may be
used but x, y and z are most common.

As a normal pattern, gradient generates a saw-tooth or ramped
wave appearance. The syntax is

  normal {gradient <Orientation> [, Bump_Size]
  [NORMAL_MODIFIERS...] }
where the vector <Orientation> is a required parameter but the
float Bump_Size which follows is optional.  Note that the comma
is required especially if Bump_Size is negative.


4.7.7.13  Granite
The granite pattern uses a simple 1/f fractal noise function to
give a good granite pattern. This pattern is used with creative
color maps in stones.inc to create some gorgeous layered stone
textures.

As a normal pattern it creates an extremely bumpy surface that
looks like a gravel driveway or rough stone.


4.7.7.14  Hexagon
The hexagon pattern is a block pattern that generates a repeating
pattern of hexagons in the x-y-plane. In this instance imagine
tall rods that are hexagonal in shape and are parallel to the y-
axis and grouped in bundles like shown in the example image.
Three separate colors should be specified as follows:

  pigment{hexagon [COLOR_1 [, COLOR_2 [, COLOR_3]]]
  [PATTERN_MODIFIERS...] }
                                
                                
                      The hexagon pattern.
                                
The three colors will repeat the hexagonal pattern with hexagon
COLOR_1 centered at the origin, COLOR_2 in the +z-direction and
COLOR_3 to either side. Each side of the hexagon is one unit
long.  The hexagonal rods of color extend infinitely in the +y-
and -y-directions. If no colors are specified then default blue,
green and red colors are used.

You may also use pigment statements in place of the colors. For
example:

  pigment {
    hexagon pigment { Jade },
            pigment { White_Marble },
            pigment { Black_Marble }
  }
This example uses normals:

  normal { hexagon 0.5 }
The float value is an optional bump size. You may also use full
normal statements. For example:

  normal {
    hexagon
      normal { gradient x scale .2 },
      normal { gradient y scale .2 },
      normal { bumps scale .2 }
  }
When used with textures, the syntax is...

  texture {
    hexagon
      texture { T_Gold_3A },
      texture { T_Wood_3A },
      texture { Stone12 }
  }
This is a block pattern which cannot use wave types, color_map,
or slope_map modifiers.


4.7.7.15  Leopard
Leopard creates regular geometric pattern of circular spots.  The
formula used is:

   value = Sqr((sin(x)+sin(y)+sin(z))/3)


4.7.7.16  Mandel
The mandel pattern computes the standard Mandelbrot fractal
pattern and projects it onto the x-y-plane. It uses the x and y
coordinates to compute the Mandelbrot set.

It is specified as

  pigment {mandel Max_Iteration [PIGMENT_MODIFIERS...] }
The pattern is specified with the keyword mandel followed by an
integer number. This number is the maximum number of iterations
to be used to compute the set. Typical values range from 10 up to
256 but any positive integer may be used. For example:

  pigment {
    mandel 25
    color_map {
      [0.0  color Cyan]
      [0.3  color Yellow]
      [0.6  color Magenta]
      [1.0  color Cyan]
    }
    scale .5
  }
The value passed to the color map is computed by the formula:

  value = number_of_iterations / max_iterations

When used as a normal pattern, the syntax is...

  normal{mandel Max_Iteration [, Bump_Size]
  [NORMAL_MODIFIERS...] }
where the integer Max_Iteration is a required parameter but the
float Bump_Size which follows is optional.  Note that the comma
is required especially if Bump_Size is negative.


4.7.7.17  Marble
The marble pattern is very similar to the gradient x pattern. The
gradient pattern uses a default ramp_wave wave type which means
it uses colors from the color map from 0.0 up to 1.0 at location
x=1 but then jumps back to the first color for x > 1 and repeats
the pattern again and again. However the marble pattern uses the
triangle_wave wave type in which it uses the color map from 0 to
1 but then it reverses the map and blends from 1 back to zero.
For example:

  pigment {
    gradient x
    color_map {
      [0.0  color Yellow]
      [1.0  color Cyan]
    }
  }
This blends from yellow to cyan and then it abruptly changes back
to yellow and repeats. However replacing gradient x with marble
smoothly blends from yellow to cyan as the x coordinate goes from
0.0 to 0.5 and then smoothly blends back from cyan to yellow by
x=1.0.

Earlier versions of POV-Ray did not allow you to change wave
types.  Now that wave types can be changed for most any pattern,
the distinction between marble and gradient x is only a matter of
default wave types.

When used with turbulence and an appropriate color map, this
pattern looks like veins of color of real marble, jade or other
types of stone. By default, marble has no turbulence.


4.7.7.18  Onion
The onion is a pattern of concentric spheres like the layers of
an onion.

  Value = mod(sqrt(Sqr(X)+Sqr(Y)+Sqr(Z)), 1.0)

Each layer is one unit thick.


4.7.7.19  Planar
The planar pattern creates a horizontal stripe plus or minus one
unit above and below the X-Z plane.  It is computed by:

  value =1.0- min(1, abs(Y))

It starts at 1.0 at the origin and increases to a minimum value
of 0.0 as the Y values approaches a distance of 1 unit from the X-
Z plane.  It remains at 0.0 for all areas beyond that distance.
This pattern was originally created for use with halo or media
but it may be used anywhere any pattern may be used.


4.7.7.20  Quilted
The quilted pattern was originally designed only to be used as a
normal pattern. The quilted pattern is so named because it can
create a pattern somewhat like a quilt or a tiled surface. The
squares are actually 3-D cubes that are 1 unit in size.

When used as a normal pattern, this pattern uses a specialized
normal perturbation function. This means that the pattern cannot
be used with normal_map, slope_map or wave type modifiers in a
normal statement.

When used as a pigment pattern or texture pattern, the quilted
pattern is similar to normal quilted but is not identical as are
most normals when compared to pigments.

The two parameters control0 and control1 are used to adjust the
curvature of the seam or gouge area between the quilts.  The
syntax is:

It is specified as

  pigment {quilted [QUILTED_MODIFIERS...] }
QUILTED_MODIFIERS:
  control0 Value_0   |   control Value_1   |   PIGMENT_MODIFIERS
The values should generally be kept to around the 0.0 to 1.0
range.  The default value is 1.0 if none is specified. Think of
this gouge between the tiles in cross-section as a sloped line.

                                
                                
     Quilted pattern with c0=0 and different values for c1.
                                
                                
                                
    Quilted pattern with c0=0.33 and different values for c1.
                                
                                
                                
    Quilted pattern with c0=0.67 and different values for c1.
                                
                                
                                
     Quilted pattern with c0=1 and different values for c1.
                                
This straight slope can be made to curve by adjusting the two
control values. The control values adjust the slope at the top
and bottom of the curve. A control values of 0 at both ends will
give a linear slope, as shown above, yielding a hard edge. A
control value of 1 at both ends will give an "s" shaped curve,
resulting in a softer, more rounded edge.


4.7.7.21  Radial
The radial pattern is a radial blend that wraps around the +y-
axis. The color for value 0.0 starts at the +x-direction and
wraps the color map around from east to west with 0.25 in the -z-
direction, 0.5 in -x, 0.75 at +z and back to 1.0 at +x. Typically
the pattern is used with a frequency modifier to create multiple
bands that radiate from the y-axis.  For example:

  pigement {
    radial color_map{[0.5 Black][0.5 White]}
    frequency 10
  }
creates 10 white bands and 10 black bands radiating from the y
axis.


4.7.7.22  Ripples
The ripples pattern was originally designed only to be used as a
normal pattern. It makes the surface look like ripples of water.
The ripples radiate from 10 random locations inside the unit cube
area <0,0,0> to <1,1,1>. Scale the pattern to make the centers
closer or farther apart.

Usually the ripples from any given center are about 1 unit apart.
The frequency keyword changes the spacing between ripples. The
phase keyword can be used to move the ripples outwards for
realistic animation.

The number of ripple centers can be changed with the global
parameter

  global_settings{number_of_waves Count }
somewhere in the scene. This affects the entire scene. You cannot
change the number of wave centers on individual patterns. See
section "Number_Of_Waves" for details.

When used as a normal pattern, this pattern uses a specialized
normal perturbation function. This means that the pattern cannot
be used with normal_map, slope_map or wave type modifiers in a
normal statement.

When used as a pigment pattern or texture pattern, the ripples
pattern is similar to normal ripples but is not identical as are
most normals when compared to pigments.


4.7.7.23  Spherical
The spherical pattern creates a one unit radius sphere along the
Y axis.  It is computed by:

  value = 1.0-min(1, sqrt(X^2 + Y^2 + Z^2))

It starts at 1.0 at the origin and increases to a max value of
0.0 as it approaches a distance of 1 unit from the origin in any
direction.  It remains at 0.0 for all areas beyond that distance.
This pattern was originally created for use with halo or media
but it may be used anywhere any pattern may be used.


4.7.7.24  Spiral1
The spiral1 pattern creates a spiral that winds around the y-axis
similar to a screw. When viewed sliced in the X-Z plane, it looks
like the spiral arms of a galaxy.  Its syntax is:

  pigment {spiral1 Number_of_Arms [PIGMENT_MODIFIERS...] }
The Number_of_Arms value determines how may arms are winding
around the y-axis.

As a normal pattern, the syntax is

  normal {spiral1 Number_of_Arms  [, Bump_Size]
  [NORMAL_MODIFIERS...] }
where the vector <Orientation> is a required parameter but the
float Bump_Size which follows is optional.  Note that the comma
is required especially if Bump_Size is negative.

The pattern uses the triangle_wave wave type by default but may
use any wave type.


4.7.7.25  Spiral2
The spiral2 pattern creates a double spiral that winds around the
y-axis similar spiral1 except it is two overlapping spirals the
twist in opposite directions.  The results sometimes looks like a
basket weave or perhaps the skin of pineapple.  The center of a
sunflower also has a similar double spiral pattern.  Its syntax
is:

  pigment {spiral2 Number_of_Arms [PIGMENT_MODIFIERS...] }
The Number_of_Arms value determines how may arms are winding
around the y-axis.

As a normal pattern, the syntax is

  normal {spiral2 Number_of_Arms  [, Bump_Size]
  [NORMAL_MODIFIERS...] }
where the vector <Orientation> is a required parameter but the
float Bump_Size which follows is optional.  Note that the comma
is required especially if Bump_Size is negative.

The pattern uses the triangle_wave wave type by default but may
use any wave type.


4.7.7.26  Spotted
The spotted pattern is identical to the bozo pattern. Early
versions of POV-Ray did not allow turbulence to be used with
spotted.  Now that any pattern can use turbulence there is no
difference between bozo and spotted. See section "Bozo" for
details.


4.7.7.27  Waves
The waves pattern was originally designed only to be used as a
normal pattern. It makes the surface look like waves on water.
The waves pattern looks similar to the ripples pattern except the
features are rounder and broader. The effect is to make waves
that look more like deep ocean waves. The waves radiate from 10
random locations inside the unit cube area <0,0,0> to <1,1,1>.
Scale the pattern to make the centers closer or farther apart.

Usually the waves from any given center are about 1 unit apart.
The frequency keyword changes the spacing between waves. The
phase keyword can be used to move the waves outwards for
realistic animation.

The number of wave centers can be changed with the global
parameter

  global_settings{number_of_waves Count }
somewhere in the scene. This affects the entire scene. You cannot
change the number of wave centers on individual patterns. See
section "Number_Of_Waves" for details.

When used as a normal pattern, this pattern uses a specialized
normal perturbation function. This means that the pattern cannot
be used with normal_map, slope_map or wave type modifiers in a
normal statement.

When used as a pigment pattern or texture pattern, the waves
pattern is similar to normal waves but is not identical as are
most normals when compared to pigments.


4.7.7.28  Wood
The wood pattern consists of concentric cylinders centered on the
z-axis. When appropriately colored, the bands look like the
growth rings and veins in real wood. Small amounts of turbulence
should be added to make it look more realistic. By default, wood
has no turbulence.

Unlike most patterns, the wood pattern uses the triangle_wave
wave type by default. This means that like marble, wood uses
color map values 0.0 to 1.0 then repeats the colors in reverse
order from 1.0 to 0.0. However you may use any wave type.


4.7.7.29  Wrinkles
The wrinkles pattern was originally designed only to be used as a
normal pattern. It uses a 1/f noise pattern similar to granite
but the features in wrinkles are sharper. The pattern can be used
to simulate wrinkled cellophane or foil. It also makes an
excellent stucco texture.

When used as a normal pattern, this pattern uses a specialized
normal perturbation function. This means that the pattern cannot
be used with normal_map, slope_map or wave type modifiers in a
normal statement.

When used as a pigment pattern or texture pattern, the wrinkles
pattern is similar to normal wrinkles but is not identical as are
most normals when compared to pigments.


4.7.8     Pattern Modifiers
Pattern modifiers are statements or parameters which modify how a
pattern is evaluated or tells what to do with the pattern. The
complete syntax is:

PATTERN_MODIFIER:
  BLEND_MAP_MODIFIER   |   AGATE_MODIFIER   |
  DENSITY_FILE_MODIFIER   |
  QUILTED_MODIFIER   |   BRICK_MODIFIER   |
  turbulence <Amount>   |   octaves Count   |   omega Amount   |
  lambda Amount   |
  warp { [WARP_ITEMS...] }   |
  TRANSFORMATION
BLEND_MAP_MODIFIER:
  frequency Amount   |   phase Amount   |
  ramp_wave   |   triangle_wave   |   sine_wave   |
  scallop_wave   |
  cubic_wave   |   poly_wave [Exponent]
AGATE_MODIFIER:
  agate_turb Value
BRICK_MODIFIER:
  brick_size Size   |   mortar Size
DENSITY_FILE_MODIFIER:
  interpolate Type
QUILTED_MODIFIER:
  control0 Value   |   control1 Value
PIGMENT_MODIFIER:
  PATTERN_MODIFIER   |   COLOR_LIST   |   PIGMENT_LIST   |
  color_map{ COLOR_MAP_BODY }   |   colour_map{ COLOR_MAP_BODY }
  |
  pigment_map{ PIGMENT_MAP_BODY }   |
  quick_color COLOR   |   quick_colour COLOR
NORMAL_MODIFIER:
  PATTERN_MODIFIER   |   NORMAL_LIST   |
  normal_map{ NORMAL_MAP_BODY }   |
  slope_map{ SLOPE_MAP_BODY }   |
  bump_size Amount
TEXTURE_PATTERN_MODIFIER:
  PATTERN_MODIFIER   |   TEXTURE_LIST   |
  texture_map{ TEXTURE_MAP_BODY }
DENSITY_MODIFIER:
  PATTERN_MODIFIER   |   DENSITY_LIST   |   COLOR_LIST   |
  color_map{ COLOR_MAP_BODY }   |   colour_map{ COLOR_MAP_BODY }
  |
  density_map{ DENSITY_MAP_BODY }
The modifiers PIGMENT_LIST, quick_color, and pigment_map apply
only to pigments. See section "Pigment" for details on these
pigment-specific pattern modifiers.

The modifiers COLOR_LIST and color_map apply only to pigments and
densities. See sections "Pigment" and "Density" for details on
these pigment-specific pattern modifiers.

The modifiers NORMAL_LIST, bump_size, slope_map and normal_map
apply only to normals. See section "Normal" for details on these
normal-specific pattern modifiers.

The TEXTURE_LIST and texture_map modifiers can only be used with
patterned textures. See section "Texture Maps" for details.

The DENSITY_LIST and density_map modifiers only work with
media{density{..}} statements.  See "Density" for details.

The agate_turb modifier can only be used with the agate pattern.
See "Agate" for details.

The brick_size and mortar modifiers can only be used with the
brick pattern.  See "Brick" for details.

The control0 and control1 modifiers can only be used with the
quilted pattern.  See "Quilted" for details.

The interpolate modifier can only be used with the density_file
pattern.  See "Density_File" for details.

The general purpose pattern modifiers in the following sections
can be used with pigment, normal, texture, or density patterns.


4.7.8.1   Transforming Patterns
The most common pattern modifiers are the transformation
modifiers translate, rotate, scale, transform, and matrix.  For
details on these commands see section "Transformations".

These modifiers may be placed inside pigment, normal, texture,
and density statements to change the position, size and
orientation of the patterns.

Transformations are performed in the order in which you specify
them.  However in general the order of transformations relative
to other pattern modifiers such as turbulence, color_map and
other maps is not important. For example scaling before or after
turbulence makes no difference. The turbulence is done first,
then the scaling regardless of which is specified first. However
the order in which transformations are performed relative to warp
statements is important. See "Warps" for details.


4.7.8.2   Frequency and Phase
The frequency and phase modifiers act as a type of scale and
translate modifiers for various blend maps.  They only have
effect when blend maps are used.  Blend maps are color_map,
pigment_map, normal_map, slope_map, density_map, and texture_map.
This discussion uses a color map as an example but the same
principles apply to the other blend map types.

The frequency keyword adjusts the number of times that a color
map repeats over one cycle of a pattern. For example gradient
covers color map values 0 to 1 over the range from x=0 to x=1. By
adding frequency 2.0 the color map repeats twice over that same
range. The same effect can be achieved using scale 0.5*x so the
frequency keyword isn't that useful for patterns like gradient.

However the radial pattern wraps the color map around the +y-axis
once. If you wanted two copies of the map (or 3 or 10 or 100)
you'd have to build a bigger map. Adding frequency 2.0 causes the
color map to be used twice per revolution. Try this:

  pigment {
    radial
    color_map{[0.5 color Red][0.5 color White]}
    frequency 6
  }
The result is six sets of red and white radial stripes evenly
spaced around the object.

The float after frequency can be any value. Values greater than
1.0 causes more than one copy of the map to be used. Values from
0.0 to 1.0 cause a fraction of the map to be used. Negative
values reverses the map.

The phase value causes the map entries to be shifted so that the
map starts and ends at a different place. In the example above if
you render successive frames at phase 0 then phase 0.1, phase
0.2, etc. you could create an animation that rotates the stripes.
The same effect can be easily achieved by rotating the radial
pigment using rotate y*Angle but there are other uses where phase
can be handy.

Sometimes you create a great looking gradient or wood color map
but you want the grain slightly adjusted in or out. You could re-
order the color map entries but that's a pain. A phase adjustment
will shift everything but keep the same scale. Try animating a
mandel pigment for a color palette rotation effect.

These values work by applying the following formula

  New_Value = fmod ( Old_Value * Frequency + Phase, 1.0 ).

The frequency and phase modifiers have no effect on block
patterns checker, brick, and hexagon nor do they effect
image_map, bump_map or material_map. They also have no effect in
normal statements when used with bumps, dents, quilted or
wrinkles because these normal patterns cannot use normal_map or
slope_map.

They can be used with normal patterns ripples and waves even
though these two patterns cannot use normal_map or slope_map
either. When used with ripples or waves, frequency adjusts the
space between features and phase can be adjusted from 0.0 to 1.0
to cause the ripples or waves to move relative to their center
for animating the features.


4.7.8.3   Waveforms
POV-Ray allows you to apply various wave forms to the pattern
function before applying it to a blend map. Blend maps are
color_map, pigment_map, normal_map, slope_map, density_map, and
texture_map.

Most of the patterns which use a blend map, use the entries in
the map in order from 0.0 to 1.0. The effect can most easily be
seen when these patterns are used as normal patterns with no
maps.  Patterns such as gradient or onion generate a grove or
slot that looks like a ramp that drops off sharply.  This is
called a  ramp_wave wave type and it is the default wave type for
most patterns. However the wood and marble patterns use the map
from 0.0 to 1.0 and then reverses it and runs it from 1.0 to 0.0.
The result is a wave form which slopes upwards to a peak, then
slopes down again in a triangle_wave. In earlier versions of POV-
Ray there was no way to change the wave types. You could simulate
a triangle wave on a ramp wave pattern by duplicating the map
entries in reverse, however there was no way to use a ramp wave
on wood or marble.

Now any pattern that takes a map can have the default wave type
overridden. For example:

  pigment { wood color_map { MyMap } ramp_wave }
Also available are sine_wave, scallop_wave, cubic_wave and
poly_wave types. These types are of most use in normal patterns
as a type of built-in slope map. The  sine_wave takes the zig-zag
of a ramp wave and turns it into a gentle rolling wave with
smooth transitions. The scallop_wave uses the absolute value of
the sine wave which looks like corduroy when scaled small or like
a stack of cylinders when scaled larger.  The cubic_wave is a
gentle cubic curve from 0.0 to 1.0 with zero slope at the start
and end.  The poly_wave is an exponential function.  It is
followed by an optional float value which specifies exponent.
For example poly_wave 2 starts low and climbs rapidly at the end
while poly_wave 0.5 climbs rapidly at first and levels off at the
end.  If no float value is specified, the default is 1.0 which
produces a linear function identical to ramp_wave.

Although any of these wave types can be used for pigments,
normals, textures, or density the effect of many of the wave
types are not as noticeable on pigments, textures, or density as
they are for normals.

Wave type modifiers have no effect on block patterns checker,
brick, and hexagon nor do they effect image_map, bump_map or
material_map. They also have no effect in normal statements when
used with bumps, dents, quilted, ripples, waves, or wrinkles
because these normal patterns cannot use normal_map or slope_map.


4.7.8.4   Turbulence
The keyword turbulence followed by a float or vector may be used
to stir up any pigment, normal, texture, irid or density. A
number of optional parameters may be used with turbulence to
control how it is computed. The syntax is:

TURBULENCE_ITEM:
  turbulence <Amount>   |   octaves Count   |   omega Amount   |
  lambda Amount
Typical turbulence values range from the default 0.0, which is no
turbulence, to 1.0 or more, which is very turbulent. If a vector
is specified different amounts of turbulence are applied in the x-
, y- and z-direction. For example

  turbulence <1.0, 0.6, 0.1>
has much turbulence in the x-direction, a moderate amount in the
y-direction and a small amount in the z-direction.

Turbulence uses a random noise function called DNoise. This is
similar to the noise used in the bozo pattern except that instead
of giving a single value it gives a direction. You can think of
it as the direction that the wind is blowing at that spot. Points
close together generate almost the same value but points far
apart are randomly different.

In general the order of turbulence parameters relative to other
pattern modifiers such as transformations, color maps and other
maps is not important. For example scaling before or after
turbulence makes no difference. The turbulence is done first,
then the scaling regardless of which is specified first. See
section "" for a way to work around this behavior.

In general, the order of turbulence parameters relative to each
other and to other pattern modifiers such as transformations or
color_map and other maps is not important. For example scaling
before or after turbulence makes no difference. The turbulence is
done first, then the scaling regardless of which is specified
first. However the order in which transformations are performed
relative to warp statements is important. You can also specify
turbulence inside warp and in this way you can force turbulence
to be applied after transformations.  See "Warps" for details.

Turbulence uses DNoise to push a point around in several steps
called octaves. We locate the point we want to evaluate, then
push it around a bit using turbulence to get to a different point
then look up the color or pattern of the new point.

It says in effect "Don't give me the color at this spot... take a
few random steps in different directions and give me that color".
Each step is typically half as long as the one before. For
example:

                                
                                
                     Turbulence random walk.
                                
The magnitude of these steps is controlled by the turbulence
value. There are three additional parameters which control how
turbulence is computed. They are octaves, lambda and omega. Each
is optional. Each is followed by a single float value. Each has
no effect when there is no turbulence.


4.7.8.5   Octaves
The octaves keyword may be followed by an integer value to
control the number of steps of turbulence that are computed.
Legal values range from 1 to 10. The default value of 6 is a
fairly high value; you won't see much change by setting it to a
higher value because the extra steps are too small. Float values
are truncated to integer. Smaller numbers of octaves give a
gentler, wavy turbulence and computes faster. Higher octaves
create more jagged or fuzzy turbulence and takes longer to
compute.


4.7.8.6   Lambda
The lambda parameter controls how statistically different the
random move of an octave is compared to its previous octave. The
default value is 2.0 which is quite random. Values close to
lambda 1.0 will straighten out the randomness of the path in the
diagram above. The zig-zag steps in the calculation are in nearly
the same direction. Higher values can look more swirly under some
circumstances.


4.7.8.7   Omega
The omega value controls how large each successive octave step is
compared to the previous value. Each successive octave of
turbulence is multiplied by the omega value. The default omega
0.5 means that each octave is 1/2 the size of the previous one.
Higher omega values mean that 2nd, 3rd, 4th and up octaves
contribute more turbulence giving a sharper, crinkly look while
smaller omegas give a fuzzy kind of turbulence that gets blurry
in places.


4.7.8.8   Warps
The warp statement is a pattern modifier that is similar to
turbulence. Turbulence works by taking the pattern evaluation
point and pushing it about in a series of random steps. However
warps push the point in very well-defined, non-random, geometric
ways. The warp statement also overcomes some limitations of
traditional turbulence and transformations by giving the user
more control over the order in which turbulence, transformation
and warp modifiers are applied to the pattern.

Currently there are three types of warps but the syntax was
designed to allow future expansion. The first two, the repeat
warp and the black_hole warp are new features for POV-Ray that
modify the pattern in geometric ways. The other warp provides an
alternative way to specify turbulence.

The syntax for using a warp statement is:

WARP:
  warp { WARP_ITEM }
WARP_ITEM:
  repeat <Directiont>  [REPEAT_ITEMS...]   |
  black_hole <Location>, Radius [BLACK_HOLE_ITEMS...]   |
  turbulence <Amount> [TURB_ITEMS...]
REPEAT_ITEMS:
  offset <Amount>   |   flip <Axis>
BLACK_HOLE_ITEMS:
  strength Strength   |   falloff Amount   |   inverse   |
  type Type   |
  repeat <Repeat>   |   turbulence <Amount>
TURB_ITEMS:
  octaves Count   |   omega Amount   |   lambda Amount
You may have as many separate warp statements as you like in each
pattern. The placement of warp statements relative to other
modifiers such as color_map or turbulence is not important.
However placement of warp statements relative to each other and
to transformations is significant. Multiple warps and
transformations are evaluated in the order in which you specify
them. For example if you translate, then warp or warp, then
translate, the results can be different.


4.7.8.8.1 Black Hole Warp
A black_hole warp is so named because of its similarity to real
black holes. Just like the real thing, you cannot actually see a
black hole. The only way to detect its presence is by the effect
it has on things that surround it.

Take, for example, a wood grain. Using POV-Ray's normal
turbulence and other texture modifier functions, you can get a
nice, random appearance to the grain. But in its randomness it is
regular - it is regularly random! Adding a black hole allows you
to create a localized disturbance in a wood grain in either one
or multiple locations. The black hole can have the effect of
either sucking the surrounding texture into itself (like the real
thing) or pushing it away. In the latter case, applied to a wood
grain, it would look to the viewer as if there were a knothole in
the wood. In this text we use a wood grain regularly as an
example, because it is ideally suitable to explaining black
holes. However, black holes may in fact be used with any texture
or pattern.  The effect that the black hole has on the texture
can be specified.  By default, it sucks with the strength
calculated exponentially (inverse-square). You can change this if
you like.

Black holes may be used anywhere a warp is permitted. The syntax
is:

BLACK_HOLE_WARP:
  warp {black_hole <Location>, Radius [BLACK_HOLE_ITEMS...] }
BLACK_HOLE_ITEMS:
  strength Strength   |   falloff Amount   |   inverse   |
  type Type   |
  repeat <Repeat>   |   turbulence <Amount>
The minimal requirement is the black_hole keyword followed by a
vector <Location> followed by a comma and a float Radius.  Black
holes effect all points within the spherical region around the
location and within the radius.  This is optionally followed by
any number of other keywords which control how the texture is
warped.

The falloff keyword may be used with a float value to specify the
power by which the effect of the black hole falls off. The
default is two. The force of the black hole at any given point,
before applying the strength modifier, is as follows.

First, convert the distance from the point to the center to a
proportion (0 to 1) that the point is from the edge of the black
hole. A point on the perimeter of the black hole will be 0.0; a
point at the center will be 1.0; a point exactly halfway will be
0.5, and so forth.  Mentally you can consider this to be a
closeness factor. A closeness of 1.0 is as close as you can get
to the center (i.e. at the center), a closeness of 0.0 is as far
away as you can get from the center and still be inside the black
hole and a closeness of 0.5 means the point is exactly halfway
between the two.

Call this value c. Raise c to the power specified in falloff. By
default Falloff is 2, so this is c2 or c squared. The resulting
value is the force of the black hole at that exact location and
is used, after applying the strength scaling factor as described
below, to determine how much the point is perturbed in space. For
example, if c is 0.5 the force is 0.52 or 0.25. If c is 0.25 the
force is 0.125. But if c is exactly 1.0 the force is 1.0.  Recall
that as c gets smaller the point is farther from the center of
the black hole. Using the default power of 2, you can see that as
c reduces, the force reduces exponentially in an inverse-square
relationship. Put in plain English, it means that the force is
much stronger (by a power of two) towards the center than it is
at the outside.

By increasing falloff, you can increase the magnitude of the
falloff. A large value will mean points towards the perimeter
will hardly be affected at all and points towards the center will
be affected strongly.  A value of 1.0 for falloff will mean that
the effect is linear. A point that is exactly halfway to the
center of the black hole will be affected by a force of exactly
0.5.  A value of falloff of less than one but greater than zero
means that as you get closer to the outside, the force increases
rather than decreases. This can have some uses but there is a
side effect.  Recall that the effect of a black hole ceases
outside its perimeter.  This means that points just within the
perimeter will be affected strongly and those just outside not at
all. This would lead to a visible border, shaped as a sphere.  A
value for falloff of 0 would mean that the force would be 1.0 for
all points within the black hole, since any number larger 0
raised to the power of 0 is 1.0.

The strength keyword may be specified with a float value to give
you a bit more control over how much a point is perturbed by the
black hole. Basically, the force of the black hole (as determined
above) is multiplied by the value of strength, which defaults to
1.0. If you set strength to 0.5, for example, all points within
the black hole will be moved by only half as much as they would
have been. If you set it to 2.0 they will be moved twice as much.

There is a rider to the latter example, though - the movement is
clipped to a maximum of the original distance from the center.
That is to say, a point that is 0.75 units from the center may
only be moved by a maximum of 0.75 units either towards the
center or away from it, regardless of the value of strength. The
result of this clipping is that you will have an exclusion area
near the center of the black hole where all points whose final
force value exceeded or equaled 1.0 were moved by a fixed amount.

If the inverted keyword is specified then points pushed away from
the center instead of being pulled in.

The repeat keyword followed by a vector, allows you to simulate
the effect of many black holes without having to explicitly
declare them. Repeat is a vector that tells POV-Ray to use this
black hole at multiple locations.  Using repeat logically divides
your scene up into cubes, the first being located at <0,0,0> and
going to <Repeat>. Suppose your repeat vector was <1,5,2>. The
first cube would be from <0,0,0> to < 1,5,2>. This cube repeats,
so there would be one at < -1,-5,-2>, <1,5,2>, <2,10,4> and so
forth in all directions, ad infinitum.

When you use repeat, the center of the black hole does not
specify an absolute location in your scene but an offset into
each block. It is only possible to use positive offsets. Negative
values will produce undefined results.

Suppose your center was <0.5,1,0.25> and the repeat vector is
<2,2,2>. This gives us a block at < 0,0,0> and <2,2,2>, etc. The
centers of the black hole's for these blocks would be <0,0,0> + <
0.5,1.0,0.25>, i. e. <0.5,1.0,0.25>, and < 2,2,2> +
<0.5,1.0,0.25>, i. e. < 2,5,3.0,2.25>.

Due to the way repeats are calculated internally, there is a
restriction on the values you specify for the repeat vector.
Basically, each black hole must be totally enclosed within each
block (or cube), with no part crossing into a neighboring one.
This means that, for each of the x, y and z dimensions, the
offset of the center may not be less than the radius, and the
repeat value for that dimension must be >=the center plus the
radius since any other values would allow the black hole to cross
a boundary. Put another way, for each of x, y and z

Radius <= Offset or Center <= Repeat - Radius.
If the repeat vector in any dimension is too small to fit this
criteria, it will be increased and a warning message issued. If
the center is less than the radius it will also be moved but no
message will be issued.

Note that none of the above should be read to mean that you can't
overlap black holes. You most certainly can and in fact this can
produce some most useful effects. The restriction only applies to
elements of the same black hole which is repeating. You can
declare a second black hole that also repeats and its elements
can quite happily overlap the first and causing the appropriate
interactions.  It is legal for the repeat value for any dimension
to be 0, meaning that POV-Ray will not repeat the black hole in
that direction.

The turbulence can only be used in a black hole with repeat. It
allows an element of randomness to be inserted into the way the
black holes repeat, to cause a more natural look. A good example
would be an array of knotholes in wood - it would look rather
artificial if each knothole were an exact distance from the
previous.

The turbulence vector is a measurement that is added to each
individual back hole in an array, after each axis of the vector
is multiplied by a different random amount ranging from 0 to 1.
The resulting actual position of the black hole's center for that
particular repeat element is random (but consistent, so renders
will be repeatable) and somewhere within the above co-ordinates.
There is a rider on the use of turbulence, which basically is the
same as that of the repeat vector. You can't specify a value
which would cause a black hole to potentially cross outside of
its particular block.

In summary: For each of x, y and z the offset of the center must
be >=radius and the value of the repeat must be >= center +
radius + turbulence. The exception being that repeat may be 0 for
any dimension, which means do not repeat in that direction.

Some examples are given by

  warp
  {
    black_hole <0, 0, 0>, 0.5
  }
  warp
  {
    black_hole <0.15, 0.125, 0>, 0.5
    falloff 7
    strength 1.0
    repeat <1.25, 1.25, 0>
    turbulence <0.25, 0.25, 0>
    inverse
  }
  warp
  {
    black_hole <0, 0, 0>, 1.0
    falloff 2
    strength 2
    inverse
  }

4.7.8.8.2 Repeat Warp
The repeat warp causes a section of the pattern to be repeated
over and over. It takes a slice out of the pattern and makes
multiple copies of it side-by-side. The warp has many uses but
was originally designed to make it easy to model wood veneer
textures. Veneer is made by taking very thin slices from a log
and placing them side-by-side on some other backing material. You
see side-by-side nearly identical ring patterns but each will be
a slice perhaps 1/32th of an inch deeper.

The syntax for a repeat warp is

REPEAT_WARP:
  warp { repeat <Directiont>  [REPEAT_ITEMS...] }
REPEAT_ITEMS:
  offset <Amount>   |   flip <Axis>
The repeat vector specifies the direction in which the pattern
repeats and the width of the repeated area. This vector must lie
entirely along an axis. In other words, two of its three
components must be 0. For example

  pigment {
    wood
    warp {repeat 2*x}
  }
which means that from x=0 to x=2 you get whatever the pattern
usually is. But from x=2 to x=4 you get the same thing exactly
shifted two units over in the x-direction. To evaluate it you
simply take the x-coordinate modulo 2. Unfortunately you get
exact duplicates which isn't very realistic. The optional offset
vector tells how much to translate the pattern each time it
repeats. For example

  pigment {
    wood
    warp {repeat x*2  offset z*0.05}
  }
means that we slice the first copy from x=0 to x=2 at z=0 but at
x=2 to x=4 we offset to z=0.05. In the 4 to 6 interval we slice
at z=0.10. At the n-th copy we slice at 0.05 n z. Thus each copy
is slightly different. There are no restrictions on the offset
vector.

Finally the flip vector causes the pattern to be flipped or
mirrored every other copy of the pattern. The first copy of the
pattern in the positive direction from the axis is not flipped.
The next farther is, the next is not, etc. The flip vector is a
three component x, y, z vector but each component is treated as a
boolean value that tells if you should or should not flip along a
given axis. For example

  pigment {
    wood
    warp {repeat 2*x  flip <1,1,0>}
  }
means that every other copy of the pattern will be mirrored about
the x- and y- axis but not the z-axis. A non-zero value means
flip and zero means do not flip about that axis. The magnitude of
the values in the flip vector doesn't matter.


4.7.8.8.3 Turbulence Warp
The POV-Ray language contains an ambiguity and limitation on the
way you specify turbulence and transformations such as translate,
rotate, scale, matrix, and transform transforms. Usually the
turbulence is done first.  Then all translate, rotate, scale,
matrix, and transform operations are always done after turbulence
regardless of the order in which you specify them. For example
this

 pigment {
   wood
   scale .5
   turbulence .2
 }
works exactly the same as

 pigment {
   wood
   turbulence .2
   scale .5
 }
The turbulence is always first. A better example of this
limitation is with uneven turbulence and rotations.

  pigment {
    wood
    turbulence 0.5*y
    rotate z*60
  }
  // as compared to
  pigment {
   wood
   rotate z*60
   turbulence 0.5*y
  }
The results will be the same either way even though you'd think
it should look different.

We cannot change this basic behavior in POV-Ray now because lots
of scenes would potentially render differently if suddenly the
order transformation vs. turbulence suddenly mattered when in the
past, it didn't.

However, by specifying our turbulence inside warp statement you
tell POV-Ray that the order in which turbulence, transformations
and other warps are applied is significant. Here's an example of
a turbulence warp.

  warp { turbulence <0,1,1> octaves 3 lambda 1.5 omega 0.3 }
The significance is that this

 pigment {
   wood
   translate <1,2,3> rotate x*45 scale 2
   warp { turbulence <0,1,1> octaves 3 lambda 1.5 omega 0.3 }
 }
produces different results than this...

 pigment {
   wood
   warp { turbulence <0,1,1> octaves 3 lambda 1.5 omega 0.3 }
   translate <1,2,3> rotate x*45 scale 2
 }
You may specify turbulence without using a warp statement.
However you cannot control the order in which they are evaluated
unless you put them in a warp.

The evaluation rules are as follows:


  1)   First any turbulence not inside a warp statement is
  applied regardless of the order in which it appears relative
  to warps or transformations.
  2)   Next each warp statement, translate, rotate, scale or
  matrix one-by-one, is applied in the order the user specifies.
  If you want turbulence done in a specific order, you simply
  specify it inside a warp in the proper place.

4.7.8.9   Bitmap Modifiers
A bitmap modifier is a modifier used inside an image_map,
bump_map or material_map to specify how the 2-D bitmap is to be
applied to the 3-D surface. Several bitmap modifiers apply to
specific kinds of maps and they are covered in the appropriate
sections. The bitmap modifiers discussed in the following
sections are applicable to all three types of bitmaps.


4.7.8.9.1 The once Option
Normally there are an infinite number of repeating image maps,
bump maps or material maps created over every unit square of the
x-y-plane like tiles. By adding the once keyword after a file
name you can eliminate all other copies of the map except the one
at (0,0) to (1,1). In image maps, areas outside this unit square
are treated as fully transparent. In bump maps, areas outside
this unit square are left flat with no normal modification.  In
material maps, areas outside this unit square are textured with
the first texture of the texture list.

For example:

  image_map {
    gif "mypic.gif"
    once
  }

4.7.8.9.2 The map_type Option
The default projection of the image onto the x-y-plane is called
a planar map type. This option may be changed by adding the
map_type keyword followed by an integer number specifying the way
to wrap the image around the object.

A map_type 0 gives the default planar mapping already described.

A map_type 1 gives a spherical mapping. It assumes that the
object is a sphere of any size sitting at the origin. The y-axis
is the north/south pole of the spherical mapping. The top and
bottom edges of the image just touch the pole regardless of any
scaling. The left edge of the image begins at the positive x-axis
and wraps the image around the sphere from west to east in a -y-
rotation. The image covers the sphere exactly once. The once
keyword has no meaning for this mapping type.

With map_type 2 you get a cylindrical mapping. It assumes that a
cylinder of any diameter lies along the y-axis. The image wraps
around the cylinder just like the spherical map but the image
remains one unit tall from y=0 to y=1. This band of color is
repeated at all heights unless the once keyword is applied.

Finally map_type 5 is a torus or donut shaped mapping. It assumes
that a torus of major radius one sits at the origin in the x-z-
plane. The image is wrapped around similar to spherical or
cylindrical maps. However the top and bottom edges of the map
wrap over and under the torus where they meet each other on the
inner rim.

Types 3 and 4 are still under development.

Note that the map_type option may also be applied to bump_map and
material_map statements.

For example:

  sphere{<0,0,0>,1
    pigment{
      image_map {
        gif "world.gif"
        map_type 1
      }
    }
  }

4.7.8.9.3 The interpolate Option
Adding the interpolate keyword can smooth the jagged look of a
bitmap. When POV-Ray asks an image map color or a bump amount for
a bump map, it often asks for a point that is not directly on top
of one pixel but sort of between several differently colored
pixels. Interpolations returns an in-between value so that the
steps between the pixels in the map will look smoother.

Although interpolate is legal in material maps, the color index
is interpolated before the texture is chosen. It does not
interpolate the final color as you might hope it would. In
general, interpolation of material maps serves no useful purpose
but this may be fixed in future versions.

There are currently two types of interpolation:  interpolate 2
gives bilinear interpolation while interpolate 4 gives normalized
distance.  For example:

  image_map {
    gif "mypic.gif"
    interpolate 2
  }
Default is no interpolation. Normalized distance is the slightly
faster of the two, bilinear does a better job of picking the
between color. Normally bilinear is used.

If your map looks jaggy, try using interpolation instead of going
to a higher resolution image. The results can be very good.


4.8  Media
The media statement is used to specify particulate matter
suspended in a medium such air or water.  It can be used to
specify smoke, haze, fog, gas, fire, dust etc.  Previous versions
of POV-Ray had two incompatible systems for generating such
effects.  One was halo for effects enclosed in a transparent or
semi-transparent object.  The other was atmosphere for effects
that  permeated the entire scene.  This duplication of systems
was complex and unnecessary.  Both halo and atmosphere have been
eliminated.  See "Why are Interior and Media Necessary?" for
further details on this change.  See "Object Media" for details
on how to use media with objects.  See "Atmospheric Media" for
details on using media for atmospheric effects outside of
objects.  This section and the sub-sections which follow explains
the details of the various media options which are useful for
either object media or atmospheric media.

Media works by sampling the density of particles at some
specified number of points along the ray's path.  Sub-samples are
also taken until the results reach a specified confidence level.
When used in an object's interior statement, sampling only occurs
inside the object.  When used for atmospheric media, the samples
run from the camera location until the ray strikes an object.
Therefore for localized effects, it is best to use an enclosing
object even though the density pattern might only produce results
in a small area whether the media was enclosed or not.

The complete syntax for a media statement is as follows:

MEDIA:
  media { [MEDIA_IDENTIFIER] [MEDIA_ITEMS...] }
MEDIA_ITEMS:
  intervals Number   |   samples Min, Max   |
  confidence Value   |   variance Value   |   ratio Value   |
  absorption  COLOR   |   emission COLOR   |
  scattering { Type, COLOR  [ eccentricity Value ] [ extinction
  Value ] }   |
  density { [DENSITY_IDENTIFIER] [PATTERN_TYPE]
  [DENSITY_MODIFIER...]  }   |
  TRANSFORMATIONS
DENSITY_MODIFIER:
  PATTERN_MODIFIER   |   DENSITY_LIST   |   COLOR_LIST   |
  color_map{ COLOR_MAP_BODY }   |   colour_map{ COLOR_MAP_BODY }
  |
  density_map{ DENSITY_MAP_BODY }
If a media identifier is specified, it must be the first item.
All other media items may be specified in any order.  All are
optional.  You may have multiple density statements in a single
media statement.  See "Multiple Density vs. Multiple Media" for
details.  Transformations apply only the density statements which
have been already specified.  Any density after a transformation
is not affected.  If the media has no density statements and none
was specified in any media identifier, then the transformation
has no effect.  All other media items except for density and
transformations override default values or any previously set
values for this media statement.

Note that some media effects depend upon light sources.  However
the participation of a light source depends upon the
media_interaction and media_attenuation keywords.  See
"Atmospheric Media Interaction" and "Atmospheric Attenuation" for
details.

Note a strange design side-effect was discovered during testing
and it was too difficult to fix.  If the enclosing object uses
transmit rather than filter for transparency, then the media
casts no shadows.  For example:

 object{MyObject pigment{rgbt 1.0} interior{media{MyMedia}}} //no
shadows
 object{MyObject pigment{rgbf 1.0} interior{media{MyMedia}}}
//shadows

4.8.1     Media Types
There are three types of particle interaction in media:
absorbing, emitting, and scattering.  All three activities may
occur in a single media.  Each of these three specifications
requires a color.  Only the red, green, and blue components of
the color are used.  The filter and transmit values are ignored.
For this reason it is permissible to use one float value to
specify an intensity of white color.  For example the following
two lines are legal and produce the same results:

  emission 0.75
  emission rgb<0.75,0.75,0.75>

4.8.1.1   Absorption
The absorption keyword specifies a color of light which is
absorbed when looking through the media.  For example absorption
rgb<0,1,0> blocks the green light but permits red and blue to get
through.  Therefore a white object behind the media will appear
magenta.

The default value is rgb<0,0,0> which means no light is absorbed
-- all light passes through normally.


4.8.1.2   Emission
The emission keyword specifies a color of the light emitted from
the particles.  Although we say they "emit" light, this only
means that they are visible without any illumination shining on
them.  They to not really emit light that is cast on to nearby
objects.  This is similar to an object with high ambient values.
The default value is rgb<0,0,0> which means no light is emitted.


4.8.1.3   Scattering
The syntax of a scattering statement is:

SCATTERING:
  scattering { Type, COLOR  [ eccentricity Value ] [ extinction
  Value ] }
The first float value specifies the type of scattering.  This is
followed by the color of the scattered light.  The default value
if no scattering statement is given is rgb<0,0,0> which means no
scattering occurs.

The scattering effect is only visible when light is shining on
the media from a light source.  This is similar to difuse
reflection off of an object.  In addition to reflecting light, a
scattering media also absorbs light like an absorption media.
The balance between how much absorption occurs for a given amount
of scattering is controlled by the optional extinction keyword
and a single float value.  The default value of 1.0 gives an
extinction effect that matches the scattering.  Values such as
extinction 0.25 give 25% the normal amount.  Using extinction 0.0
turns it off completely.  Any value other than the 1.0 default is
contrary to the real physical model but decreasing extinction can
give you more artistic flexibility.

The integer value Type specifies one of five different scattering
phase functions representing the different models: isotropic, Mie
(haze and murky atmosphere), Rayleigh, and Henyey-Greenstein.

Type 1, isotropic scattering is the simplest form of scattering
because it is independent of direction. The amount of light
scattered by particles in the atmosphere does not depend on the
angle between the viewing direction and the incoming light.

Types 2 and 3 are Mie haze and Mie murky scattering which are
used for relatively small particles such as minuscule water
droplets of fog, cloud particles, and particles responsible for
the polluted sky. In this model the scattering is extremely
directional in the forward direction i.e. the amount of scattered
light is largest when the incident light is anti-parallel to the
viewing direction (the light goes directly to the viewer). It is
smallest when the incident light is parallel to the viewing
direction. The haze and murky atmosphere models differ in their
scattering characteristics. The murky model is much more
directional than the haze model.

                                
                                
               The Mie "haze" scattering function.
                                
                                
                                
              The Mie "murky" scattering function.
                                
Type 3 Rayleigh scattering models the scattering for extremely
small particles such as molecules of the air. The amount of
scattered light depends on the incident light angle. It is
largest when the incident light is parallel or anti-parallel to
the viewing direction and smallest when the incident light is
perpendicular to the viewing direction. You should note that the
Rayleigh model used in POV-Ray does not take the dependency of
scattering on the wavelength into account.

                                
                                
                The Rayleigh scattering function.
                                
Type 5 is the Henyey-Greenstein scattering model.  It is based on
an analytical function and can be used to model a large variety
of different scattering types. The function models an ellipse
with a given eccentricity e. This eccentricity is specified by
the optional keyword eccentricity which is only used for
scattering type five. The default eccentricity value of zero
defines isotropic scattering while positive values lead to
scattering in the direction of the light and negative values lead
to scattering in the opposite direction of the light. Larger
values of e (or smaller values in the negative case) increase the
directional property of the scattering.

                                
                                
     The Heyney-Greenstein scattering function for different
                      eccentricity values.
                                

4.8.2     Sampling Parameters
Media effects are calculated by sampling the media along the path
of the ray.  It uses a method called Monte Carlo integration.
The intervals keyword may be used to specify the integer number
of intervals used to sample the ray.  The default number of
intervals is 10.  For object media the intervals are spread
between the entry and exit points as the ray passes through the
container object.  For atmospheric media, the intervals span
entire length of the ray from its start until it hits an object.

For media types which interact with spotlights or cylinder
lights, the intervals which are not illuminated by these light
types are weighted differently than the illuminated intervals
when distributing samples.  The ratio keyword distributes
intervals differently between lit and unlit areas.  The default
value of ratio 0.9 means that lit intervals get more samples than
unlit intervals.  Note that the total number of intervals must
exceed the number of illuminated intervals.  If a ray passes in
and out of 8 spotlights but you've only specified 5 intervals
then an error occurs.

The samples Min, Max keyword specifies the minimum and maximum
number of samples taken per interval.  The default values are
samples 1,1.

As each interval is sampled, the variance is computed.  If the
variance is below a threshold value, then no more samples are
needed.  The variance and confidence keywords specify the
permitted variance allowed and the confidence that you are within
that variance.  The exact calculations are quite complex and
involve chi-squared tests and other statistical principles too
messy to describe here.  The default values are varience 1.0/128
and confidence 0.9.  For slower more accurate results, decrease
the variance and increase the confidence.  Note however that the
maximum number of samples limits the calculations even if the
proper variance and confidence are never reached.


4.8.3     Density
Particles of media are normally distributed in constant density
throughout the media.  However the density statement allows you
to vary the density across space using any of POV-Ray's pattern
functions such as those used in textures.  If no density
statement is given then the density remains a constant value of
1.0 throughout the media.  More than one density may be specified
per media statement.  See "Multiple Density vs. Multiple Media".

The syntax for density is:

DENSITY:
  density { [DENSITY_IDENTIFIER] [DENSITY_TYPE]
[DENSITY_MODIFIER...]  }
DENSITY_TYPE:
  PATTERN_TYPE   |   COLOR
DENSITY_MODIFIER:
  PATTERN_MODIFIER   |   DENSITY_LIST   |
  color_map{ COLOR_MAP_BODY }   |   colour_map{ COLOR_MAP_BODY }
  |
  density_map{ DENSITY_MAP_BODY }
The density statement may begin with an optional density
identifier.  All subsequent values modify the defaults or the
values in the identifier.  The next item is a pattern type.  This
is any one of POV-Ray's pattern functions such as bozo, wood,
gradient, waves, etc.  Of particular usefulness are the
spherical, planar, cylindrical, and boxed patterns which were
previously available only for use with our discontinued halo
feature.  All patterns return a value from 0.0 to 1.0.  This
value is interpreted as the density of the media at that
particular point.  See "Patterns" for details on particular
pattern types.   Although a solid COLOR pattern is legal, in
general it is used only when the density statement is inside a
density_map.


4.8.3.1   General Density Modifiers
A density statement may be modified by any of the general pattern
modifiers such as transformations, turbulence and warp.  See
"Pattern Modifiers" for details.  In addition there are several
density-specific modifiers which can be used.


4.8.3.2   Density with color_map
Typically a media uses just one constant color throughout.  Even
if you vary the density, it is usually just one color which is
specified by the absorption, emission, or scattering keywords.
However when using emission to simulate fire or explosions, the
center of the flame (high density area) is typically brighter and
white or yellow.  The outer edge of the flame (less density)
fades to orange, red, or in some cases deep blue.  To model the
density-dependent change in color which is visible, you may
specify a color_map.  The pattern function returns a value from
0.0 to 1.0 and the value is passed to the color map to compute
what color or blend of colors is used.  See "Color Maps" for
details on how pattern values work with color_map. This resulting
color is multiplied by the absorption, emission and scattering
color.  Currently there is no way to specify different color maps
for each media type within the same media statement.

Consider this example:

  media{
    emission 0.75
    scattering {1, 0.5}
    density { spherical
      color_map{
        [0.0 rgb <0,0,0.5>]
        [0.5 rgb <0.8, 0.8, 0.4>]
        [1.0 rgb <1,1,1>]
      }
    }
  }
The color map ranges from white at density 1.0 to bright yellow
at density 0.5 to deep blue at density 0.  Assume we sample a
point at density 0.5.  The emission is 0.75*<0.8,0.8,0.4> or
<0.6,0.6,0.3>.  Similarly the scattering color is
0.5*<0.8,0.8,0.4> or <0.4,0.4,0.2>.

For block pattern types checker, hexagon, and brick you may
specify a color list such as this:

  density{checker rgb<1,0,0>, rgb<0,0,0>}
See "Color List Pigments" which describes how pigment uses a
color list.  The same principles apply when using them with
density.


4.8.3.3   Density Maps and Density Lists
In addition to specifying blended colors with a color map you may
create a blend of densities using a density_map. The syntax for a
density map is identical to a color map except you specify a
density in each map entry (and not a color).

The syntax for density_map is as follows:

DENSITY_MAP:
  density_map{ DENSITY_MAP_BODY }
DENSITY_MAP_BODY:
  DENSITY_MAP_IDENTIFIER   |   DENSITY_MAP_ENTRY...
DENSITY_MAP_ENTRY:
  [ Value  DENSITY_BODY ]
Where Value is a float value between 0.0 and 1.0 inclusive and
each DENSITY_BODY is anything which can be inside a density{...}
statement.  The density keyword and {} braces need not be
specified.

Note that the [] brackets are part of the actual
DENSITY_MAP_ENTRY. They are not notational symbols denoting
optional parts. The brackets surround each entry in the density
map. There may be from 2 to 256 entries in the map.

Density maps may be nested to any level of complexity you desire.
The densities in a map may have color maps or density maps or any
type of density you want.

Entire densities may also be used with the block patterns such as
checker, hexagon and brick. For example...

  density {
    checker
    density { Flame scale .8 }
    density { Fire scale .5 }
  }
Note that in the case of block patterns the density wrapping is
required around the density information.

A density map is also used with the average density type. See
"Average" for details.

You may declare and use density map identifiers but the only way
to declare a density block pattern list is to declare a density
identifier for the entire density.


4.8.3.4   Multiple Density vs. Multiple Media
It is possible to have more than one media specified per object
and it is legal to have more than one density per media.  The
effects are quite different.  Consider this example:

  object{MyObject
    pigment{rgbf 1}
    interior{
      media{
        density{Some_Density}
        density{Another_Density}
      }
    }
  }
As the media is sampled, calculations are performed for each
density pattern at each sample point.  The resulting samples are
multiplied together.  Suppose one density returned rgb<.8,.8,.4>
and the other returned rgb<.25,.25,0>.  The resulting color is
rgb<.2,.2,0>.  Note that in areas where one density returns zero,
it will wipe out the other density.  The end result is that only
density areas which overlap will be visible.  This is similar to
a CSG intersection operation.  Now consider

  object{MyObject
    pigment{rgbf 1}
    interior{
      media{
        density{Some_Density}
      }
      media{
        density{Another_Density}
      }
    }
  }
In this case each media is computed independently.  The resulting
colors are added together.  Suppose one density and media
returned rgb<.8,.8,.4> and the other returned rgb<.25,.25,0>.
The resulting color is rgb<1.05,1.05,.4>.  The end result is that
density areas which overlap will be especially bright and all
areas will be visible.  This is similar to a CSG union operation.
See the sample scene scenes/interior/media/media4.pov for an
example which illustrates this.



4.9  Atmospheric Effects
Atmospheric effects are a loosely-knit group of features that
affect the background and/or the atmosphere enclosing the scene.
POV-Ray includes the ability to render a number of atmospheric
effects, such as fog, haze, mist, rainbows and skies.


4.9.1     Atmospheric Media
Atmospheric effects such as fog, dust, haze, or visible gas may
be simulated by a media statement specified in the scene but not
attached to any object.  All areas not inside a non-hollow object
in the entire scene.  A very simple approach to add fog to a
scene is explained in section "Fog" however this kind of fog does
not interact with any light sources like media does. It will not
show light beams or other effects and is therefore not very
realistic.

The atmosphere media effect overcomes some of the fog's
limitations by calculating the interaction between light and the
particles in the atmosphere using volume sampling. Thus shaft of
light beams will become visible and objects will cast shadows
onto smoke or fog.

With spotlights you'll be able to create the best results because
their cone of light will become visible. Pointlights can be used
to create effects like street lights in fog. Lights can be made
to not interact with the atmosphere by adding media_interaction
off to the light source. They can be used to increase the overall
light level of the scene to make it look more realistic.

Complete details on media are given in the section "Media".
Earlier versions of POV-Ray used an atmosphere statement for
atmospheric effects but that system was incompatible with the old
object halo system.  So atmosphere has been eliminated and
replaced with a simpler and more powerful media feature.  The
user now only has to learn one media system for either
atmospheric or object use.

If you only want media effects in a particular area, you should
use object media rather than only relying upon the media pattern.
In general it will be faster and more accurate because it only
calculates inside the constraining object.

You should note that the atmosphere feature will not work if the
camera is inside a non-hollow object (see section "Empty and
Solid Objects" for a detailed explanation).


4.9.2     Background
A background color can be specified if desired. Any ray that
doesn't hit an object will be colored with this color. The
default background is black. The syntax for background is:

BACKGROUND:
  background {COLOR}

4.9.3     Fog
If it is not necessary for light beams to interact with
atmospheric media, then fog may be a faster way to simulate haze
or fog.  This feature artificially adds color to every pixel
based on the distance the ray has traveled.  The syntax for fog
is:

FOG:
  fog { [FOG_IDENTIFIER] [FOG_ITEMS...] }
FOG_ITEMS:
  fog_type Fog_Type   |   distance Distance   |   COLOR   |
  turbulence <Turbulence>   |   turb_depth Turb_Depth   |
  omega Omega   |   lambda Lambda   |   octaves Octaves   |
  fog_offset Fog_Offset   |   fog_alt Fog_Alt   |
  up <Fog_Up>   |   TRANSFORMATION
Currently there are two fog types, the default fog_type 1 is a
constant fog and fog_type 2 is ground fog. The constant fog has a
constant density everywhere while the ground fog has a constant
density for all heights below a given point on the up axis and
thins out along this axis.

The color of a pixel with an intersection depth d is calculated
by

  PIXEL_COLOR = exp(-d/D) * OBJECT_COLOR + (1-exp(-d/D)) *
FOG_COLOR

where D is the specified value of the required fog distance
keyword. At depth 0 the final color is the object's color. If the
intersection depth equals the fog distance the final color
consists of 64% of the object's color and 36% of the fog's color.

For ground fog, the height below which the fog has constant
density is specified by the fog_offset keyword. The fog_alt
keyword is used to specify the rate by which the fog fades away.
The default values for both are 0.0 so be sure to specify them if
ground fog is used.  At an altitude of Fog_Offset+Fog_Alt the fog
has a density of 25%. The density of the fog at height less than
or equal to Fog_Alt is 1.0 and for height y less than Fog_Alt is
calculated by

  1/(1 + (y - Fog_Offset) / Fog_Alt) ^2)

The total density along a ray is calculated by integrating from
the height of the starting point to the height of the end point.

The optional up vector specifies a direction pointing up,
generally the same as the camera's up vector. All calculations
done during the ground fog evaluation are done relative to this
up vector, i. e. the actual heights are calculated along this
vector. The up vector can also be modified using any of the known
transformations described in "Transformations". Though it may not
be a good idea to scale the up vector - the results are hardly
predictable - it is quite useful to be able to rotate it. You
should also note that translations do not affect the up direction
(and thus don't affect the fog).

The required fog color has three purposes. First it defines the
color to be used in blending the fog and the background. Second
it is used to specify a translucency threshold. By using a
transmittance larger than zero one can make sure that at least
that amount of light will be seen through the fog.  With a
transmittance of 0.3 you'll see at least 30% of the background.
Third it can be used to make a filtering fog. With a filter value
larger than zero the amount of background light given by the
filter value will be multiplied with the fog color. A filter
value of 0.7 will lead to a fog that filters 70% of the
background light and leaves 30% unfiltered.

Fogs may be layered. That is, you can apply as many layers of fog
as you like. Generally this is most effective if each layer is a
ground fog of different color, altitude and with different
turbulence values. To use multiple layers of fogs, just add all
of them to the scene.

You may optionally stir up the fog by adding turbulence. The
turbulence keyword may be followed by a float or vector to
specify an amount of turbulence to be used. The omega, lambda and
octaves turbulence parameters may also be specified. See section
"Pattern Modifiers" for details on all of these turbulence
parameters.

Additionally the fog turbulence may be scaled along the direction
of the viewing ray using the turb_depth amount. Typical values
are from 0.0 to 1.0 or more. The default value is 0.5 but any
float value may be used.

You should note that the fog feature will not work if the camera
is inside a non-hollow object (see section "Empty and Solid
Objects" for a detailed explanation).


4.9.4     Sky Sphere
The sky sphere is used create a realistic sky background without
the need of an additional sphere to simulate the sky. Its syntax
is:

SKY_SPHERE:
  sky_sphere { [SKY_SPHERE_IDENTIFIER] [SKY_SPHERE_ITEMS...] }
SKY_SPHERE_ITEM:
  PIGMENT   |   TRANSFORMATION
The sky sphere can contain several pigment layers with the last
pigment being at the top, i. e. it is evaluated last, and the
first pigment being at the bottom, i. e. it is evaluated first.
If the upper layers contain filtering and/or transmitting
components lower layers will shine through. If not lower layers
will be invisible.

The sky sphere is calculated by using the direction vector as the
parameter for evaluating the pigment patterns. This leads to
results independent from the view point which pretty good models
a real sky where the distance to the sky is much larger than the
distances between visible objects.

If you want to add a nice color blend to your background you can
easily do this by using the following example.

  sky_sphere {
    pigment {
      gradient y
      color_map {
        [ 0.5  color CornflowerBlue ]
        [ 1.0  color MidnightBlue ]
      }
      scale 2
      translate -1
    }
  }
This gives a soft blend from CornflowerBlue at the horizon to
MidnightBlue at the zenith. The scale and translate operations
are used to map the direction vector values, which lie in the
range from <-1, -1, -1> to <1, 1, 1>, onto the range from <0, 0,
0> to <1, 1, 1>. Thus a repetition of the color blend is avoided
for parts of the sky below the horizon.

In order to easily animate a sky sphere you can transform it
using the usual transformations described in "Transformations".
Though it may not be a good idea to translate or scale a sky
sphere - the results are hardly predictable - it is quite useful
to be able to rotate it. In an animation the color blendings of
the sky can be made to follow the rising sun for example.

You should note that only one sky sphere can be used in any
scene. It also will not work as you might expect if you use
camera types like the orthographic or cylindrical camera. The
orthographic camera uses parallel rays and thus you'll only see a
very small part of the sky sphere (you'll get one color skies in
most cases). Reflections in curved surface will work though, e.
g. you will clearly see the sky in a mirrored ball.


4.9.5     Rainbow
Rainbows are implemented using fog-like, circular arcs. Their
syntax is:

RAINBOW:
  rainbow { [RAINBOW_IDENTIFIER] [RAINBOW_ITEMS...] }
RAINBOW_ITEM:
  direction <Dir>   |   angle Angle   |   width Width   |
distance Distance   |
  COLOR_MAP   |   jitter Jitter   |   up <Up>   |
  arc_angle Arc_Angle   |   falloff_angle Falloff_Angle
The required direction vector determines the direction of the
(virtual) light that is responsible for the rainbow. Ideally this
is an infinitely far away light source like the sun that emits
parallel light rays. The position and size of the rainbow are
specified by the required angle and width keywords. To understand
how they work you should first know how the rainbow is
calculated.

For each ray the angle between the rainbow's direction vector and
the ray's direction vector is calculated. If this angle lies in
the interval from Angle-Width/2 to Angle+Width/2 the rainbow is
hit by the ray. The color is then determined by using the angle
as an index into the rainbow's color_map. After the color has
been determined it will be mixed with the background color in the
same way like it is done for fogs.

Thus the angle and width parameters determine the angles under
which the rainbow will be seen. The optional jitter keyword can
be used to add random noise to the index. This adds some
irregularity to the rainbow that makes it look more realistic.

The required distance keyword is the same like the one used with
fogs. Since the rainbow is a fog-like effect it's possible that
the rainbow is noticeable on objects. If this effect is not
wanted it can be avoided by using a large distance value. By
default a sufficiently large value is used to make sure that this
effect does not occur.

The color_map statement is used to assign a color map that will
be mapped onto the rainbow. To be able to create realistic
rainbows it is important to know that the index into the color
map increases with the angle between the ray's and rainbow's
direction vector. The index is zero at the innermost ring and one
at the outermost ring. The filter and transmittance values of the
colors in the color map have the same meaning as the ones used
with fogs (see section "Fog").

The default rainbow is a 360 degree arc that looks like a circle.
This is no problem as long as you have a ground plane that hides
the lower, non-visible part of the rainbow. If this isn't the
case or if you don't want the full arc to be visible you can use
the optional keywords up, arc_angle and falloff_angle to specify
a smaller arc.

The arc_angle keyword determines the size of the arc in degrees
(from 0 to 360 degrees). A value smaller than 360 degrees results
in an arc that abruptly vanishes. Since this doesn't look nice
you can use the falloff_angle keyword to specify a region in
which the rainbow will smoothly blend into the background making
it vanish softly. The falloff angle has to be smaller or equal to
the arc angle.

The up keyword determines were the zero angle position is. By
changing this vector you can rotate the rainbow about its
direction. You should note that the arc goes from -Arc_Angle/2 to
+Arc_Angle/2. The soft regions go from -Arc_Angle/2 to -
Falloff_Angle/2 and from +Falloff_Angle/2 to +Arc_Angle/2.

The following example generates a 120 degrees rainbow arc that
has a falloff region of 30 degrees at both ends:

  rainbow {
    direction <0, 0, 1>
    angle 42.5
    width 5
    distance 1000
    jitter 0.01
    color_map { Rainbow_Color_Map }
    up <0, 1, 0>
    arc_angle 120
    falloff_angle 30
  }
It is possible to use any number of rainbows and to combine them
with other atmospheric effects.





4.10  C4A-Global Settings
The global_settings statement is a catch-all statement that
gathers together a number of global parameters. The statement may
appear anywhere in a scene as long as it is not inside any other
statement. You may have multiple global_settings statements in a
scene. Whatever values were specified in the last global_settings
statement override any previous settings.  Regardless of where
you specify the statement, the feature applies to the entire
scene.

Note that some items which were language directives in earlier
versions of POV-Ray have been moved inside the global_settings
statement so that it is more obvious to the user that their
effect is global. The old syntax is permitted but generates a
warning.  The new syntax is:

GLOBAL_SETTINGS:
  global_settings { [GLOBAL_SETTINGS_ITEMS...] }
GLOBAL_SETTINGS_ITEM:
  adc_bailout Value   |   ambient_light COLOR   |
  assumed_gamma Value   |
  hf_gray_16 [Bool}   |   irid_wavelength COLOR   |
  max_intersections Number   |
  max_trace_level Number   |   number_of_waves Number   |
  radiosity { RADIOSITY_ITEMS... }
Each item is optional and may appear in and order. If an item is
specified more than once, the last setting overrides previous
values. Details on each item are given in the following sections.


4.10.1     ADC_Bailout
In scenes with many reflective and transparent surfaces, POV-Ray
can get bogged down tracing multiple reflections and refractions
that contribute very little to the color of a particular pixel.
The program uses a system called Adaptive Depth Control (ADC) to
stop computing additional reflected or refracted rays when their
contribution is insignificant.

You may use the global setting adc_bailout keyword followed by
float value to specify the point at which a ray's contribution is
considered insignificant.  For example:

  global_settings { adc_bailout 0.01 }
The default value is 1/255, or approximately 0.0039, since a
change smaller than that could not be visible in a 24 bit image.
Generally this setting is perfectly adequate and should be left
alone. Setting adc_bailout to 0 will disable ADC, relying
completely on max_trace_level to set an upper limit on the number
of rays spawned.

See section "Max_Trace_Level" for details on how ADC and
max_trace_level interact.


4.10.2     Ambient Light
Ambient light is used to simulate the effect of inter-diffuse
reflection that is responsible for lighting areas that partially
or completely lie in shadow.  POV-Ray provides the ambient_light
keyword to let you easily change the brightness of the ambient
lighting without changing every ambient value in all finish
statements. It also lets you create interesting effects by
changing the color of the ambient light source. The syntax is:

  global_settings { ambient_light COLOR }
The default is a white ambient light source set at rgb <1,1,1>.
Only the rgb components are used.  The actual ambient used is:
Ambient = Finish_Ambient * Global_Ambient.

See section "Ambient" for more information.


4.10.3     Assumed_Gamma
Many people may have noticed at one time or another that some
images are too bright or dim when displayed on their system. As a
rule, Macintosh users find that images created on a PC are too
bright, while PC users find that images created on a Macintosh
are too dim.

The assumed_gamma global setting works in conjunction with the
Display_Gamma INI setting (see section "Display Hardware
Settings") to ensure that scene files render the same way across
the wide variety of hardware platforms that POV-Ray is used on.
The assumed gamma setting is used in a scene file by adding

  global_settings { assumed_gamma Value }
where the assumed gamma value is the correction factor to be
applied before the pixels are displayed and/or saved to disk. For
scenes created in older versions of POV-Ray, the assumed gamma
value will be the same as the display gamma value of the system
the scene was created on. For PC systems, the most common display
gamma is 2.2, while for scenes created on Macintosh systems
should use a scene gamma of 1.8. Another gamma value that
sometimes occurs in scenes is 1.0.

Scenes that do not have an assumed_gamma global setting will not
have any gamma correction performed on them, for compatibility
reasons. If you are creating new scenes or rendering old scenes,
it is strongly recommended that you put in an appropriate
assumed_gamma global setting. For new scenes, you should use an
assumed gamma value of 1.0 as this models how light appears in
the real world more realistically.

The following sections explain more thoroughly what gamma is and
why it is important.


4.10.3.1   Monitor Gamma
The differences in how images are displayed is a result of how a
computer actually takes an image and displays it on the monitor.
In the process of rendering an image and displaying it on the
screen, several gamma values are important, including the POV
scene file or image file gamma and the monitor gamma.

Most image files generated by POV-Ray store numbers in the range
from 0 to 255 for each of the red, green and blue components of a
pixel. These numbers represent the intensity of each color
component, with 0 being black and 255 being the brightest color
(either 100% red, 100% green or 100% blue). When an image is
displayed, the graphics card converts each color component into a
voltage which is sent to the monitor to light up the red, green
and blue phosphors on the screen.  The voltage is usually
proportional to the value of each color component.

Gamma becomes important when displaying intensities that aren't
the maximum or minimum possible values. For example, 127 should
represent 50% of the maximum intensity for pixels stored as
numbers between 0 and 255. On systems that don't do gamma
correction, 127 will be converted to 50% of the maximum voltage,
but because of the way the phosphors and the electron guns in a
monitor work, this may be only 22% of the maximum color intensity
on a monitor with a gamma of 2.2.  To display a pixel which is
50% of the maximum intensity on this monitor, we would need a
voltage of 73% of the maximum voltage, which translates to
storing a pixel value of 186.

The relationship between the input pixel value and the displayed
intensity can be approximated by an exponential function obright
= ibright ^ display_gamma where obright is the output intensity
and ibright is the input pixel intensity. Both values are in the
range from 0 to 1 (0% to 100%). Most monitors have a fixed gamma
value in the range from 1.8 to 2.6. Using the above formula with
display_gamma values greater than 1 means that the output
brightness will be less than the input brightness. In order to
have the output and input brightness be equal an overall system
gamma of 1 is needed. To do this, we need to gamma correct the
input brightness in the same manner as above but with a gamma
value of 1/display_gamma before it is sent to the monitor. To
correct for a display gamma of 2.2, this pre-monitor gamma
correction uses a gamma value of 1.0/2.2 or approximately 0.45.

How the pre-monitor gamma correction is done depends on what
hardware and software is being used. On Macintosh systems, the
operating system has taken it upon itself to insulate
applications from the differences in display hardware. Through a
gamma control panel the user may be able to set the actual
monitor gamma and Mac will then convert all pixel intensities so
that the monitor will appear to have the specified gamma value.
On Silicon Graphics machines, the display adapter has built-in
gamma correction calibrated to the monitor which gives the
desired overall gamma (the default is 1.7). Unfortunately, on PCs
and most UNIX systems, it is up to the application to do any
gamma correction needed.


4.10.3.2   Image File Gamma
Since most PC and UNIX applications and image file formats don't
understand display gamma, they don't do anything to correct for
it.  As a result, users creating images on these systems adjust
the image in such a way that it has the correct brightness when
displayed. This means that the data values stored in the files
are made brighter to compensate for the darkening effect of the
monitor. In essence, the 0.45 gamma correction is built in to the
image files created and stored on these systems. When these files
are displayed on a Macintosh system, the gamma correction built
in to the file, in addition to gamma correction built into MacOS,
means that the image will be too bright. Similarly, files that
look correct on Macintosh or SGI systems because of the built-in
gamma correction will be too dark when displayed on a PC.

The new PNG format files generated by POV-Ray 3.0 overcome the
problem of too much or not enough gamma correction by storing the
image file gamma (which is 1.0/display_gamma) inside the PNG file
when it is generated by POV-Ray. When the PNG file is later
displayed by a program that has been set up correctly, it uses
this gamma value as well as the current display gamma to correct
for the potentially different display gamma used when originally
creating the image.

Unfortunately, of all the image file formats POV-Ray supports,
PNG is the only one that has any gamma correction features and is
therefore preferred for images that will be displayed on a wide
variety of platforms.


4.10.3.3   Scene File Gamma
The image file gamma problem itself is just a result of how
scenes themselves are generated in POV-Ray. When you start out
with a new scene and are placing light sources and adjusting
surface textures and colors, you generally make several attempts
before the lighting is how you like it. How you choose these
settings depends upon the preview image or the image file stored
to disk, which in turn is dependent upon the overall gamma of the
display hardware being used.

This means that as the artist you are doing gamma correction in
the POV-Ray scene file for your particular hardware. This scene
file will generate an image file that is also gamma corrected for
your hardware and will display correctly on systems similar to
your own.  However, when this scene is rendered on another
platform, it may be too bright or too dim, regardless of the
output file format used.  Rather than have you change all the
scene files to have a single fixed gamma value (heaven forbid!),
POV-Ray 3.0 allows you to specify in the scene file the display
gamma of the system that the scene was created on.

The assumed_gamma global setting, in conjunction with the
Display_Gamma INI setting lets POV-Ray know how to do gamma
correction on a given scene so that the preview and output image
files will appear the correct brightness on any system. Since the
gamma correction is done internally to POV-Ray, it will produce
output image files that are the correct brightness for the
current display, regardless of what output format is used. As
well, since the gamma correction is performed in the high-
precision data format that POV-Ray uses internally, it produces
better results than gamma correction done after the file is
written to disk.

Although you may not notice any difference in the output on your
system with and without an assumed_gamma setting, the assumed
gamma is important if the scene is ever rendered on another
platform.


4.10.4     HF_Gray_16
The hf_gray_16 setting is useful when using POV-Ray to generate
heightfields for use in other POV-Ray scenes. The syntax is...

  global_settings { hf_gray_16 [Bool] }
The boolean value turns the option on or off. If the keyword is
specified without the boolean value then the option is turned on.
If hf_gray_16 is not specified in any global_settings statement
in the entire scene then the default is off.

When hf_gray_16 is on, the output file will be in the form of a
heightfield, with the height at any point being dependent on the
brightness of the pixel. The brightness of a pixel is calculated
in the same way that color images are converted to grayscale
images:  height = 0.3 * red + 0.59 * green + 0.11 * blue.

Setting the hf_gray_16 option will cause the preview display, if
used, to be grayscale rather than color. This is to allow you to
see how the heightfield will look because some file formats store
heightfields in a way that is difficult to understand afterwards.
See section "Height Field" for a description of how POV-Ray
heightfields are stored for each file type.


4.10.5     Irid_Wavelength
Iridescence calculations depend upon the dominant wavelengths of
the primary colors of red, green and blue light. You may adjust
the values using the global setting irid_wavelength as follows...

  global_settings { irid_wavelength COLOR }
The default value is rgb <0.25,0.18,0.14> and any filter or
transmit values are ignored. These values are proportional to the
wavelength of light but they represent no real world units.

In general, the default values should prove adequate but we
provide this option as a means to experiment with other values.


4.10.6     Max_Trace_Level
In scenes with many reflective and transparent surfaces POV-Ray
can get bogged down tracing multiple reflections and refractions
that contribute very little to the color of a particular pixel.
The global setting max_trace_level defines the integer maximum
number of recursive levels that POV-Ray will trace a ray.

  global_settings { max_trace_level Level }
This is used when a ray is reflected or is passing through a
transparent object and when shadow rays are cast. When a ray hits
a reflective surface, it spawns another ray to see what that
point reflects. That is trace level one. If it hits another
reflective surface another ray is spawned and it goes to trace
level two.  The maximum level by default is five.

One speed enhancement added to POV-Ray in version 3.0 is Adaptive
Depth Control (ADC). Each time a new ray is spawned as a result
of reflection or refraction its contribution to the overall color
of the pixel is reduced by the amount of reflection or the filter
value of the refractive surface. At some point this contribution
can be considered to be insignificant and there is no point in
tracing any more rays. Adaptive depth control is what tracks this
contribution and makes the decision of when to bail out. On
scenes that use a lot of partially reflective or refractive
surfaces this can result in a considerable reduction in the
number of rays fired and makes it safer to use much higher
max_trace_level values.

This reduction in color contribution is a result of scaling by
the reflection amount and/or the filter values of each surface,
so a perfect mirror or perfectly clear surface will not be
optimizable by ADC. You can see the results of ADC by watching
the Rays Saved and Highest Trace Level displays on the statistics
screen.

The point at which a ray's contribution is considered
insignificant is controlled by the adc_bailout value. The default
is 1/255 or approximately 0.0039 since a change smaller than that
could not be visible in a 24 bit image.  Generally this setting
is perfectly adequate and should be left alone. Setting
adc_bailout to 0 will disable ADC, relying completely on
max_trace_level to set an upper limit on the number of rays
spawned.

If max_trace_level is reached before a non-reflecting surface is
found and if ADC hasn't allowed an early exit from the ray tree
the color is returned as black. Raise max_trace_level if you see
black areas in a reflective surface where there should be a
color.

The other symptom you could see is with transparent objects. For
instance, try making a union of concentric spheres with a clear
texture on them. Make ten of them in the union with radius's from
1 to 10 and render the scene. The image will show the first few
spheres correctly, then black. This is because a new level is
used every time you pass through a transparent surface. Raise
max_trace_level to fix this problem.

Note that raising max_trace_level will use more memory and time
and it could cause the program to crash with a stack overflow
error, although ADC will alleviate this to a large extent. Values
for max_trace_level are not restricted, so it can be set to any
number as long as you have the time and memory. However,
increasing its setting does not necessarily equate to increased
image quality unless such depths are really needed by the scene.


4.10.7     Max_Intersections
POV-Ray uses a set of internal stacks to collect ray/object
intersection points. The usual maximum number of entries in these
I-Stacks is 64. Complex scenes may cause these stacks to
overflow.  POV-Ray doesn't stop but it may incorrectly render
your scene. When POV-Ray finishes rendering, a number of
statistics are displayed. If you see I-Stack Overflows reported
in the statistics you should increase the stack size. Add a
global setting to your scene as follows:

  global_settings { max_intersections Integer }
If the I-Stack Overflows remain increase this value until they
stop.


4.10.8     Number_Of_Waves
The waves and ripples pattern are generated by summing a series
of waves, each with a slightly different center and size. By
default, ten waves are summed but this amount can be globally
controlled by changing the number_of_waves setting.

  global_settings { number_of_waves Integer }
Changing this value affects both waves and ripples alike on all
patterns in the scene.


4.10.9     Radiosity
Important notice: The radiosity features in POV-Ray are somewhat
experimental. There is a high probability that the design and
implementation of these features will be changed in future
versions. We cannot guarantee that scenes using these features in
this version will render identically in future releases or that
full backwards compatibility of language syntax can be
maintained.

Radiosity is an extra calculation that more realistically
computes the diffuse interreflection of light. This diffuse
interreflection can be seen if you place a white chair in a room
full of blue carpet, blue walls and blue curtains. The chair will
pick up a blue tint from light reflecting off of other parts of
the room. Also notice that the shadowed areas of your
surroundings are not totally dark even if no light source shines
directly on the surface. Diffuse light reflecting off of other
objects fills in the shadows. Typically ray-tracing uses a trick
called ambient light to simulate such effects but it is not very
accurate.

Radiosity is more accurate than simplistic ambient light but it
takes much longer to compute. For this reason, POV-Ray does not
use radiosity by default. Radiosity is turned on using the
Radiosity INI file option or the +QR command line switch.

The following sections describes how radiosity works, how to
control it with various global settings and tips on trading
quality vs.  speed.


4.10.9.1   How Radiosity Works
The problem of ray-tracing is to figure out what the light level
is at each point that you can see in a scene. Traditionally, in
ray tracing, this is broken into the sum of these components:

  -  Diffuse, the effect that makes the side of things facing the
  light brighter;
  -  Specular, the effect that makes shiny things have dings or
  sparkles on them;
  -  Reflection, the effect that mirrors give; and
  -  Ambient, the general all-over light level that any scene
  has, which keeps things in shadow from being pure black.
POV-Ray's radiosity system, based on a method by Greg Ward,
provides a way to replace the last term - the constant ambient
light value - with a light level which is based on what surfaces
are nearby and how bright in turn they are.

The first thing you might notice about this definition is that it
is circular: the light of everything is dependent on everything
else and vice versa. This is true in real life but in the world
of ray-tracing, we can make an approximation. The approximation
that is used is: the objects you are looking at have their
ambient values calculated for you by checking the other objects
nearby. When those objects are checked during this process,
however, a traditional constant ambient term is used.

How does POV-Ray calculate the ambient term for each point? By
sending out more rays, in many different directions, and
averaging the results. A typical point might use 200 or more rays
to calculate its ambient light level correctly.

Now this sounds like it would make the ray-tracer 200 times
slower. This is true, except that the software takes advantage of
the fact that ambient light levels change quite slowly (remember,
shadows are calculated separately, so sharp shadow edges are not
a problem). Therefore, these extra rays are sent out only once in
a while (about 1 time in 50), then these calculated values are
saved and reused for nearby pixels in the image when possible.

This process of saving and reusing values is what causes the need
for a variety of tuning parameters, so you can get the scene to
look just the way you want.


4.10.9.2   Adjusting Radiosity
As described earlier, radiosity is turned on by using the
Radiosity INI file option or the +QR command line switch. However
radiosity has many parameters that are specified in a radiosity
statement inside a global_settings statement as follows:

  global_settings { radiosity { [RADIOSITY_ITEMS...] }}
RADIOSITY_ITEMS:
  brightness Float   |   count Integer   |   distance_maximum
  Float   |
  error_bound Float   |   gray_threshold Float   |
  low_error_factor Float   |
  minimum_reuse Float   |   nearest_count Integer   |
  recursion_limit Integer
Each item is optional and may appear in and order. If an item is
specified more than once the last setting overrides previous
values. Details on each item is given in the following sections.


4.10.9.2.1 brightness
This brightness keyword specifies a float value that is the
degree to which ambient values are brightened before being
returned upwards to the rest of the system. If an object is red
rgb<1,0 0>, with an ambient value of 0.3, in normal situations a
red component of 0.3 will be added in. With radiosity on, assume
it was surrounded by an object of gray color rgb<0.6,0.6,0.6>.
The average color returned by the gathering process will be the
same. This will be multiplied by the texture's ambient weight
value of 0.3, returning rgb<0.18,0.18,0.18>. This is much darker
than the 0.3 which would be added in normally. Therefore, all
returned values are brightened by the inverse of the average of
the calculated values, so the average ambient added in does not
change.  Some will be higher than specified (higher than 0.3 in
this example) and some will be lower but the overall scene
brightness will be unchanged.  The default value is 3.3.


4.10.9.2.2 count
The integer number of rays that are sent out whenever a new
radiosity value has to be calculated is given by count. Values of
100 to 150 make most scenes look good.  Higher values might be
needed for scenes with high contrast between light levels or
small patches of light causing the illumination.  This would be
used only for a final rendering on an image because it is very
compute intensive. Since most scenes calculate the ambient value
at 1% to 2% of pixels, as a rough estimate, your rendering will
take 1% to 2% of this number times as long. If you set it to 300
your rendering might take 3 to 6 times as long to complete (1% to
2% times 300).

When this value is too low, the light level will tend to look a
little bit blotchy, as if the surfaces you're looking at were
slightly warped. If this is not important to your scene (as in
the case that you have a bump map or if you have a strong
texture) then by all means use a lower number.  The default value
is 100.


4.10.9.2.3 distance_maximum
The distance_maximum float value is the only tuning value that
depends upon the size of the objects in the scene. This one must
be set for scenes to render properly... the rest can be ignored
for a first try. It is difficult to describe the meaning simply
but it sets the distance in model units from a sample at which
the error is guaranteed to hit 100% (radiosity_error_bound >=1):
no samples are reused at a distance larger than this from their
original calculation point.

Imagine an apple at the left edge of a table. The goal is to make
sure that samples on the surface of the table at the right are
not used too close to the apple and definitely not underneath the
apple.  If you had enough rays there wouldn't be a problem since
one of them would be guaranteed to hit the apple and set the
reuse radius properly for you. In practice, you must limit this.

We use this technique: find the object in your scene which might
have the following problem: a small object on a larger flatter
surface that you want good ambient light near. Now, how far from
this would you have to get to be sure that one of your rays had a
good chance of hitting it? In the apple-on-the-table example,
assuming I used one POV-Ray unit as one inch, I might use 30
inches. A theoretically sound way (when you are running lots of
rays) is the distance at which this object's top is 5 degrees
above the horizon of the sample point you are considering. This
corresponds to about 11 times the height of the object. So, for a
3-inch apple, 33 inches makes some sense. For good behavior under
and around a 1/3 inch pea, use 3 inches etc. Another VERY rough
estimate is one third the distance from your eye position to the
point you are looking at. The reasoning is that you are probably
no more than 90 inches from the apple on the table, if you care
about the shading underneath it.  The default value is 0.


4.10.9.2.4 error_bound
The error_bound float value is one of the two main speed/quality
tuning values (the other is of course the number of rays shot).
In an ideal world, this would be the only value needed. It is
intended to mean the fraction of error tolerated. For example, if
it were set to 1 the algorithm would not calculate a new value
until the error on the last one was estimated at as high as 100%.
Ignoring the error introduced by rotation for the moment, on flat
surfaces this is equal to the fraction of the reuse distance,
which in turn is the distance to the closest item hit. If you
have an old sample on the floor 10 inches from a wall, an error
bound of 0.5 will get you a new sample at a distance of about 5
inches from the wall. 0.5 is a little rough and ready, 0.33 is
good for final renderings. Values much lower than 0.3 take
forever. The default value is 0.4.


4.10.9.2.5 gray_threshold
Diffusely interreflected light is a function of the objects
around the point in question. Since this is recursively defined
to millions of levels of recursion, in any real life scene, every
point is illuminated at least in part by every other part of the
scene. Since we can't afford to compute this, we only do one
bounce and the calculated ambient light is very strongly affected
by the colors of the objects near it. This is known as color
bleed and it really happens but not as much as this calculation
method would have you believe. The gray_threshold float value
grays it down a little, to make your scene more believable. A
value of .6 means to calculate the ambient value as 60% of the
equivalent gray value calculated, plus 40% of the actual value
calculated. At 0%, this feature does nothing. At 100%, you always
get white/gray ambient light, with no hue. Note that this does
not change the lightness/darkness, only the strength of
hue/grayness (in HLS terms, it changes S only).  The default
value is 0.5


4.10.9.2.6 low_error_factor
If you calculate just enough samples, but no more, you will get
an image which has slightly blotchy lighting. What you want is
just a few extra interspersed, so that the blending will be nice
and smooth.  The solution to this is the mosaic preview: it goes
over the image one or more times beforehand, calculating
radiosity values. To ensure that you get a few extra, the
radiosity algorithm lowers the error bound during the pre-final
passes, then sets it back just before the final pass. The
low_error_factor is a float tuning value which sets the amount
that the error bound is dropped during the preliminary image
passes. If your low error factor is 0.8 and your error bound is
set to 0.4 it will really use an error bound of 0.32 during the
first passes and 0.4 on the final pass.  The default value is
0.8.


4.10.9.2.7 minimum_reuse
The minimum effective radius ratio is set by minimum_reuse float
value. This is the fraction of the screen width which sets the
minimum radius of reuse for each sample point (actually, it is
the fraction of the distance from the eye but the two are roughly
equal). For example, if the value is 0.02 the radius of maximum
reuse for every sample is set to whatever ground distance
corresponds to 2% of the width of the screen. Imagine you sent a
ray off to the horizon and it hits the ground at a distance of
100 miles from your eye point. The reuse distance for that sample
will be set to 2 miles. At a resolution of 300*400 this will
correspond to (very roughly) 8 pixels. The theory is that you
don't want to calculate values for every pixel into every crevice
everywhere in the scene, it will take too long. This sets a
minimum bound for the reuse. If this value is too low, (which it
should be in theory) rendering gets slow, and inside corners can
get a little grainy. If it is set too high, you don't get the
natural darkening of illumination near inside edges, since it
reuses. At values higher than 2% you start getting more just
plain errors, like reusing the illumination of the open table
underneath the apple.  Remember that this is a unitless ratio.
The default value is 0.015.


4.10.9.2.8 nearest_count
The nearest_count integer value is the maximum number of old
ambient values blended together to create a new interpolated
value. It will always be the n geometrically closest reusable
points that get used. If you go lower than 4, things can get
pretty patchy. This can be good for debugging, though. Must be no
more than 10, since that is the size of the array allocated.  The
default value is 6.


4.10.9.2.9 recursion_limit
The recursion_limit is an integer value which determines how many
recursion levels are used to calculate the diffuse inter-
reflection. Valid values are one and two. The default value is 1.


4.10.9.3   Tips on Radiosity
If you want to see where your values are being calculated set
radiosity count down to about 20, set radiosity nearest_count to
1 and set gray_threshold to 0. This will make everything
maximally patchy, so you'll be able to see the borders between
patches. There will have been a radiosity calculation at the
center of most patches. As a bonus, this is quick to run. You can
then change the error_bound up and down to see how it changes
things. Likewise modify minimum_reuse and distance_maximum.

One way to get extra smooth results: crank up the sample count
(we've gone as high as 1300) and drop the low_error_factor to
something small like 0.6. Bump up the nearest_count to 7 or 8.
This will get better values, and more of them, then interpolate
among more of them on the last pass. This is not for people with
a lack of patience since it is like a squared function. If your
blotchiness is only in certain corners or near certain objects
try tuning the error bound instead. Never drop it by more than a
little at a time, since the run time will get very long.

If your scene looks good but right near some objects you get
spots of the right (usually darker) color showing on a flat
surface of the wrong color (same as far away from the object),
then try dropping distance_maximum. If that still doesn't work
well increase your ray count by 100 and drop the error bound just
a bit. If you still have problems, drop nearest_count to about 4.



5.0  APPENDICES

5.1  Copyright, Legal Information and License -- POVLEGAL.DOC
The following sections contain the legal information and license
for the Persistence of Vision(tm) Ray-Tracer, also called POV-Ray(tm).
Before you use this program you have to read the sections below.


5.1.1     General License Agreement -- POVLEGAL.DOC
Revised May 1999.

THIS NOTICE MUST ACCOMPANY ALL OFFICIAL OR CUSTOM PERSISTENCE OF
VISION FILES. IT MAY NOT BE REMOVED OR MODIFIED. THIS INFORMATION
PERTAINS TO ALL USE OF THE PACKAGE WORLDWIDE.  THIS DOCUMENT
SUPERSEDES ALL PREVIOUS GENERAL LICENSES OR DISTRIBUTION
POLICIES. ANY INDIVIDUALS, COMPANIES OR GROUPS WHO HAVE BEEN
GRANTED SPECIAL LICENSES MAY CONTINUE TO DISTRIBUTE VERSION 2.x
BUT MUST RE-APPLY FOR VERSION 3.00 OR LATER.

This document pertains to the use and distribution of the
Persistence of Vision(tm) Ray Tracer a.k.a POV-Ray(tm). It applies to
all POV-Ray program source files, executable (binary) files,
scene files, documentation files, help file, bitmaps and INI
files contained in official POV-Ray Team(tm) archives.  All of these
are referred to here as "the software". The POV-Team reserves the
right to revise these rules in future versions and to make
additional rules to address new circumstances at any time.

All of this software is Copyright 1991,1999 by the POV-Ray Team(tm).
Although it is distributed as freeware, it is NOT PUBLIC DOMAIN.

The copyrighted package may ONLY be distributed and/or modified
according to the license granted herein.  The spirit of the
license is to promote POV-Ray as a standard ray tracer, provide
the full POV-Ray package freely to as many users as possible,
prevent POV-Ray users and developers from being taken advantage
of, enhance the life quality of those who come in contact with
POV-Ray.  This license was created so these goals could be
realized.  You are legally bound to follow these rules, but we
hope you will follow them as a matter of ethics, rather than fear
of litigation.


5.1.2     Usage Provisions
Permission is granted to the user to use the software and
associated files in this package to create and render images. The
use of this software for the purpose of creating images is
completely free. The creator of a scene file and the image
created from the scene file, retains all rights to the image and
scene file they created and may use them for any purpose
commercial or non-commercial.

The user is also granted the right to use the scenes files,
fonts, bitmaps, and include files distributed in the INCLUDE and
SCENES\INCDEMO sub-directories in their own scenes.  Such
permission does not extend to files in the SCENES directory or
its sub-directories.  The SCENES files are for your enjoyment and
education but may not be the basis of any derivative works.


5.1.3     General Rules For All Distribution
The permission to distribute this package under certain very
specific conditions is granted in advance, provided that the
following conditions are met.

These archives must not be re-archived using a different method
without the explicit permission of the POV-Team.  You may rename
the archives only to meet the file name conventions of your
system or to avoid file name duplications but we ask that you try
to keep file names as similar to the originals as possible.  (For
example: POVSRC.ZIP to POVSRC30.ZIP)

Ready-to-run unarchived distribution on CD-ROM is also permitted
if the files are arranged in our standard directory or folder
structure as though it had been properly installed on a hard
disk.

You must distribute a FULL PACKAGE of files as described in the
next section.  No portion of this package may be separated from
the package and distributed separately other than under the
conditions specified in the provisions given below.

Non-commercial distribution in which no money or compensation is
charged (such as a user copying the software for a personal
friend or colleague) is permitted with no other restrictions.

Teachers and educational institutions may also distribute the
material to students for free or they may charge minimal copying
costs if the software is to be used in a course.


5.1.4     Definition Of "Full Package"
A "full package" contains an executable program, documentation,
and sample scenes.  For generic Unix platforms, there are no
executables available so the portable C source code must be
included instead of the executable program.

POV-Ray is officially distributed for MS-Dos; Windows 95/98/NT;
Linux for Intel x86 series; Apple Macintosh; Apple PowerPC;
SunOS; and Amiga. Other systems may be added in the future.

Distributors need not support all platforms but for each platform
you support you must distribute a full package. For example a
Macintosh only CD-ROM need not distribute the Windows versions.

This software may ONLY be bundled with other software packages
according to the conditions specified in the provisions below.


5.1.5     Conditions For CD-ROM or Shareware/Freeware
     Distribution
Shareware and freeware distribution companies may distribute the
software included in software-only compilations using media such
as, but not limited to, floppy disk, CD-ROM, tape backup, optical
disks, hard disks, or memory cards. This section only applies to
distributors of collected programs. Anyone wishing to bundle the
package with a shareware product must use the commercial bundling
rules.

Distribution on CD-ROM or high capacity media such as backup tape
is permitted if the total cost to the user is no more than $0.08
U.S. dollars per megabyte of data. For example a CD-ROM with 600
meg could cost no more than $48.00 US.

Any bundling with books, magazines or other print media is
permitted if the total cost of the book or magazine with CD is
less than the $48.00 limit. Bundling with more expensive
publications or distributions should also use the commercial
rules.

For floppy disk distribution, no more than five dollars U.S. ($5)
can be charged per disk for the copying of this software and the
media it is provided on. Space on each disk must be used as fully
as possible. You may not spread the files over more disks than
are necessary.


5.1.6     Conditions For On-Line Services And Bbs's Including
     Internet
On-line services, BBS's and internet sites may distribute the POV-
Ray software under the conditions in this section. Sites which
allow users to run POV-Ray from remote locations must use
separate provisions in the section below.

The archives must all be easily available on the service and
should be grouped together in a similar on-line area.

It is strongly requested that sites remove prior versions of POV-
Ray to avoid user confusion and simplify or minimize our support
efforts.

The site may only charge standard usage rates for the downloading
of this software. A premium may not be charged for this package.
I.E. CompuServe or America On-Line may make these archives
available to their users, but they may only charge regular usage
rates for the time required to download.


5.1.7     Online Or Remote Execution Of POV-Ray
Some internet sites have been set up so that remote users can
actually run POV-Ray software on the internet server. Other
companies sell CPU time for running POV-Ray software on
workstations or high-speed computers. Such use of POV-Ray
software is permitted under the following conditions.

Fees or charges, if any, for such services must be for connect
time, storage or processor usage ONLY. No premium charges may be
assessed for use of POV-Ray beyond that charged for use of other
software. Users must be clearly notified that they are being
charged for use of the computer and not for use of POV-Ray
software.

Users must be prominently informed that they are using POV-Ray
software, that such software is free, and where they can find
official POV-Ray software. Any attempt to obscure the fact that
the user is running POV-Ray is expressly prohibited.

All files normally available in a full package distribution,
especially a copy of this license and full documentation must be
available for download or readable online so that users of an
online executable have access to all of the material of a full
user package.

If the POV-Ray software has been modified in any way, it must
also follow the provisions for custom versions below.


5.1.8     Permitted Modification And Custom Versions
Although the full source code for POV-Ray is distributed, there
are strict rules for the use of the source code. The source
distribution is provided to;  1) promote the porting of POV-Ray
to hardware and operating systems which the POV-Team cannot
support.  2) promote experimentation and development of new
features to the core code which might eventually be incorporated
into the official version.  3) provide insight into the inner
workings of the program for educational purposes.

These license provisions have been established to promote the
growth of POV-Ray and prevent difficulties for users and
developers alike. Please follow them carefully for the benefit of
all concerned when creating a custom version.

The user is granted the privilege to modify and compile the
source code for their own personal use in any fashion they see
fit. What you do with the software in your own home is your
business.

However severe restrictions are imposed if the user wishes to
distribute a modified version of the software, documentation or
other parts of the package (here after referred to as a "custom
version"). You must follow the provisions given below. This
includes any translation of the documentation into other
languages or other file formats.

A "custom version" is defined as a fully functional version of
POV-Ray with all existing features intact. ANY OTHER USE OF ANY
POV-Ray SOURCE CODE IS EXPRESSLY PROHIBITED. The POV-Team does
not license source code for any use outside POV-Ray. No portion
of the POV-Ray source code may be incorporated into another
program unless it is clearly a custom version of POV-Ray that
includes all of the basic functions of POV-Ray.

All executables, documentation, modified files and descriptions
of the same must clearly identify themselves as a modified and
unofficial version of POV-Ray. Any attempt to obscure the fact
that the user is running POV-Ray or to obscure that this is an
unofficial version expressly prohibited.

POV-Ray may not be linked into other software either at compile-
time using an object code linker nor at run-time as a DLL,
ActiveX, or other system. Such linkage can tend to blur the end-
user's perception of which program provides which functions and
thus qualifies as an attempt to obscure what is running.

To allow POV-Ray to communicate with outside programs, the
official versions of POV-Ray include several internal
communication "hooks" for it to call other tasks, often called an
Application Programming Interface, or API. For example: the
generic part of POV-Ray provides operating system shell-out API
commands. The Windows version has a GUI-extension API and the
ability to replace the text editor. Modification to these APIs or
other officially supported communication mechanisms to increase
functionality beyond that of the official version IS EXPRESSLY
PROHIBITED.


5.1.9     Conditions For Distribution Of Custom Versions
If your re-compiled version meets all requirements for custom
versions listed above, the following conditions apply to its
distribution:

You must provide all POV-Ray support for all users who use your
custom version. You must provide information so that user may
contact you for support for your custom version. The POV-Ray Team
is not obligated to provide you or your users any technical
support.

Include contact information in the DISTRIBUTION_MESSAGE macros in
the source file OPTOUT.H and insure that the program prominently
displays this information. Display all copyright notices and
credit screens for the official version.

Custom versions may only be distributed as freeware. You must
make all of your modifications to POV-Ray freely and publicly
available with FULL SOURCE CODE to the modified portions of POV-
Ray and must freely distribute full source to any new parts of
the custom version. The goal is that users must be able to re-
compile the program themselves using readily available compilers
and run-time libraries and to be able to further improve the
program with their own modifications.

You must provide documentation for any and all modifications that
you have made to the program that you are distributing. Include
clear and obvious information on how to obtain the official POV-
Ray.

The user is encouraged to send enhancements and bug fixes to the
POV-Ray Team, but the team is in no way required to utilize these
enhancements or fixes. By sending material to the team, the
contributor asserts that he owns the materials or has the right
to distribute these materials. He authorizes the team to use the
materials any way they like. The contributor still retains rights
to the donated material, but by donating, grants unrestricted,
irrevocable usage and distribution rights to the POV- Team. The
team doesn't have to use the material, but if we do, you do not
acquire any rights related to POV-Ray. The team will give you
credit as the creator of new code if applicable.

Include a copy of this document (POVLEGAL.DOC).


5.1.10    Conditions For Commercial Bundling
Vendors wishing to bundle POV-Ray with commercial software
(including shareware) or other distribution not already described
above must first obtain explicit permission from the POV-Team.
Such permission is rarely granted. The POV-Team will decide if
such distribution will be allowed on a case-by-case basis and may
impose certain restrictions as it sees fit. The minimum terms are
given below. Other conditions may be imposed.

  *    The product must be an existing product that has proven
  itself as commercially viable without POV-Ray included.
  *    The inclusion of POV-Ray should be promoted only as a
  free bonus and not as a feature designed to encourage
  customers to purchase or upgrade solely for the POV-Ray
  capability.
  *    Purchasers of your product must not be led to believe
  that they are paying for POV-Ray. Any mention of the POV-Ray
  bundle on the box, in advertising or in instruction manuals
  must be clearly marked with a disclaimer that POV-Ray is free
  software and can be obtained for free or nominal cost from
  various sources.
  *    Include clear and obvious information on how to obtain
  the official POV-Ray.
  *    You must provide all POV-Ray support for all users who
  acquired POV-Ray through your product. The POV-Team is not
  obligated to provide you or your customers any technical
  support.
  *    Include a credit page or pages in your documentation for
  POV-Ray.
  *    If you modify any portion POV-Ray for use with your
  hardware or software, you must follow the custom version rules
  in addition to these rules.
  *    Include contact and support information for your product.
  *    Include a full user package as described above.

5.1.11    POV-Team Endorsement Prohibitions
On rare occasions, the POV-Team endorses distributions in which
POV-Team members are compensated participants and which the POV-
Team has given approval.

Without specific approval, distributors (whether free or
commercial) must not claim or imply in any way that the POV-Team
officially endorses or supports the distributor or the product
(such as CD, book, or magazine) associated with the distribution.

You may not claim or imply that the POV-Team derives any benefit
from your distribution.

If you wish to emphasize that your distribution is legal, you may
use this language "This distribution of the official version of
POV-Ray is permitted under the terms of the General License in
the file POVLEGAL.DOC. The POV- Team does not endorse the
distributor or its products. The POV-Team receives no
compensation for this distribution."


5.1.12    Retail Value Of This Software
Although POV-Ray is, when distributed within the terms of this
agreement, free of charge, the retail value (or price) of this
program is determined as US$20.00 per copy distributed or copied.
If the software is distributed or copied without authorization
you are legally liable to this debt to the copyright holder or
any other person or organization delegated by the copyright
holder for the collection of this debt, and you agree that you
are legally bound by the above and will pay this debt within 30
days of the event.

However, none of the above paragraph constitutes permission for
you to distribute this software outside of the terms of this
agreement. In particular, the conditions and debt mentioned above
(whether paid or unpaid) do not allow you to avoid statutory
damages or other legal penalties and does not constitute any
agreement that would allow you to avoid such other legal remedies
as are available to the copyright holder.

Put simply, POV-Ray is only free if you comply with our
distribution conditions; it is not free otherwise. The copyright
holder of this software chooses to give it away free under these
and only these conditions.

For the purpose of copyright regulations, the retail value of
this software is US$20.00 per copy.


5.1.13    Other Provisions
The team permits and encourages the creation of programs,
including commercial packages, which import, export or translate
files in the POV-Ray Scene Description Language. There are no
restrictions on use of the language itself. We reserve the right
to add or remove or change any part of the language.

"POV-Ray", "Persistence of Vision", "POV-Team" and "POV-Help" are
trademarks of the POV-Team.

While we do not claim any restrictions on the letters "POV"
alone, we humbly request that you not use POV in the name of your
product. Such use tends to imply it is a product of the POV-Team.
Existing programs which used "POV" prior to the publication of
this document need not feel guilty for doing so provided that you
make it clear that the program is not the work of the team nor
endorsed by us.


5.1.14    Revocation Of License
VIOLATION OF THIS LICENSE IS A VIOLATION OF COPYRIGHT LAWS. IT
WILL RESULT IN REVOCATION OF ALL DISTRIBUTION PRIVILEGES AND MAY
RESULT IN CIVIL OR CRIMINAL PENALTY.

Such violators who are prohibited from distribution will be
identified in this document.

In this regard, "PC Format", a magazine published by Future
Publishing, Ltd. in the United Kingdom, distributed incomplete
versions of POV-Ray 1.0 in violation the license which was effect
at the time. They later attempted to distribute POV-Ray 2.2
without prior permission of the POV- Team in violation the
license which was in effect at the time. There is evidence that
other Future Publishing companies have also violated our terms.
Therefore "PC Format", and any other magazine, book or CD-ROM
publication owned by Future Publishing is expressly prohibited
from any distribution of POV-Ray software until further notice.


5.1.15    Disclaimer
This software is provided as is without any guarantees or
warranty. Although the authors have attempted to find and correct
any bugs in the package, they are not responsible for any damage
or losses of any kind caused by the use or misuse of the package.
The authors are under no obligation to provide service,
corrections, or upgrades to this package.


5.1.16    Technical Support
We sincerely hope you have fun with our program. If you have any
problems with the program, the team would like to hear about
them. Also, if you have any comments, questions or enhancements,
please the POV-Ray Team on the internet at http://www.povray.org
or our private news server news.povray.org with over a dozen
povray-related news groups.  The USENET group
comp.graphics.rendering.raytracing is also a great source of
information on POV-Ray and related topics.

License inquiries should be made via email and limited technical
support is available via email to:

POV-Ray Team Coordinator  team-coord@povray.org

The following postal address is only for official license
business and only if email is impossible.

We do not provide technical support via regular mail, only email.
We don't care if you don't have a modem or online access. We will
not mail you disks with updated versions. Do not send money.

Chris Young; 3119 Cossell Drive; Indianapolis, IN 46224 U.S.A.

The other authors' contact information may be found in the
documentation.


5.2  Authors
Following is a list in alphabetic order of all people who have
ever worked on the POV-Ray Team or who have made a note-worthy
contribution. If you want to contact or thank the authors read
the sections "Contacting the Authors" or use email addresses
below.


                 CURRENT POV-Team MEMBERS
NAME            PARTICIPATION            EMAIL
Dieter Bayer    Wrote sor, lathe,        dbayer@tomtec.de
                prism, media and many
                other features
Thomas Baier    New 3.1 team member,     thbaier@ibm.net
                tester
Chris Cason     Windows version          
                coordinator and other
                contributions
Dale C. Brodin  Alpha & Beta tester,     brodin@execpc.com
                forum support
Thorsten        Mac developer            ThorstenFroehlich@
Froehlich                                compuserve.com
Alan Kong       Alpha & Beta tester,     akong@pacbell.net
                forum support
Lutz            Moray author, MS-Dos 24- lutz@stmuc.com
Kretzschmar     bit VGA, part of the
                anti-aliasing code
Joel Newkirk    Primary Amiga developer  newkirk@snip.net
Nathan O'Brien  Artist, tester           no13@no13.net
Redaelli Paolo  Amiga developer          redaelli@inc.it
Anton Raves     Alpha & Beta tester,     100022.2603@compus
                Mac contributor          erve.com
Eduard Schwan   Mac version              espsw@home.com
                coordinator, mosaic
                preview, docs
Erkki           Alpha & Beta tester,     
Sondergaard     3.0 Scene files
Timothy Wegner  Fractal objects, PNG     twegner@phoenix.ne
                support                  t
Chris Young     POV-Team coordinator,    team-
                parser code              coord@povray.org


           PAST POV-Team MEMBERS and CONTRIBTORS
NAME            PARTICIPATION            EMAIL
Claire          Tutorials for the POV-   
Amundsen        Ray User Guide
Steve Anger     POV-Ray 2.0/3.0          sanger@globalserve
                developer                .net
Randy Antler    MS-Dos display code      
                enhancements
John Baily      RLE targa code           
Eric Barish     Ground fog code          
Kendall         PMODE library support    
Bennett
Steve Bennett   GIF support              
David Buck      Original author of       
                DKBTrace
                POV-Ray 1.0 developer
Aaron Collins   Co-author of DKBTrace    
                2.12
                POV-Ray 1.0 developer
Chris Dailey    POV-Ray 3.0 developer    
Steve Demlow    POV-Ray 3.0 developer    
Andreas Dilger  Former Unix              adilger@enel.ucalg
                coordinator, Linux       ary.ca
                developer, PNG support   www-
                                         mddsp.enel.ucalgar
                                         y.ca/People/adilge
                                         r/
Joris van       Mac beta tester          
Drunen Littel
Alexander       POV-Ray 1.0/2.0/3.0      xander@mitre.com
Enzmann         developer
Dan Farmer      POV-Ray 1.0/2.0/3.0      
                developer
Charles Fusner  Blob, lathe and prism    
                tutorial tutorials for
                the POV-Ray User Guide
David Harr      Mac balloon help and     
                palette code
Jimmy Hoeks     Help file for Windows    
                user interface
Terry Kanakis   Camera fix               
Kari Juharvi    Ground fog code          
Kivisalo
Charles         MS-Dos display code      
Marslett
Pascal          Fractal objects          
Massimino
Jim McElhiney   POV-Ray 3.0 developer    
Robert A.       Artist, 3.0 docs         ram@iu.net
Mickelsen       contributor              www.mickelsenstudi
                                         os.com
Mike Miller     Artist, scene files,     
                stones.inc
Douglas Muir    Bump maps, height        
                fields
Jim Nitchals    Mac version, scene       
                files (Jim passed away
                in June 1998 but his
                contributions to POV-
                Ray will not be
                forgotten)
Paul Novak      Texture contributions    
Dave Park       Amiga support, AGA       
                video code
David Payne     RLE targa code           
Bill Pulver     Time code                
Dan Richardson  3.0 Docs                 
Tim Rowley      PPM and Windows-         trowley@geom.umn.e
                specific BMP image       du
                format support
Robert Skinner  Noise functions          
Zsolt           Halo code which was      zsolt@cg.tuwien.ac
Szalavari       later turned into media  .at
Scott Taylor    Leopard and onion        
                textures
Drew Wells      POV-Ray 1.0 developer,   
                POV-Ray 1.0 team
                coordinator


5.2.1     Contacting the Authors
The POV-Team is a collection of volunteer programmers, designers,
animators and artists meeting via the internet at
http://www.povray.org. The POV-Team's goal is to create freely
distributable, high quality rendering and animation software
written in C that can be easily ported to many different
computers.

If you have any questions about POV-Ray, please contact

  POV-Team Coordinator
  team-coord@povray.org
We love to hear about how you're using and enjoying the program.
We also will do our best try to solve any problems you have with
POV-Ray and incorporate good suggestions into the program.

If you have a question regarding commercial use or distribution
of POV-Ray, or anything else particularly sticky, please contact
Chris Young, the development team coordinator. Otherwise, spread
the mail around. We all love to hear from you!

Please do not send large files to us through the e-mail without
asking first. Send a query before you send the file, thanks!


5.3  What to do if you don't have POV-Ray
This documentation assumes you already have POV-Ray installed and
running however the POV-Team does distribute this file by itself
in various formats including online on the internet.  If you
don't have POV-Ray or aren't sure you have the official version
or the latest version, then the following sections will tell you
what to get and where to get it.


5.3.1     Which Version of POV-Ray should you use?
POV-Ray can be used under MS-Dos, Windows 3.x, Windows for
Workgroups 3.11, Windows 95, Windows NT, Apple Macintosh 68k,
Power PC, Amiga, Linux, UNIX and other platforms.  The latest
versions of the necessary files are available on our web site at
http://www.povray.org and through various CD distributions.  See
section "Where to Find POV-Ray Files" for more info.  If your
platform is not supported and you are proficient in compiling
source code programs written in C then, see section "Compiling
POV-Ray" for more information.


5.3.1.1   Microsoft Windows 95/98/NT
The Windows version runs under Windows 95, Windows 98, and
Windows NT4 also should run under OS/2 Warp.

Windows 3.1 and Windows for Workgroups are no longer supported
however the MS-Dos version will run as a dos application under
those operating systems.

Required hardware and software:

  Minimum - 486/100 with 16mb RAM and Windows 95.
  Disk space - 15 megabytes
Required POV-Ray files:

  User archive POVWIN3.EXE - a self-extracting archive
     containing the program, sample scenes, standard include
     files and documentation. This file may be split into smaller
     files for easier downloading. Check the directory of your
     download or ftp site to see if other files are needed.
Recommended:

  Pentium 200 or Pentium II with 32mb and Windows 95 or NT4.
  SVGA display preferably with high color or true color ability
     and drivers installed.  (Note: accelerated graphics hardware
     will not improve performance.)
Optional: The source code is not needed to use POV-Ray. It is
provided for the curious and adventurous.

  POVWIN_S.ZIP --- The C source code for POV-Ray for Windows.
     Contains generic parts and Windows specific parts. It does
     not include sample scenes, standard include files and
     documentation so you should also get the executable archive
     as well.  POV-Ray can only be compiled using C compilers
     that create 32-bit Windows applications. We support Watcom
     10.5a or higher, Borland 4.52/5.0 compilers.

5.3.1.2   MS-Dos & Windows 3.x
 The MS-Dos version runs under MS-Dos or as a DOS application
under Windows 3.1 or Windows for Workgroups 3.11. Although it
also runs under Windows 95/98/NT4 and OS/2 Warp, users of those
systems should use the Windows version..

Required hardware and software:

  A 386 or better CPU and at least 8 meg of RAM.
  About 6 meg disk space to install and 2-10 meg or more beyond
     that for working space.
  A text editor capable of editing plain ASCII text files. The
     EDIT program that comes with MS-Dos will work for moderate
     size files.
  Graphic file viewer capable of viewing GIF and perhaps TGA and
     PNG formats.
Required POV-Ray files:

  POVMSDOS.EXE - a self-extracting archive containing the
     program, sample scenes, standard include files and
     documentation in plain ASCII text format. This file may be
     split into smaller files for easier downloading. Check the
     directory of your download or ftp site to see if other files
     are needed.
Recommended:

  Pentium 200 or Pentium II (faster the better) 32 meg or more
     RAM.  SVGA display preferably with VESA interface and high
     color or true color ability.    (Note: accelerated graphics
     hardware will not improve performance.)

Optional: The source code is not needed to use POV-Ray. It is
provided for the curious and adventurous.

  POVMSD_S.ZIP - The C source code for POV-Ray for MS-Dos.
     Contains generic parts and MS-Dos specific parts. It does
     not include sample scenes, standard include files and
     documentation so you should also get the executable archive
     as well. Requires a C compiler that can create 32-bit
     protected mode applications. We support Watcom 11, Borland
     4.52 with DOS Power Pack and DJGPP 2.

5.3.1.3   Linux for Intel x86
Required hardware and software:

  A 386 or better CPU and at least 8 meg of RAM.
  About 6 meg disk space to install and 2-10 meg or more beyond
     that for working space.
  A text editor capable of editing plain ASCII text files.
  Graphic file viewer capable of viewing PPM, TGA or PNG
     formats.
  Any recent (1994 onwards) Linux kernel and support for ELF
     format binaries. POV-Ray for Linux is not in a.out-format.
     ELF libraries libc.so.5, libm.so.5 and one or both of
     libX11.so.6 or libvga.so.1.
  
Required POV-Ray files:

  POVLINUX.TGZ or POVLINUX.TAR.GZ - archive containing an
     official binary for each SVGALib and X-Windows modes. Also
     contains sample scenes, standard include files and
     documentation in plain ASCII text.
Recommended:

  Pentium 200 or Pentium II (faster the better) 32 meg or more
     RAM.  SVGA display preferably with VESA interface and high
     color or true color ability.  If you want display, you'll
     need either SVGALib or X-Windows.  (Note: accelerated
     graphics hardware will not improve performance.)
Optional: The source code is not needed to use POV-Ray. It is
provided for the curious and adventurous.

  POVUNI_S.TAR.GZ or POVUNI_S.TGZ - The C source code for POV-
     Ray for Linux. Contains generic parts and Linux specific
     parts. It does not include sample scenes, standard include
     files and documentation so you should also get the
     executable archive as well.  Requires the GNU C compiler and
     (optionally) the X include files and libraries.

5.3.1.4   Apple Macintosh
The MacOS versions run under Apple's MacOS operating system
version 7.1 or newer, on any 68020/030/040-based Macintosh-
compatible computer (with or without a floating point
coprocessor) or any of the PowerPC Macintosh-compatible
computers.

Required hardware and software:

  A 68020 or better CPU without a floating point unit (LC or
     Performa or Centris series); at least 8 MB RAM or
  A 68020 or better CPU *with* a floating point unit (Mac II or
     Quadra series); at least 8 MB RAM or
  Any PowerPC Macintosh computer and at least 8 MB RAM.
  System 7.1 or newer and color QuickDraw (System 6 is no longer
     supported).
  Appearance Extension is also required now.  This comes
     standard in MacOS 8, but can be downloaded from Apple's web
     site <http://developer.apple.com/sdk/> and installed on any
     Mac running 7.1 or newer.
  Navigation Services is not required, but will enhance the
     open/save dialogs if it is present.  It is also a free
     extension available from Apple's web site, which can be used
     in 7.5.5 or newer.
  About 6 MB free disk space to install and an additional 2-10
     MB free space for your own creations (scenes and images).
  Graphic file viewer utility capable of viewing Mac PICT, GIF
     and perhaps TGA and PNG formats (the shareware
     GraphicConverter or GIFConverter applications are good.)
Required POV-Ray files:

  POVMACNF.SIT or POVMACNF.SIT.HQX - a Stuffit archive
     containing the non-FPU 68K Macintosh application, sample
     scenes, standard include files and documentation (slower
     version for Macs without an FPU) or
  POVMAC68.SIT or POVMAC68.SIT.HQX - a Stuffit archive
     containing the FPU 68K Macintosh application, sample scenes,
     standard include files and documentation (faster version for
     Macs WITH an FPU) or
  POVPMAC.SIT or POVPMAC.SIT.HQX - a Stuffit archive containing
     the native Power Macintosh application, sample scenes,
     standard include files and documentation.
Recommended:

  68030/33 or faster with FPU, or any Power Macintosh
  8 MB or more RAM for 68K Macintosh;
  16 MB or more for Power Macintosh systems.
  Color monitor preferred, 256 colors OK, but thousands or
     millions of colors is even better.
Optional: The source code is not needed to use POV-Ray. It is
provided for the curious and adventurous. POV-Ray can be compiled
using Apple's MPW 3.3, Metrowerks CodeWarrior Pro or Symantec 8.

  POVMACS.SIT or POVMACS.SIT.HQX - The full C source code for
     POV-Ray for Macintosh. Contains generic parts and Macintosh
     specific parts. It does not include sample scenes, standard
     include files and documentation so you should also get the
     executable archive as well.
  

5.3.1.5   Amiga
The Amiga version comes in several flavors, 68000/68020 without
FPU, (not recommended, very slow) 68020/68030 with FPU, 68040,
and 68060. There's two way to use POV: Shell only and using the
provided GUI interface which requires MUI 3.8. All versions run
under OS3.x and up. Support exists for pensharing and window
display under OS3.x with 256 color palettes, plus CyberGraphics
and Picasso 96 24-bit display.

Required:

  At least 4 meg of RAM.
  At least 2 meg of hard disk space for the necessities, 5-20
     more recommended for workspace.
  An ASCII text editor, GUI configurable to launch the editor of
     your choice.
  Graphic file viewer - POV-Ray outputs to PNG, Targa (TGA), and
     PPM formats. POV-Ray Amiga can load any image format with
     Picture.Datatype V43 and the appropriate datatype.
Required POV-Ray files:

  POVAMIx0.LHA -- a LHA archive containing executable, sample
     scenes, standard include files, and documentation for the
     680x0 version of POV-Ray (i.e.: POVAMI60.LHA stands for
     68060 version); 68020 version needs FPU.
Recommended:

  8 meg or more of RAM.
  68030 & 68882 or higher processor.
  24bit display card (CyberGFX and Picasso 96 library supported)
Amiga PowerPC version of POV-Ray is now in beta testing. Watch
the or www.povray.org for further news.

Optional: The source code is not needed to use POV-Ray. It is
provided for the curious and adventurous.

  POVAMI_S.LHA --- The C source code for POV-Ray for Amiga.
     Contains generic parts and Amiga specific parts. It does not
     include sample scenes, standard include files, and
     documentation so you should also get the executable archive
     as well.

5.3.1.6   SunOS
Required hardware and software:

  A Sun SPARC processor and at least 4 meg of RAM.
  About 6 meg disk space to install and 2-10 meg or more beyond
     that for working space.
  Graphic file viewer capable of viewing PPM, TGA or PNG
     formats.
  A text editor capable of editing plain ASCII text files.
  SunOS 4.1.3 or other operating system capable of running such
     a binary (Solaris or possibly Linux for Sparc).
Required POV-Ray files:

  POVSUNOS.TGZ or POVSUNOS.TAR.GZ - archive containing an
     official binary for each text-only and X-Windows modes. Also
     contains sample scenes, standard include files and
     documentation.
Recommended:

  8 meg or more RAM.
  If you want display, you'll need X-Windows or an X-Term.-
     preferably 24-bit TrueColor display ability, although the X
     display code is known to work with ANY combination of visual
     and color depth.
  Graphic file viewer capable of viewing PPM, TGA or PNG
     formats.
Optional: The source code is not needed to use POV-Ray. It is
provided for the curious and adventurous.

  POVUNI_S.TGZ or POVUNI_S.TAR.GZ - The C source code for POV-
     Ray for UNIX.  Contains generic parts and Unix/Linux
     specific parts. It does not include sample scenes, standard
     include files and documentation so you should also get the
     executable archive as well. You will need a C compiler and
     (optionally) the X include files and libraries and knowledge
     of how to use it. Although we provide source code for
     generic Unix systems, we do not provide technical support on
     how to compile the program.

5.3.1.7   Generic Unix
Because Unix runs on a wide variety of hardware and CPUs, the POV-
Team cannot provide executable versions for every type of Unix.
We distribute generic Unix source code in portable ANSI C source
code.  You will need a C compiler and (optionally) the X include
files and libraries and knowledge of how to use it. Although we
provide source code for generic Unix systems, we do not provide
technical support on how to compile the program.

Required:

  POVUNI_S.TGZ or POVUNI_S.TAR.GZ - The C source code for POV-
     Ray for UNIX.  Contains generic parts and Unix/Linux
     specific parts. It does not include sample scenes, standard
     include files and documentation so you should also get an
     executable archive for another platform or get
  POVUNI_D.TGZ or POVUNI_D.TAR.GZ which contains the sample
     scenes, standard include files and documentation.
  A C compiler for your computer and KNOWLEDGE OF HOW TO USE IT.
  Graphic file viewer capable of viewing PPM, TGA or PNG
     formats.
  A text editor capable of editing plain ASCII text files.
Recommended:

  Math co-processor.
  8 meg or more RAM.
Optional:

  X Windows if you want to be able to display as you render.
  You will need the X-Windows include files as well. If you're
     not familiar with compiling programs for X-Windows you may
     need some help from someone who is knowledgeable at your
     installation because the X include files and libraries are
     not always in a standard place.

5.3.1.8   All Versions
Each executable archive includes full documentation for POV-Ray
itself as well as specific instructions for using POV-Ray with
your type of platform. All versions of the program share the same
ray-tracing features like shapes, lighting and textures. In other
words, an MS-Dos-PC can create the same pictures as a Cray
supercomputer as long as it has enough memory. The user will want
to get the executable that best matches their computer hardware.

In addition to the files listed above, the POV-Team also
distributes the user documentation in two alternate forms.  Note
this is the same documentation distributed in other archives but
in a different format.  This may be especially useful for MS-Dos
or Unix users because their documentation is plain ASCII text
only.

  POVUSER.PDF - Tutorial and Reference documentation in Adobe
     Acrobat PDF format.  Requires Adobe Acrobat Reader available
     for Windows 3.x, Windows 95/98/NT, Mac and some Unix
     systems.  Go to
     http://www.adobe.com/prodindex/acrobat/readstep.html to get
     the reader for free.
  POVHTML.ZIP - Archive containing Tutorial and Reference
     documentation in html for viewing with any internet browser.
  POV31W97.ZIP - Archive containing Tutorial and Reference
     documentation in Microsoft Word 97 format.
See the section "Where to Find POV-Ray Files" for where to find
these files. You can contact those sources to find out what the
best version is for you and your computer.


5.3.2     Where to Find POV-Ray Files
The latest versions of the POV-Ray software are available from
the following sources.


5.3.2.1   World Wide Website www.povray.org
The internet home of POV-Ray is reachable on the World Wide Web
via the address http://www.povray.org and via ftp as
ftp.povray.org. Please stop by often for the latest files,
utilities, news and images from the official POV-Ray internet
site.

The comp.graphics.rendering.raytracing newsgroup has many
competent POV-Ray users that are very willing to share their
knowledge. They generally ask that you first browse a few files
to see if someone has already answered the same question, and of
course, that you follow proper "netiquette". If you have any
doubts about the qualifications of the folks that frequent the
group, a few minutes spend at the Ray Tracing Competition pages
at www.povray.org will quickly convince you!

Also the POV-Team operates its own news server on the internet
with several news groups related to POV-Ray and other interesting
programs.  For more information about the server see
http://www.povray.org/groups.html.


5.3.2.2   Books, Magazines and CD-ROMs
Unfortunately all English language books on POV-Ray are out of
print and there are no plans to reprint them.  However there is
now a POV-Ray 3.02 book and CD-ROM available in Japanese.  It
talks about the Windows and Mac versions of POV-Ray, and various
utilities.  The CD-ROM is dual format, Windows/Mac. It was
written in Japan by Hideki Komuro-san, and published by ASCII
Corp. in June 1998, ISBN 4-7561-1831-3.

Many popular computer magazines have been authorized to
distribute POV-Ray on cover CDs.  Note that such distributions of
the official version of POV-Ray is permitted under the terms of
the General License in the file POVLEGAL.DOC.  The POV-Team does
not endorse the distributor or its products.  The POV-Team
receives no compensation for this distribution.

The POV-Team does endorse some CD-ROMs containing POV-Ray which
are prepared by team members.  A portion of the proceeds from
these CDs support our internet sites and other team activities.
You can always find the latest information on what is available
at our web site www.povray.org.


5.4  Compiling POV-Ray
The following sections will help you to compile the portable C
source code into a working executable version of POV-Ray. They
are only for those people who want to compile a custom version of
POV-Ray or to port it to an unsupported platform or compiler.

The first question you should ask yourself before proceeding is
"Do I really need to compile POV-Ray at all?" Official POV-Team
executable versions are available for MS-Dos, Windows 95/98/NT,
Mac 68k, Mac Power PC, Amiga, Linux for Intel x86, and SunOS.
Other unofficial compiles may soon be available for other
platforms. If you do not intend to add any custom or experimental
features to the program and if an executable already exists for
your platform then you need not compile this program yourself.

If you do want to proceed you should be aware that you are very
nearly on your own. The following sections and other related
compiling documentation assume you know what you are doing. It
assumes you have an adequate C compiler installed and working. It
assumes you know how to compile and link large, multi-part
programs using a "make" utility or an IDE project file if your
compiler supports them. Because makefiles and project files often
specify drive, directory or path information, we cannot promise
our makefiles or projects will work on your system. We assume you
know how to make changes to makefiles and projects to specify
where your system libraries and other necessary files are
located.

In general you should not expect any technical support from the
POV-Team on how to compile the program. Everything is provided
here as is.  All we can say with any certainty is that we were
able to compile it on our systems. If it doesn't work for you we
probably cannot tell you why.

There is no technical documentation for the source code itself
except for the comments in the source files. We try our best to
write clear, well- commented code but some sections are barely
commented at all and some comments may be out dated. We do not
provide any technical support to help you to add features. We do
not explain how a particular feature works. In some instances,
the person who wrote a part of the program is no longer active in
the Team and we don't know exactly how it works.

When making any custom version of POV-Ray or any unofficial
compile, please make sure you read and follow all provisions of
our license in POVLEGAL.DOC.  In general you can modify and use
POV-Ray on your own however you want but if you distribute your
unofficial version you must follow our rules. You may not under
any circumstances use portions of POV-Ray source code in other
programs.


5.4.1     Directory Structure
POV-Ray source code is distributed in archives with files
arranged in a particular hierarchy of directories or folders.
When extracting the archives you should do so in a way that keeps
the directory structure intact. In general we suggest you create
a directory called povray3 or povray31 and extract the files from
there. The extraction will create a directory called source with
many files and sub-directories.

In general, there are separate archives for each hardware
platform and operating system but each of these archives may
support more than one compiler. For example here is the directory
structure for the MS-Dos archive.  Other platforms use similar
structures.

  SOURCE
  SOURCE\LPNG101
  SOURCE\ZLIB
  SOURCE\MSDOS
  SOURCE\MSDOS\PMODE
  SOURCE\MSDOS\BORLAND
  SOURCE\MSDOS\DJGPP
  SOURCE\MSDOS\WATCOM
The source directory contains source files for the generic parts
of POV-Ray that are the same on all platforms. The source\lpng101
contains files for compiling a library of routines used in
reading and writing PNG (Portable Network Graphics) image files.
The source\zlib contains files for compiling a library of
routines used by libpng to compress and uncompress data streams.
All of these files are used by all platforms and compilers.  They
are in every version of the source archives.

The source\msdos directory contains all source files for the MS-
Dos version common to all supported MS-Dos compilers. The pmode
sub-directory contains source files for pmode.lib which is
required by all MS-Dos versions. The borland, djgpp, and watcom
sub-directories contain source, makefiles and project files for C
compilers by Borland, DJGPP and Watcom.

The source\msdos directory is only in the MS-Dos archive.
Similarly the Windows archive contains a source\windows
directory. The Unix archive contains source/unix etc.

The source\msdos directory contains a file cmpl_msd.doc which
contains compiling information specific to the MS-Dos version.
Other platform specific directories contain similar cmpl_xxx.doc
files and the compiler specific sub-directories also contain
compiler specific cmpl_xxx.doc files.  Be sure to read all
pertinent cmpl_xxx.doc files for your platform and compiler.


5.4.2     Configuring POV-Ray Source
Every platform has a header file config.h that is generally in
the platform specific directory but may be in the compiler
specific directory. Some platforms have multiple versions of this
file and you may need to copy or rename it as config.h. This file
is included in every module of POV-Ray. It contains any
prototypes, macros or other definitions that may be needed in the
generic parts of POV-Ray but must be customized for a particular
platform or compiler.

For example different operating systems use different characters
as a separator between directories and file names. MS-Dos uses
back slash, Unix a front slash or Mac a colon. The config.h file
for MS-Dos and Windows contains the following:

  #define FILENAME_SEPARATOR '\'

which tells the generic part of POV-Ray to use a back slash.

Every customization that the generic part of the code needs has a
default setting in the file source\frame.h which is also included
in every module after config.h. The frame.h header contains many
groups of defines such as this:

  #ifndef FILENAME_SEPARATOR
  #define FILENAME_SEPARATOR '/'
  #endif
which basically says "If we didn't define this previously in
config.h then here's a default value". See frame.h to see what
other values you might wish to configure.

If any definitions are used to specify platform specific
functions you should also include a prototype for that function.
The file source\msdos\config.h, for example, not only contains
the macro:

  #define POV_DISPLAY_INIT(w,h) MSDOS_Display_Init ((w), (h));
to define the name of the graphics display initialization
function, it contains the prototype:

  void MSDOS_Display_Init (int w, int h);
If you plan to port POV-Ray to an unsupported platform you should
probably start with the simplest, non-display generic Unix
version. Then add new custom pieces via the config.h file.


5.4.3     Conclusion
We understand that the above sections are only the most trivial
first steps but half the fun of working on POV-Ray source is
digging in and figuring it out on your own. That's how the POV-
Team members got started. We've tried to make the code as clear
as we can.

Be sure to read the cmpl_xxx.doc files in your platform specific
and compiler specific directories for some more minor help if you
are working on a supported platform or compiler.

Good luck!


5.5  Suggested Reading
Beside the POV-Ray material mentioned in "Books, Magazines and CD-
ROMs" there are several good books or periodicals that you should
be able to locate in your local computer book store or your local
university library.

  "An Introduction to Ray tracing"  Andrew S. Glassner (editor)
ISBN 0-12-286160-4;  Academic Press 1989

  "3D Artist" Newsletter,  "The Only Newsletter about Affordable
PC 3D Tools and Techniques")  Publisher: Bill Allen;  P.O. Box
4787; Santa Fe, NM 87502-4787;  (505) 982-3532

  "Image Synthesis:  Theory and Practice" Nadia Magnenat-Thalman
and Daniel Thalmann; Springer-Verlag; 1987

  "The RenderMan Companion" Steve Upstill; Addison Wesley; 1989

  "Graphics Gems" Andrew S. Glassner (editor); Academic Press;
1990

  "Fundamentals of Interactive Computer Graphics"  J. D. Foley
and A. Van Dam;  ISBN 0-201-14468-9; Addison-Wesley 1983

  "Computer Graphics:  Principles and Practice (2nd Ed.)"  J. D.
Foley, A. van Dam, J. F. Hughes;  ISBN 0-201-12110-7;  Addison-
Wesley, 1990

  "Computers, Pattern, Chaos, and Beauty" Clifford Pickover;  St.
Martin's Press; "SIGGRAPH Conference Proceedings";   Association
for Computing Machinery Special Interest Group on Computer
Graphics

  "IEEE Computer Graphics and Applications";  The Computer
Society; 10662, Los Vaqueros Circle; Los Alamitos, CA 90720

  "The CRC Handbook of Mathematical Curves and Surfaces"  David
von Seggern; CRC Press; 1990

  "The CRC Handbook of Standard Mathematical Tables"  CRC Press



