% ****************************************************************************
%
% POV-Ray 3.6 documentation in LaTeX format
% HTML, PDF and PostScript versions of the POV-ray documentation are
% available for download on our webserver http://www.povray.org!
%
% from Persistence of Vision(tm) Ray Tracer version 3.6.
% Copyright 1991-2003 Persistence of Vision Team
% Copyright 2003-2004 Persistence of Vision Raytracer Pty. Ltd.
%
%----------------------------------------------------------------------------
%
% There are strict rules regarding how you are permitted to use this file. 
% These rules are contained in the distribution and derivative versions
% licenses which should have been provided with this file.
%
% These licences may be found online, linked from the end-user license
% agreement that is located at http://www.povray.org/povlegal.html
%
% ----------------------------------------------------------------------------
%
% This an automatically generated LaTeX version of the POV-Ray documentation.
% This file is by no means perfect as it was generated completely automatic!
% It is *not* the basis of the POV-Ray documentation.  It is only provided
% for those whow wish to output the documentation in special formats.  It has
% also been used to generate the PDF and PostScript versions of the official
% POV-Ray documentation.  The master documentation format of POV-Ray is not
% available. If you which to write extensions to the POV-Ray documentation,
% please use HTML without layout. Only mathematical equations may be supplied
% in TeX format.
%
% NOTE: The POV-Team cannot make use individual changes to this file because
% it was generated automatically, without manual changes afterwards. If you
% have practical changes you think would help to make this file and the PDF
% and PostScript versions of the documentation better, please post such
% suggestion on our news server news.povray.org in the newsgroups
% povray.documentation.inbuilt together with the suggested LaTeX.  However,
% please be not disappointed if we cannot make use of extensive suggested
% changes for some reason. As such, it is recommended to ask in the newsgroup
% prior to putting extensive work into any such extension as we might simply
% not be able to integrate it into our automatic build process for this file.
%
% ****************************************************************************

\documentclass[a4paper,10pt,twoside]{book}

\addtolength{\hoffset}{-72pt}
\addtolength{\voffset}{-72pt}
\setlength{\textwidth}{\paperwidth}
\addtolength{\textwidth}{-6.00cm}
\setlength{\oddsidemargin}{3.00cm}
\setlength{\evensidemargin}{3.00cm}
\setlength{\marginparwidth}{3.00cm}
\setlength{\marginparsep}{0.00cm}
\setlength{\marginparpush}{0.00cm}
\setlength{\topmargin}{2.50cm}
\setlength{\headsep}{0.75cm}
\setlength{\textheight}{\paperheight}
\addtolength{\textheight}{-7.25cm}

\usepackage{txfonts}
\usepackage{pslatex}
\usepackage{textcomp} 
\usepackage{parskip}
\usepackage{makeidx}
\usepackage{float}
\usepackage{afterpage}
\usepackage{multicol}
\usepackage{fancyhdr}
\usepackage{graphicx}
\usepackage[latin1]{inputenc}

\makeindex

\restylefloat{figure}
\restylefloat{table}
\newfloat{mathequ}{htbp}{loe}[chapter]
\floatname{mathequ}{Equation}
\floatplacement{figure}{tbhp}
\floatname{figure}{Figure}
\floatplacement{table}{htbp}
\floatname{table}{Table}

\pagestyle{fancy}

% with this we ensure that the chapter and section headings are in lowercase.
\renewcommand{\chaptermark}[1]{\markboth{#1}{}}
\renewcommand{\sectionmark}[1]{\markright{\thesection\ #1}}

% delete current setting for header and footer
\fancyhf{}
\fancyhead[LE,RO]{\textsf{\thepage}}
\fancyhead[LO]{\textsf{\rightmark}}
\fancyhead[RE]{\textsf{\leftmark}}
\renewcommand{\headrulewidth}{0.5pt}
\renewcommand{\footrulewidth}{0pt}

% make space for the rule
\addtolength{\headheight}{0.5pt}

% get rid of headers and the line on plain pages
\fancypagestyle{plain}{\fancyhead{}\renewcommand{\headrulewidth}{0pt}}

% allow sightly more sloppy layout than the default
\pretolerance=125
\tolerance=250
\setlength{\emergencystretch}{2em}

% adjust figure placement to decrease number of figures on dedicated pages
\renewcommand{\topfraction}{0.85}
\renewcommand{\textfraction}{0.1}
\renewcommand{\floatpagefraction}{0.75}


\begin{document}

\author{POV-Team}
\date{for POV-Ray Version 3.6.1}


\title{Introduction to POV-\discretionary{}{}{}Ray} \pagenumbering{roman} \maketitle \tableofcontents \listof{figure}{Figures} \cleardoublepage \pagenumbering{arabic}

\clearpage \chapter{Introduction}

% tutorial/000001.html



   This book provides a tutorial for the Persistence of Vision Ray-\discretionary{}{}{}Tracer (POV-\discretionary{}{}{}Ray). The documentation applies to all platforms to which this version of POV-\discretionary{}{}{}Ray 
 is ported. The platform-\discretionary{}{}{}specific documentation is available for each platform separately. 



   This book is divided into five main parts: 


\begin{enumerate}
 
 \item 
   This introduction which explains what POV-\discretionary{}{}{}Ray is and what ray-\discretionary{}{}{}tracing is. It gives a brief overview of how to create ray-\discretionary{}{}{}traced images. 
 

 \item 
   A ``Beginning Tutorial'' which explains step by step how to use the different features of POV-\discretionary{}{}{}Ray. 
 

 \item 
   An ``Advanced Tutorial'' which contains more advanced tutorial topics. 
 

 \item 
   ``POV-\discretionary{}{}{}Ray questions and tips'' gives answers to many frequently-\discretionary{}{}{}asked questions about POV-\discretionary{}{}{}Ray. 
 

 \item 
   In the ``Appendices'' you will find some tips and hints, where to get the latest version and versions for other platforms, the POV-\discretionary{}{}{}Ray licence, 
  information on compiling custom versions of POV-\discretionary{}{}{}Ray, suggested reading, contact addresses and legal information. 
 

\end{enumerate}


   POV-\discretionary{}{}{}Ray runs on Windows 9x/ME/NT/2000/XP, Macintosh Mac OS and Mac OS X, x86 Linux, UNIX, and other platforms. 



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



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



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



   The Windows version documentation is available on the POV-\discretionary{}{}{}Ray program's Help menu or by pressing the F1 key while in the program. 



   The Mac platform documentation is available via the ``Help'' menu as well as for viewing using a regular web browser. Details may be found in the 
 ``{\small\texttt{POV-\discretionary{}{}{}Ray MacOS Read Me}}'' which contains information specific to the Mac version of POV-\discretionary{}{}{}Ray. It is best to read this document first. 



   The Unix / Linux version documentation can be found at the same place as the platform independent part. Usually that is {\small\texttt{/usr/local/share/povray-3.?/html}} 
 


\section{Program Description}

% tutorial/000018.html


\begin{description}
 
 \item 
   \textit{You know you have been raytracing too long when ...\newline  ... You wonder which raytracer God used.} 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   \textit{-- David Kraics} 
 \end{list}

\end{description}


   The Persistence of Vision Ray-\discretionary{}{}{}Tracer creates three-\discretionary{}{}{}dimensional, photo-\discretionary{}{}{}realistic images using a rendering technique called ray-\discretionary{}{}{}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-\discretionary{}{}{}tracing is not a fast process by any means, but it produces very high quality images with realistic reflections, shading, perspective 
 and other effects. 


\section{What is Ray-\discretionary{}{}{}Tracing?}

% tutorial/000019.html

\index{Ray-\discretionary{}{}{}Tracing! what is}

   Ray-\discretionary{}{}{}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-\discretionary{}{}{}tracing programs like POV-\discretionary{}{}{}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-\discretionary{}{}{}diffuse reflection (radiosity), atmospheric effects and area lights make it necessary to shoot a lot of additional rays into the 
 scene for every pixel. 


\section{What is POV-\discretionary{}{}{}Ray?}

% tutorial/000020.html



   The Persistence of Vision Ray-\discretionary{}{}{}Tracer(tm) was developed from DKBTrace 2.12 (written by David K. Buck and Aaron A. Collins) by a bunch of people (called the 
 POV-\discretionary{}{}{}Team\texttrademark ) in their spare time. The headquarters of the POV-\discretionary{}{}{}Team is on the internet\footnote{ http://\discretionary{www.}{}{www.}\discretionary{povray.}{}{povray.}org/} 
 (see ``Where to Find POV-\discretionary{}{}{}Ray Files'' for more details). 



   The POV-\discretionary{}{}{}Ray package includes detailed instructions on using the ray-\discretionary{}{}{}tracer and creating scenes. Many stunning scenes are included with POV-\discretionary{}{}{}Ray so you can 
 start creating images immediately when you get the package. These scenes can be modified so you do not have to start from scratch. 



   In addition to the pre-\discretionary{}{}{}defined scenes, a large library of pre-\discretionary{}{}{}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. 


\section{Features}

% tutorial/000021.html



   Here are some highlights of POV-\discretionary{}{}{}Ray's features: 


\begin{itemize}
 
 \item 
   Easy to use scene description language. 
 

 \item 
   Large library of stunning example scene files. 
 

 \item 
   Standard include files that pre-\discretionary{}{}{}define many shapes, colors and textures. 
 

 \item 
   Very high quality output image files (up to 48-bit color). 
 

 \item 
   16 and 24 bit color display on many computer platforms using appropriate hardware. 
 

 \item 
   Create landscapes using smoothed height fields. 
 

 \item 
   Many camera types, including perspective, orthographic, fisheye, etc. 
 

 \item 
   Spotlights, cylindrical lights and area lights for sophisticated lighting. 
 

 \item 
   Photons for realistic, reflected and refracted, caustics. Photons also interact with media. 
 

 \item 
   Phong and specular highlighting for more realistic-\discretionary{}{}{}looking surfaces. 
 

 \item 
   Inter-\discretionary{}{}{}diffuse reflection (radiosity) for more realistic lighting. 
 

 \item 
   Atmospheric effects like atmosphere, ground-\discretionary{}{}{}fog and rainbow. 
 

 \item 
   Particle media to model effects like clouds, dust, fire and steam. 
 

 \item 
   Several image file output formats including Targa, BMP (Windows only), PNG and PPM. 
 

 \item 
   Basic shape primitives such as ... spheres, boxes, quadrics, cylinders, cones, triangle and planes. 
 

 \item 
   Advanced shape primitives such as ... Tori (donuts), bezier patches, height fields (mountains), blobs, quartics, smooth triangles, text, superquadrics, surfaces 
  of revolution, prisms, polygons, lathes, fractals, isosurfaces and the parametric object. 
 

 \item 
   Shapes can easily be combined to create new complex shapes using Constructive Solid Geometry (CSG). POV-\discretionary{}{}{}Ray supports unions, merges, intersections and 
  differences. 
 

 \item 
   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''). 
 

 \item 
   Built-\discretionary{}{}{}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. Or build your own pattern using functions. 
 

 \item 
   Users can create their own textures or use pre-\discretionary{}{}{}defined textures such as ... Brass, Chrome, Copper, Gold, Silver, Stone, Wood. 
 

 \item 
   Combine textures using layering of semi-\discretionary{}{}{}transparent textures or tiles of textures or material map files. 
 

 \item 
   Display preview of image while rendering (not available on all platforms). 
 

 \item 
   Halt and save a render part way through, and continue rendering the halted partial render later. 
 

\end{itemize}

\section{The Early History of POV-\discretionary{}{}{}Ray}

% tutorial/000022.html


\begin{description}
 
 \item 
   \textit{You know you have been raytracing too long when ...\newline  ... You hear a name beginning with the letter K and wonder if it's David Buck's 
  middle name. } 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   \textit{-- Alex McLeod} 
 \end{list}

\end{description}


   OK, here's a not-\discretionary{}{}{}so brief history of POV-\discretionary{}{}{}Ray (from the horse's mouth, so to speak): 



   Back in 1986 or so, I had an Amiga. A friend who also has an Amiga downloaded the C code for a raytracer for Unix from the Internet and brought it over. I 
 thought it looked interesting and I ported it to the Amiga and wrote the drivers to display it with Amiga graphics. The program only rendered untextured 
 spheres with a planar floor in black and white, but I was still impressed by it. I played with it a bit adding support for color, but I eventually decided 
 that I could do a better job writing a raytracer from scratch, so I scrapped the C program and started my own - DKBTrace had begun. 



   I decided to start with general quadric surfaces since they could represent spheres, ellipsoids, cylinders, planes, and more. I worked out the ray-\discretionary{}{}{}quadric 
 intersection calculations and used some calculus to work out the surface normal to a quadric surface at a point. For the program structure, I decided to use 
 an object-\discretionary{}{}{}oriented style since I had learned Smalltalk at university and it fit nicely. To make modeling more flexible, I added CSG and procedural textures. 
 In the end, I had an interesting little raytracer and I decided to release it as freeware since I was planning to return to university to start my Master's 
 degree and didn't have time to develop a commercial raytracer. Besides, there were already commercial renders for the Amiga that had user interfaces (not just 
 text files) and I felt I couldn't sell it as a commercial product. I called it DKBTrace and released it to local BBS'es and to the Internet. 



   DKBTrace was an Amiga-\discretionary{}{}{}only program, but it attracted quite a lot of interest. I released several versions of it adding in new features, better primitives, 
 more texturing options, etc. Eventually I released version 2.01. 



   Sometime around 1987 or 1988, I was contacted by Aaron Collins. He had found the C code for DKBTrace and ported it to the PC. He also added a Phong lighting 
 model and a few more goodies. I was interested in what he had done, so I contacted him to see if he wanted to help develop a new version of the program. This 
 one would be portable across more platforms (at university I had access to Unix workstations). We eventually came up with version \discretionary{2.}{}{2.}l2 which was the last 
 version of DKBTrace ever released (1989). 



   While Aaron and I were working up to version 2.12, there was a group of people on CompuServe who were very excited about DKBTrace and were creating all sorts 
 of neat scenes for it. They were also expressing frustration that Aaron and I weren't able to add new features into DKBTrace fast enough. They started talking 
 about building a whole new raytracer from scratch that they could control and add the features they wanted. At that time, I was starting to pursue other areas 
 and was starting to drift away from raytracing. So, I posted a message on CompuServe with the following offer: We could form a team to develop a new raytracer 
 using DKBTrace as a base. I had three requirements for this team. The resulting code had to be freeware with the source code freely available, it had to 
 remain portable between different platforms, and it had to have a different name than DKBTrace. 



   The name DKBTrace was, of course, based on my initials: David Kirk Buck (there's some little known trivia for you). With a package developed by a team of 
 people, it was inappropriate to use my initials. I was also starting to drift away from raytracing (as I mentioned) and I didn't want people thinking that I 
 was the head of the team forever. The name that was proposed was ``Persistance Of Vision Raytracer'' which was shortened to POV-\discretionary{}{}{}Ray. It worked in 
 three ways. It was the result of a persistent vision of the developers, it was a reference to the Salvador Dali work which depicted a distorted but realistic 
 world, and the term ``persistance of vision'' in biology referred to the ability to see an image that was presented briefly - almost an after image. 



   In 1989, then, DKBTrace 2.12 was officially released and the POV-\discretionary{}{}{}Ray project had begun. I worked with the team for a few years after that. I was responsible 
 for the Amiga port among other things. Drew Wells was the project leader. Aaron Collins dropped out of the project around that time as well. Other early 
 members included Chris Young, Steve Anger, Tim Wegner, Dan Farmer, Bill Pulver (IBM drivers), and Alexander Enzmann (quartics and cool math stuff). Chris 
 Cason joined shortly after (my apologies if I left anyone out - lots of people were involved). The reference to Robert Skinner in the credits for POV-\discretionary{}{}{}Ray was 
 because we had a hard time finding a good noise function. In another raytracer, he had a great noise function written by Robert Skinner, so we asked for and 
 received permission to use it in POV-\discretionary{}{}{}Ray. 



   There was so much demand for us to release a new version that we created POV-\discretionary{}{}{}Ray 0.5 and released it. It was basically an enhanced DKBTrace with a similar 
 grammar but many more features. Eventually, we released POV-\discretionary{}{}{}Ray 1.0 which had the new grammar and lots of new stuff. Drew dropped out later and Chris Young 
 took over as project leader. 



   It was around that time that I started to drift away from the POV-\discretionary{}{}{}Ray team. The project had momentum and could continue on without me. I was getting into 
 different areas (physically based modeling and animation) and no longer had the time to continue with POV-\discretionary{}{}{}Ray. Around the release of version 2.0, I left the 
 project and the POV-\discretionary{}{}{}Ray team developed it to its current state. Chris Cason is now the project leader. 



   Even though I'm no longer on the POV-\discretionary{}{}{}Ray development team, I still like to follow its progress. I haven't built my own scene by hand for years now (although 
 I occasionally use Moray). I still enjoy the one thing that drove me back in the DKBTrace days - I love seeing the works of other people who used my software. 
 Even though I can no longer call POV-\discretionary{}{}{}Ray ``my software'', I still enjoy admiring the artwork people create with it. I'm constantly amazed at what 
 people can do. It was always the feedback from user community that drove me. 



   David Buck,\newline  david [at] \discretionary{simberon.}{}{simberon.}com\newline \newline  august 2001 


\subsection{The Original Creation Message}

% tutorial/000097.html


{\small\begin{verbatim}
11906 S16/Raytraced Images
   07-Mar-91 18:56:37
Sb: DKB Development
Fm: David Buck 70521,1371
To: All

Greetings all.  This is my first posting to this group, so you'll
have to excuse me if I make any mistakes in this post.

Finally, after several weeks of waiting, I've received my CompuServe
account.  It's nice to see that people are enjoying my raytracer
(DKB, of course). I have noticed, however, that you are less than
satisfied at the support I've been able to provide <grin>.
True, I'm the first to admit that the support is poor.  I have 
little time these days to work on graphics - it takes long enough
to answer all the questions I get asked on a daily basis from all
across the world.

My motivation for releasing the raytracer as Freely Distributable
software in the first place was to allow people to have some fun
with a program I'd developed for just that purpose.  I don't 
consider it to be a professional package - I know it's nowhere near
that good.  I didn't make it shareware, however, because I knew I
wouldn't have much time for support.  I didn't want the hassles of
maintaining user lists, sending updates and notices, etc.

There has recently been a proposal in this forum that you write
your own raytracer to use instead of DKB.  Perhaps I can make that
prospect a little bit easier.  Suppose we take DKB and use it as a
base for a completely new system (the name "Renderdog" has
been tossed around, but I'm not fond of that one <g>). I would
like to propose the name "Software Taskforce on Animation and
Rendering" or STAR.  I would imagine that there would be
several packages developed such as:

 STAR Light  - the raytracer
 STAR Guider - an animation system
 STAR Maker - a user interface for StarLight

If you decide to do this, I would like to place a few rules on the
packages (or at least those developed from DKB):

  - they will remain freely distributable
  - support and maintenance of this new product will be undertaken
    by the STAR team (including but not limited to myself)
  - the programs will remain as portable as possible

What do you think of this proposal?

David Buck
\end{verbatim}}

\subsection{The Name}

% tutorial/000099.html



   More on how POV-\discretionary{}{}{}Ray came to its name. 


{\small\begin{verbatim}
**************************************************************
from Chris Young, to whom I asked if POV's name was related
to the title of a sci-fi book I had just found on a flea market.
**************************************************************
 
Varley is one of my favorite authors and I've owned that book 
long before POV-Ray existed.  POV-Ray was originally going to be 
called Starlight or StarLite or something similar but somebody 
else, I don't know who, said we'd get in trademark trouble over 
some existing product.  Drew Wells was team leader and he picked 
Persistence of Vision based on the properties of the human visual 
system. I also felt there was a double meaning in that POV-Ray 
was the continuation (or persistance) of David K. Buck's DKB-Trace.  
I warned Drew about Varley's book but book titles aren't as messy 
as product names.  Note also that Public Broadcasting System has 
a documentary series called POV but that stands for Point Of View 
which is the filmmaking term for hand-held camera, cinema-verite 
style used in many documentaries.
 
I wanted to take our team name from the Fractint Stone Soup Group 
and call us the Crystal Soup Group but I got voted down.
 
        Chris Young, POV-Team Coordinator
\end{verbatim}}

{\small\begin{verbatim}

**************************************************************
from unknown source
**************************************************************
 
After the recent thread on the starting time I POV-Ray I did
a search and found this post to this very news group from
David Buck himself. The message places the birth of the POV-Ray
project to be in May of 1991. A very historic event!
 
I hope I'm not stepping on toes by re-posting
it  :-)
 
Harold
 
Sun, 19 Feb 1995 19:14:44 GMT
(STEERPIKE) says:
>I had always presumed that Persistance of Vision was a pun on
>the name of Salvador Dali's painting "The Persistance of
>Memory". Is this right, and if not, how did POV-Ray come to 
> have such a poetic name? :)
 
The POV-Ray project started in May 1991 when I first proposed the
idea to a group of people on CompuServe.  They liked my DKBTrace
raytracer but didn't like the fact that I was too slow adding new
features to it.  They were going to re-write a raytracer from
scratch, but I suggested that after version 2.12 of DKBTrace, they
could take the code as is and develop it from there into a new
raytracer.  The first name was STAR - an acronym for something or
other.  Then someone in the group came up with "Persistance of
Vision".  We liked it because of its reference to Dali (I
believe the painting was actually called Persistance of Vision - am
I mistaken?).  Moreover, it seemed to symbolize the team who 
"Persisted" to achieve their "Vision".  The 
third reference was to the phychological effect that seeing an image
flashed on a screen causes you to retain that image in short term
memory.  Thus, your memory was a representation of reality but not
really reality. They all seemed to fit together to make a nice name.
Early on, we were abbreviating the name to PVRay, but we were
concerned about a commercial product called PV-Wave.  We agreed to
change the abbreviation to POV-Ray and standardize on the spelling.
 
>David Buck
\end{verbatim}}

\subsection{A Historic 'Version History'}

% tutorial/000098.html



   The version history as it was included in PV-\discretionary{}{}{}Ray 0.5 BETA. Notice the name changes... 


{\small\begin{verbatim}
Persistence of Vision Raytracer Version History
-------------------------------------------------

 PV-Ray was originally DKBTrace Ver. 2.12 written by David Buck. He 
donated the rights to his source code so the PV-Team could enhance
this raytracer as a group project similar to Fractint. The source
code for PV-Ray will always be freely distributable subject to the
restrictions in the header files. Thanks David, for your generous
gift!
	
Version 0.02 BETA Release 7/29/91 (as STAR-Light)
----------------------------------
 First version is still basically DKBTrace 2.12 with a few new
 features.
 
 - Materials mapping added by Drew Wells.(see matmap.dat)
 - ONION \& LEOPARD textures added by Scott Taylor.
 - Time to trace display added by Bill Pulver.
 - Grayscale display (+g) for IBM-PC's added by Scott Taylor.
 - Small wood texture bug fixed to create true cylinders.
 - Verbose now displays more info including file being traced.
 - Option +vO added to enable old-style terse verbose.
 - Texture.c broken into smaller modules.
 - PAINTED1, 2, \& 3 added for developers.
 - BUMPY1, 2, \& 3 added for developers.
  
PvRay Version 0.5 BETA Release 9/07/91
----------------------------------
 Many more changes this time around, including...

- Many enhancements from Alexander Enzmann
   - Bezier bicubic subpatches
   - Polynomial surfaces
   - New mapping types (sphere, etc.)
   - Sturmian sequences
   - Clipping shapes
   - (have I forgotten anything??)
- Lots of hard work and enhancements by Aaron Collins
- Height fields by Doug Muir
- Bump Mapping by Doug Muir and Drew Wells
- Interpolation by Girish T. Hagan adapted for mapping by Drew Wells
- # and ; are now ignored. 
- case_sensitive keywords and commandline option added by Drew Wells
  > case_sensitive_yes -- All words checked for exact case.
                             Keywords must be in upper case.
                             (*Old DKB Style*)
  > case_sensitive_no  -- Case is ignored for all words.
  > case_sensitive_opt -- DEFAULT - All words checked for exact
                             case except keywords. Keywords will be
                             accepted in upper and/or lower case. 
  > command line -- /ty = yes, /tn = no, /to = opt
- cnvdat.c to convert old dat files included with pvsrc.
- C++ style commenting - // ignore to end of line. 
  and /* ignore between braces */ nesting not allowed.
- New default style verbose trace info (+v1) 
- Old-new style verbose (+v0)
- Verbose trace info outputs to stderr so that stats can be
  redirected to file.
- New stats display outputs to stdout for better redirection.
- New lighting routines by David Buck.
- The declared colors Red, Green, and Blue in colors.dat are now
  CRed, CBlue, CGreen.
- The declared quadric Sphere in shapes.dat is now QSphere.
- Textures.dat has been cleaned up and commented.
\end{verbatim}}

\section{How Do I Begin?}

% tutorial/000023.html



   POV-\discretionary{}{}{}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-\discretionary{}{}{}Ray will read it to create the image. The process of running POV-\discretionary{}{}{}Ray is a little different on each platform or operating system. You 
 should read the platform-\discretionary{}{}{}specific documentation as suggested earlier in this introduction. It will tell you how to command POV-\discretionary{}{}{}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-\discretionary{}{}{}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-\discretionary{}{}{}Ray language. 


\section{Notation and Basic Assumptions}

% tutorial/000024.html



   Throughout the tutorial and reference books, the consistent notation is used to mark keywords of the scene description language, command line switches, INI 
 file keywords and file names. All POV-\discretionary{}{}{}Ray scene descriptionlanguage keywords, punctuation and command-\discretionary{}{}{}line switches are mono-\discretionary{}{}{}spaced. For example {\small\texttt{sphere}}, 
 {\small\texttt{4.0 * sin(45.0)}} or {\small\texttt{+W640 +H480}}. Syntax descriptions are mono-\discretionary{}{}{}spaced and all caps. For example required syntax items are 
 written like {\small\texttt{SYNTAX\_\-ITEM}}, while optional syntax items are written in square braces like {\small\texttt{[SYNTAX\_\-ITEM]}}. If one or more syntax 
 items are required, the ellipsis will be appended like {\small\texttt{SYNTAX\_\-ITEM...}}. In case zero or more syntax items are allowed, the syntax item will be 
 written in square braces with appended ellipsis like {\small\texttt{[SYNTAX\_\-ITEM...]}}. A float value or expression is written mixed case like {\small\texttt{Value\_\-1}}, 
 while a vector value or expression is written in mixed case in angle braces like {\small\texttt{$<$Value\_\-1$>$}}. Choices are represented by a vertical bar 
 between syntax items. For example a choice between three items would be written as {\small\texttt{ITEM1 | ITEM2 | ITEM3}}. Further, a certain lists and arrays 
 also require square braces as part of the language rather than the language description. When square braces are required as part of the syntax, they will be 
 separated from the contained syntax item specification with a spaces like {\small\texttt{[ ITEM ]}}. 



   \textbf{Note:} POV-\discretionary{}{}{}Ray is a command-\discretionary{}{}{}line program on Unix and other text-\discretionary{}{}{}based operating systems and is menu-\discretionary{}{}{}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-\discretionary{}{}{}folders with a slash character ({\small\texttt{/}}), 
 back-\discretionary{}{}{}slash character ({\small\texttt{$\backslash$}}), 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 is no way to escape 
 it. Here are some assumptions we make... 


\begin{enumerate}
 
 \item 
   You installed POV-\discretionary{}{}{}Ray in the ``{\small\texttt{C:$\backslash$POVRAY36}}'' directory. For MS-\discretionary{}{}{}Dos this is probably true but for Unix it might be ``{\small\texttt{/usr/povray3}}'', 
  or for Windows it might be ``{\small\texttt{C:$\backslash$Program Files$\backslash$\discretionary{}{}{}POV-\discretionary{}{}{}Ray for Windows v3.6}}'', for Mac it might be ``{\small\texttt{\discretionary{MyHD:}{}{MyHD:}\discretionary{Apps:}{}{Apps:}POV-\discretionary{}{}{}Ray 
  36:}}'', or you may have used some other drive or directory. So if we tell you that ``Include files are stored in the {\small\texttt{$\backslash$povray36$\backslash$\discretionary{}{}{}include}} 
  directory,'' we assume you can translate that to something like ``{\small\texttt{::\discretionary{POVRAY36:}{}{POVRAY36:}INCLUDE}}'' or ``{\small\texttt{C:$\backslash$Program 
  Files$\backslash$\discretionary{}{}{}POV-\discretionary{}{}{}Ray for Windows v3.6$\backslash$\discretionary{}{}{}include}}'' or whatever is appropriate for your platform, operating 
  system and installation. 
 

 \item 
   POV-\discretionary{}{}{}Ray uses INI files and/or command-\discretionary{}{}{}line switches (if available) 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-\discretionary{}{}{}specific documentation on menu and 
  dialogs. 
 

 \item 
   Some of you are reading this using a help-\discretionary{}{}{}reader, built-\discretionary{}{}{}in help, web-\discretionary{}{}{}browser, formatted printout, or plain text file. We assume you know how to get 
  around in which ever medium you are using. We will say ``See the chapter on ''Setting POV-\discretionary{}{}{}Ray Options`` we assume you can click, scroll, browse, 
  flip pages or whatever to get there. 
 

\end{enumerate}

\clearpage \chapter{Getting Started}

% tutorial/000002.html


\begin{description}
 
 \item 
   \textit{You know you have been raytracing too long when ...\newline  ... You actually read all the documentation that comes with programs.} 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   \textit{-- AmaltheaJ5} 
 \end{list}

\end{description}


   The beginning tutorial explains step by step how to use POV-\discretionary{}{}{}Ray's scene description language to create your own scenes. The use of almost every feature of 
 POV-\discretionary{}{}{}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. 


\section{Our First Image}

% tutorial/000025.html


\begin{description}
 
 \item 
   \textit{You know you have been raytracing too long when ...\newline  ... You have gone full circle and find your self writing a scene that contains 
  only a shiny sphere hovering over a green and yellow checkered plane ...} 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   \textit{-- Ken Tyler} 
 \end{list}

\end{description}


   We will create the scene file for a simple picture. Since ray-\discretionary{}{}{}tracers thrive on spheres, that is what we will render first. 


\subsection{Understanding POV-\discretionary{}{}{}Ray's Coordinate System}

% tutorial/000017.html

\index{Coordinate System! understanding}

   First, we have to tell POV-\discretionary{}{}{}Ray where our camera is and where it is looking. To do this, we use 3D coordinates. The usual coordinate system for POV-\discretionary{}{}{}Ray has 
 the positive y-\discretionary{}{}{}axis pointing up, the positive x-\discretionary{}{}{}axis pointing to the right, and the positive z-\discretionary{}{}{}axis pointing into the screen as follows:\index{The Left-\discretionary{}{}{}Handed coordinate system}\index{Left-\discretionary{}{}{}Handed coordinate system} 
 



   \begin{figure} \centering\includegraphics[scale=0.30]{../final/tex/images/tutorial/handed} \caption{The left-\discretionary{}{}{}handed coordinate system} \end{figure} 
 



   This kind of coordinate system is called a left-\discretionary{}{}{}handed coordinate system. If we use our left hand's fingers we can easily see why it is called left-\discretionary{}{}{}handed. 
 We just point our thumb in the direction of the positive x-\discretionary{}{}{}axis (to the right), the index finger in the direction of the positive y-\discretionary{}{}{}axis (straight up) and the 
 middle finger in the positive z-\discretionary{}{}{}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 ''\textit{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. 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/aerobics} \caption{Computer Graphics Aerobics} \end{figure} 



   In the above illustration, the left hand is curling around the x-\discretionary{}{}{}axis. The thumb points in the positive x direction and the fingers curl over in the positive 
 rotation direction. 



   \index{Right-\discretionary{}{}{}Handed coordinate system} If we want to use a right-\discretionary{}{}{}handed system, as some CAD systems and modelers do, the {\small\texttt{right}} 
 vector in the camera specification needs to be changed. See the detailed description in ''Handedness``. In a right-\discretionary{}{}{}handed system we use our right hand 
 for the ''Aerobics``. 



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


\subsection{Adding Standard Include Files}

% tutorial/000026.html

\index{Standard Include Files! adding}\index{keyword:\#include}
\begin{description}
 
 \item 
   \textit{You know you have been raytracing too long when ...\newline  ... you've just seen \discretionary{Monsters.}{}{Monsters.}Inc at the movies, and you are wondering when they 
  will release \discretionary{Monsters.}{}{Monsters.}Pov.} 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   \textit{-- Fabien Mosen} 
 \end{list}

\end{description}


   Using our personal favorite text editor, we create a file called {\small\texttt{\discretionary{demo.}{}{demo.}pov}}. Some versions of POV-\discretionary{}{}{}Ray come with their own built-\discretionary{}{}{}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. 


{\small\begin{verbatim}
  #include "colors.inc"    // The include files contain
  #include "stones.inc"    // pre-defined scene elements
\end{verbatim}}


   The first include statement reads in definitions for various useful colors. The second include statement reads in a collection of stone textures. POV-\discretionary{}{}{}Ray 
 comes with many standard include files. Others of interest are: 


{\small\begin{verbatim}
  #include "textures.inc"    // pre-defined scene elements
  #include "shapes.inc"
  #include "glass.inc"
  #include "metals.inc"
  #include "woods.inc"
\end{verbatim}}


   They read pre-\discretionary{}{}{}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-\discretionary{}{}{}Ray are quite large and we should better save the parsing 
 time and memory if we do not need them. In the following examples we will only use the {\small\texttt{\discretionary{colors.}{}{colors.}inc}}, and {\small\texttt{\discretionary{stones.}{}{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-\discretionary{}{}{}Ray searches any ``library paths'' that you have specified. Library paths are options set by the {\small\texttt{+L}} command-\discretionary{}{}{}line switch 
 or {\small\texttt{Library\_\-Path}} option. See the chapter ``Setting POV-\discretionary{}{}{}Ray Options'' for more information on library paths. 



   Because it is more useful to keep include files in a separate directory, standard installations of POV-\discretionary{}{}{}Ray place these files in the c:$\backslash$povray3$\backslash$\discretionary{}{}{}include 
 directory (replace 'c:$\backslash$povray3' with the actual directory that you installed POV-\discretionary{}{}{}Ray in). If you get an error message saying that POV-\discretionary{}{}{}Ray cannot open ``{\small\texttt{\discretionary{colors.}{}{colors.}inc}}'' 
 or other include files, make sure that you specify the library path properly. 


\subsection{Adding a Camera}

% tutorial/000027.html

\index{Camera! adding}

   The {\small\texttt{camera}} statement describes where and how the camera sees the scene. It gives x-, y- and z-\discretionary{}{}{}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-\discretionary{}{}{}part \textit{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. 


{\small\begin{verbatim}
  camera {
    location <0, 2, -3>
    look_at  <0, 1,  2>
  }
\end{verbatim}}


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



   Also {\small\texttt{look\_\-at $<$\discretionary{0,}{}{0,}\discretionary{1,}{}{1,}2$>$}} rotates the camera to point at the coordinates $<$\discretionary{0,}{}{0,}\discretionary{1,}{}{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 {\small\texttt{look\_\-at}} point should be the center of attention of 
 our image. 


\subsection{Describing an Object}

% tutorial/000028.html

\index{Object! describing}

   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: 


{\small\begin{verbatim}
  sphere {
    <0, 1, 2>, 2
    texture {
      pigment { color Yellow }
    }
  }
\end{verbatim}}


   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. 


\subsection{Adding Texture to an Object}

% tutorial/000029.html

\index{Object! adding texture to}

   After we have defined the location and size of the sphere, we need to describe the appearance of the surface. The {\small\texttt{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-\discretionary{}{}{}tracing takes care of that for you. We only need to pick the basic color 
 inherent in the object and POV-\discretionary{}{}{}Ray brightens or darkens it depending on the lighting in the scene. Because we are defining the basic color the object actually \textbf{ 
 has} rather than how it \textbf{looks} the parameter is called {\small\texttt{pigment}}. 



   Many types of color patterns are available for use in a pigment statement. The keyword {\small\texttt{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 {\small\texttt{ 
 \discretionary{colors.}{}{colors.}inc}}. 



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


{\small\begin{verbatim}
  color red 1.0 green 0.8 blue 0.8
\end{verbatim}}


   \textbf{Note:} the international - rather than American - form ``colour'' is also acceptable and may be used anywhere that ``color'' may be 
 used. 



   The values after each keyword should be in the range from 0.0 to 1.0. 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: 


{\small\begin{verbatim}
  color rgb <1.0, 0.8, 0.8>
\end{verbatim}}


   In many cases the {\small\texttt{color}} keyword is superfluous, so the shortest way to specify the pink color is: 


{\small\begin{verbatim}
  rgb <1.0, 0.8, 0.8>
\end{verbatim}}


   Colors are explained in more detail in section ``Specifying Colors''. 


\subsection{Defining a Light Source}

% tutorial/000030.html

\index{light\_\-source! defining}

   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 


{\small\begin{verbatim}
  light_source { <2, 4, -3> color White}
\end{verbatim}}


   to the scene file to get our first complete POV-\discretionary{}{}{}Ray scene file as shown below. 


{\small\begin{verbatim}
  #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}
\end{verbatim}}


   The vector in the {\small\texttt{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-\discretionary{}{}{}Ray also created a file. 



   \textbf{Note:} 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 is not 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. 


\section{Basic Shapes}

% tutorial/000031.html

\index{Shapes! basic}

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


\subsection{Box Object}

% tutorial/000032.html

\index{box! tutorial}

   The {\small\texttt{box}} is one of the most common objects used. We try this example in place of the sphere: 


{\small\begin{verbatim}
  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>"
  }
\end{verbatim}}


   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-\discretionary{}{}{}coordinates and the 2nd vector should be the maximum x-, y- and z-\discretionary{}{}{}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. 



   \textbf{Note:} we can perform simple math on values and vectors. In the rotate parameter we multiplied the vector identifier {\small\texttt{y}} by 20. This 
 is the same as $<$\discretionary{0,}{}{0,}\discretionary{1,}{}{1,}0$>$*20 or $<$\discretionary{0,}{}{0,}\discretionary{20,}{}{20,}0$>$. 


\subsection{Cone Object}

% tutorial/000033.html

\index{cone! tutorial}

   Here is another example showing how to use a {\small\texttt{cone}}: 


{\small\begin{verbatim}
  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 }
  }
\end{verbatim}}


   The cone shape is defined by the center and radius of each end. In this example one end is at location $<$\discretionary{0,}{}{0,}\discretionary{1,}{}{1,}0$>$ and has a radius of 0.3 while the other 
 end is centered at $<$\discretionary{1,}{}{1,}\discretionary{2,}{}{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 {\small\texttt{open}} after the 2nd radius 
 like this: 


{\small\begin{verbatim}
  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 }
  }
\end{verbatim}}

\subsection{Cylinder Object}

% tutorial/000034.html

\index{cylinder! tutorial}

   We may also define a {\small\texttt{cylinder}} like this: 


{\small\begin{verbatim}
  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 }
  }
\end{verbatim}}

\subsection{Plane Object}

% tutorial/000035.html

\index{plane! tutorial}

   Let's try out a computer graphics standard \textit{``The Checkered Floor''.} We add the following object to the first version of the {\small\texttt{\discretionary{demo.}{}{demo.}pov}} 
 file, the one including the sphere. 


{\small\begin{verbatim}
  plane { <0, 1, 0>, -1
    pigment {
      checker color Red, color Blue
    }
  }
\end{verbatim}}


   The object defined here is an infinite plane. The vector $<$\discretionary{0,}{}{0,}\discretionary{1,}{}{1,}0$>$ is the surface normal of the plane (\discretionary{i.}{}{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. 



   \textbf{Note:} even though there is no {\small\texttt{texture}} statement there is an implied texture here. We might find that continually typing statements 
 that are nested like {\small\texttt{texture \{pigment}}\} can get to be tiresome so POV-\discretionary{}{}{}Ray let's us leave out the {\small\texttt{ texture}} statement under 
 many circumstances. In general we only need the texture block surrounding a texture identifier (like the {\small\texttt{ 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 $<$\discretionary{1,}{}{1,}\discretionary{0,}{}{0,}0$>$, $<$\discretionary{0,}{}{0,}\discretionary{1,}{}{1,}0$>$ and $<$\discretionary{0,}{}{0,}\discretionary{0,}{}{0,}1$>$ are used frequently, POV-\discretionary{}{}{}Ray has three built-\discretionary{}{}{}in vector identifiers {\small\texttt{ x}}, {\small\texttt{ 
 y}} and {\small\texttt{z}} respectively that can be used as a shorthand. Thus the plane could be defined as: 


{\small\begin{verbatim}
  plane { y, -1
    pigment { ... }
  }
\end{verbatim}}


   \textbf{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-\discretionary{}{}{}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. 


\subsection{Torus Object}

% tutorial/000036.html

\index{torus! tutorial}

   A {\small\texttt{torus}} can be thought of as a donut or an inner-\discretionary{}{}{}tube. It is a shape that is vastly useful in many kinds of CSG so POV-\discretionary{}{}{}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 {\small\texttt{\discretionary{tordemo.}{}{tordemo.}pov}} and edit it as follows: 


{\small\begin{verbatim}
  #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 }
  }
\end{verbatim}}


   We trace the scene. Well, it is a donut alright. Let's try changing the major and minor radius values and see what happens. We change them as follows: 


{\small\begin{verbatim}
  torus { 5, .25      // major and minor radius
\end{verbatim}}


   That looks more like a hula-\discretionary{}{}{}hoop! Let's try this: 


{\small\begin{verbatim}
  torus { 3.5, 2.5    // major and minor radius
\end{verbatim}}


   Whoa! A donut with a serious weight problem! 



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



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


{\small\begin{verbatim}
  difference {
    torus {
      4, 1
      rotate x*-90  // so we can see it from the top
    }
    box { <-5, -5, -1>, <5, 0, 1> }
    pigment { Green }
  }
\end{verbatim}}


   Interesting... a half-\discretionary{}{}{}torus. Now we add another one flipped the other way. Only, let's declare the original half-\discretionary{}{}{}torus and the necessary transformations so 
 we can use them again: 


{\small\begin{verbatim}
  #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
\end{verbatim}}


   Now we create a union of two {\small\texttt{Half\_\-Torus}} objects: 


{\small\begin{verbatim}
  union {
    object { Half_Torus }
    object { Half_Torus
      rotate Flip_It_Over
      translate Torus_Translate*x
    }
  }
\end{verbatim}}


   This makes an S-\discretionary{}{}{}shaped object, but we cannot 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-\discretionary{}{}{}direction and rotate it about the +y-\discretionary{}{}{}axis so we can see more of it. We also notice that there appears to be a small gap where the half 
 Tori meet. This is due to the fact that we are viewing this scene from directly on the x-\discretionary{}{}{}z-\discretionary{}{}{}plane. We will change the camera's y-\discretionary{}{}{}coordinate from 0 to 0.1 to 
 eliminate this. 


{\small\begin{verbatim}
  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
  }
\end{verbatim}}


   Rendering this we see a cool, undulating, snake-\discretionary{}{}{}like something-\discretionary{}{}{}or-\discretionary{}{}{}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 {\small\texttt{ \discretionary{tordemo.}{}{tordemo.}pov}}: 


{\small\begin{verbatim}
  #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;
\end{verbatim}}


   Now, we make a complete torus of two half tori: 


{\small\begin{verbatim}
  union {
    object { Half_Torus }
    object { Half_Torus rotate Flip_It_Over }
  }
\end{verbatim}}


   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: 


{\small\begin{verbatim}
  #declare Chain_Segment = cylinder {
    <0, 4, 0>, <0, -4, 0>, 1
    pigment { Green }
  }
\end{verbatim}}


   We then add two {\small\texttt{Chain\_\-Segments}} to the union and translate them so that they line up with the minor radius of the torus on each side: 


{\small\begin{verbatim}
  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 }
  }
\end{verbatim}}


   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 {\small\texttt{Torus\_\-Translate}}: 


{\small\begin{verbatim}
  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
    }
  }
\end{verbatim}}


   We render this and voila! A single link of a chain. But we are not 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 tori and cylinders. Then we add a declaration for a golden texture just before the union that 
 creates the link. Finally, we add the texture to the union and declare it as a single link: 


{\small\begin{verbatim}
  #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> }
  }
    
  #declare Chain_Segment = cylinder {
    <0, 4, 0>, <0, -4, 0>, 1
  }

  #declare Chain_Gold = texture {
    pigment { BrightGold }
    finish {
      ambient .1
      diffuse .4
      reflection .25
      specular 1
      metallic
    }
  }

  #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 }
  }  
  \end{verbatim}}


   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 {\small\texttt{Torus\_\-Translate}} minus 2 (twice the minor radius). This can 
 be described by the expression: 


{\small\begin{verbatim}
  Torus_Translate*2-2*y
\end{verbatim}}


   We declare this expression as follows: 


{\small\begin{verbatim}
  #declare Link_Translate = Torus_Translate*2-2*y;
\end{verbatim}}


   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 {\small\texttt{ 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: 


{\small\begin{verbatim}
  union {
    object { Link }
    object { Link translate y*Link_Translate rotate y*90 }
    scale .25
  }
\end{verbatim}}


   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: 


{\small\begin{verbatim}
  #declare Link_Pair =
  union {
    object { Link }
    object { Link translate y*Link_Translate rotate y*90 }
  }
\end{verbatim}}


   Now we declare our chain: 


{\small\begin{verbatim}
  #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 }
  }
\end{verbatim}}


   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: 


{\small\begin{verbatim}
  object { Chain scale .1 rotate <0, 45, -45> }
\end{verbatim}}
\begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/torchain} \caption{The torus object can be used to create chains.} \end{figure}

   We render this and we should see a very realistic gold chain stretched diagonally across the screen. 


\section{CSG Objects}

% tutorial/000037.html

\index{Constructive Solid Geometry}
\begin{description}
 
 \item 
   \textit{You know you have been raytracing too long when ...\newline  ... Your friends are used to the fact that you will suddenly stop walking in order 
  to look at objects and figure out how to do them as CSGs.} 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   \textit{-- Jeff Lee} 
 \end{list}

\end{description}


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


\subsection{What is CSG?}

% tutorial/000038.html

\index{CSG! what is}

   \textit{CSG} stands for \textit{Constructive Solid Geometry}. POV-\discretionary{}{}{}Ray allows us to construct complex solids by combining primitive shapes in four different 
 ways. In the {\small\texttt{union}} statement, two or more shapes are added together. With the {\small\texttt{intersection}} statement, two or more shapes are 
 combined to make a new shape that consists of the area common to both shapes. The {\small\texttt{difference}} statement, an initial shape has all subsequent 
 shapes subtracted from it. 



   And last but not least {\small\texttt{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-\discretionary{}{}{}bounding and can be transformed like any other POV primitive shape. 


\subsection{CSG Union}

% tutorial/000039.html

\index{Union! CSG}\index{union! tutorial}

   Let's try making a simple union. Create a file called {\small\texttt{ \discretionary{csgdemo.}{}{csgdemo.}pov}} and edit it as follows: 


{\small\begin{verbatim}
  #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 }
  }
\end{verbatim}}


   Let's add two spheres each translated 0.5 units along the x-\discretionary{}{}{}axis in each direction. We color one blue and the other red. 


{\small\begin{verbatim}
  sphere { <0, 0, 0>, 1
    pigment { Blue }
    translate -0.5*x
  }
  sphere { <0, 0, 0>, 1
    pigment { Red }
    translate 0.5*x
  }
\end{verbatim}}


   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. 


{\small\begin{verbatim}
  union{
    sphere { <0, 0, 0>, 1
      pigment { Blue }
      translate -0.5*x
    }
    sphere { <0, 0, 0>, 1
      pigment { Red }
      translate 0.5*x
    }
  }
\end{verbatim}}


   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. 


{\small\begin{verbatim}
  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>
  }
\end{verbatim}}


   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. 


\subsection{CSG Intersection}

% tutorial/000040.html

\index{Intersection! CSG}\index{intersection! tutorial}

   Now let's use these same spheres to illustrate the{\small\texttt{intersection}} CSG object. We change the word {\small\texttt{union}} to {\small\texttt{intersection}} 
 and delete the {\small\texttt{scale}} and {\small\texttt{rotate}} statements: 


{\small\begin{verbatim}
  intersection {
    sphere { <0, 0, 0>, 1
      translate -0.5*x
    }
    sphere { <0, 0, 0>, 1
      translate 0.5*x
    }
    pigment { Red }
  }
\end{verbatim}}


   We trace the file and will see a lens-\discretionary{}{}{}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-\discretionary{}{}{}shaped area where the two spheres overlap. We like this lens-\discretionary{}{}{}shaped object so we will use it to demonstrate differences. 


\subsection{CSG Difference}

% tutorial/000041.html

\index{Difference! CSG}\index{difference! tutorial}

   We rotate the lens-\discretionary{}{}{}shaped intersection about the y-\discretionary{}{}{}axis so that the broad side is facing the camera. 


{\small\begin{verbatim}
  intersection{
    sphere { <0, 0, 0>, 1
      translate -0.5*x
    }
    sphere { <0, 0, 0>, 1
      translate 0.5*x
    }
    pigment { Red }
    rotate 90*y
  }
\end{verbatim}}


   Let's create a cylinder and stick it right in the middle of the lens. 


{\small\begin{verbatim}
  cylinder { <0, 0, -1> <0, 0, 1>, .35
    pigment { Blue }
  }
\end{verbatim}}


   We render the scene to see the position of the cylinder. We will place a {\small\texttt{difference}} block around both the lens-\discretionary{}{}{}shaped intersection and the 
 cylinder like this: 


{\small\begin{verbatim}
  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 }
    }
  }
\end{verbatim}}


   We render the file again and see the lens-\discretionary{}{}{}shaped intersection with a neat hole in the middle of it where the cylinder was. The cylinder has been {\small\texttt{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 black, as this is the default color if no color is specified. 



   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. 


{\small\begin{verbatim}
  #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 }
  }
\end{verbatim}}


   Let's use a union to build a complex shape composed of copies of this object. 


{\small\begin{verbatim}
  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 }
  }
\end{verbatim}}


   We render the scene. An interesting object to be sure. But let's try something more. Let's make it a partially-\discretionary{}{}{}transparent object by adding some filter to 
 the pigment block. 


{\small\begin{verbatim}
  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 }
  }
\end{verbatim}}


   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. 


\subsection{CSG Merge}

% tutorial/000042.html

\index{Merge! CSG}\index{merge! tutorial}

   This brings us to the fourth kind of CSG object, the {\small\texttt{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. 


{\small\begin{verbatim}
  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 }
  }
\end{verbatim}}


   Sure enough, it does! 


\subsection{CSG Pitfalls}

% tutorial/000043.html

\index{Pitfalls! CSG}

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


\subsubsection{Co-\discretionary{}{}{}incident Surfaces}

% tutorial/000273.html

\index{Surfaces! co-\discretionary{}{}{}incident}

   POV-\discretionary{}{}{}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 the computer's floating-\discretionary{}{}{}point accuracy) 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. 


{\small\begin{verbatim}
  difference {
    box { -1, 1 pigment { Red } }
    cylinder { -z, z, 0.5 pigment { Green } }
  }
\end{verbatim}}


   \textbf{Note:} that the vectors -1 and 1 in the box definition expand to $<$-1,-1,-1$>$ and $<$\discretionary{1,}{}{1,}\discretionary{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: 


{\small\begin{verbatim}
  difference {
    box { -1, 1 pigment { Red } }
    cylinder { -1.001*z, 1.001*z, 0.5 pigment { Green } }
  }
\end{verbatim}}


   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. 


\section{The Light Source}

% tutorial/000044.html

\index{Light Source! the}\index{light\_\-source! tutorial}
\begin{description}
 
 \item 
   \textit{You know you have been raytracing too long when ...\newline  ... You take a photo course just to learn how to get the lighting right.} 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   \textit{-- Christoph Rieder} 
 \end{list}

\end{description}


   In any ray-\discretionary{}{}{}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-\discretionary{}{}{}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. 


\subsection{The Pointlight Source}

% tutorial/000045.html

\index{Pointlight Source! the}

   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 {\small\texttt{\discretionary{litedemo.}{}{litedemo.}pov}}. We edit it as follows: 


{\small\begin{verbatim}
  #include "colors.inc"
  #include "textures.inc"
  camera {
    location  <-4, 3, -9>
    look_at   <0, 0, 0>
    angle 48
  }
\end{verbatim}}


   We add the following simple objects: 


{\small\begin{verbatim}
  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>
  }
\end{verbatim}}


   Now we add a pointlight: 


{\small\begin{verbatim}
  light_source {
    <2, 10, -3>
    color White
  }
\end{verbatim}}


   We render this at 200x150 {\small\texttt{-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. 


\subsection{The Spotlight Source}

% tutorial/000046.html

\index{Spotlight Source! the}\index{light\_\-source! spotlight, tutorial}

   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 {\small\texttt{spotlight}} keyword to a regular point light. There are a few more parameters with spotlights 
 than with pointlights. These are {\small\texttt{radius}}, {\small\texttt{falloff}}, {\small\texttt{tightness}} and {\small\texttt{point\_\-at}}. The {\small\texttt{radius}} 
 parameter is the angle of the fully illuminated cone. The {\small\texttt{falloff}} parameter is the angle of the \textit{umbra} cone where the light falls off 
 to darkness. The {\small\texttt{tightness}} is a parameter that determines the rate of the light falloff. The {\small\texttt{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: 


{\small\begin{verbatim}
  light_source {
    <0, 10, -3>
    color White
    spotlight
    radius 15
    falloff 20
    tightness 10
    point_at <0, 0, 0>
  }
\end{verbatim}}


   We render this at 200x150 {\small\texttt{-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: 


{\small\begin{verbatim}
  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>
  }
\end{verbatim}}


   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. 


\subsection{The Cylindrical Light Source}

% tutorial/000047.html

\index{Cylindrical Light Source! the}\index{light\_\-source! cylinder, tutorial}

   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 {\small\texttt{spotlight}} 
 keyword with the {\small\texttt{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! 


\subsection{The Area Light Source}

% tutorial/000048.html

\index{Area Light Source! the}\index{light\_\-source! area\_\-light, tutorial}
\begin{description}
 
 \item 
   \textit{You know you have been raytracing too long when ...\newline  ... You wear fuzzy clothing to soften your shadow.} 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   \textit{-- Mark Kadela} 
 \end{list}

\end{description}


   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 \textit{umbra}, or an area of fuzziness where there is neither total light or shade. In 
 order to simulate these \textit{ soft} shadows, a ray-\discretionary{}{}{}tracer must give its light sources dimension. POV-\discretionary{}{}{}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 {\small\texttt{ adaptive}} keyword tells the ray-\discretionary{}{}{}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 {\small\texttt{ jitter}} keyword. This tells the ray-\discretionary{}{}{}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: 


{\small\begin{verbatim}
  light_source {
    <2, 10, -3>
    color White
    area_light <5, 0, 0>, <0, 0, 5>, 5, 5
    adaptive 1
    jitter
  }
\end{verbatim}}


   This is a white area light centered at $<$\discretionary{2,}{}{2,}10,-3$>$. It is 5 units (along the x-\discretionary{}{}{}axis) by 5 units (along the z-\discretionary{}{}{}axis) in size and has 25 (5*5) lights in it. 
 We have specified adaptive 1 and jitter. We render this at 200x150 {\small\texttt{-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: 


{\small\begin{verbatim}
  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>
  }
\end{verbatim}}


   We now have three area-\discretionary{}{}{}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 {\small\texttt{-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. 


\subsection{The Ambient Light Source}

% tutorial/000049.html

\index{ambient\_\-light! tutorial}

   The \textit{ambient light source} is used to simulate the effect of inter-\discretionary{}{}{}diffuse reflection. If there was not inter-\discretionary{}{}{}diffuse reflection all areas not 
 directly lit by a light source would be completely dark. POV-\discretionary{}{}{}Ray uses the {\small\texttt{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 ({\small\texttt{rgb $<$\discretionary{1,}{}{1,}\discretionary{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. 


{\small\begin{verbatim}
  global_settings { ambient_light rgb<1, 0, 0> }
\end{verbatim}}

\subsection{Light Source Specials}

% tutorial/000050.html

\index{Light Sources! special}
\subsubsection{Using Shadowless Lights}

% tutorial/000051.html

\index{Shadowless Lights! using}\index{light\_\-source! shadowless, tutorial}

   Light sources can be assigned the {\small\texttt{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 \textit{fill lights} around the scene. Fill lights are simply dimmer 
 lights with the {\small\texttt{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-\discretionary{}{}{}comment them and comment out any other lights we have made. Now we add the following: 


{\small\begin{verbatim}
  light_source {
    <0, 20, 0>
    color Gray50
    shadowless
  }
\end{verbatim}}


   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. 


\subsubsection{Assigning an Object to a Light Source}

% tutorial/000052.html

\index{Light Source! assigning an object to}\index{Object Lights}\index{light\_\-source! looks\_\-like, tutorial}

   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 {\small\texttt{looks\_\-like}} keyword. We can specify that our light source can look like any object we choose. When we 
 use {\small\texttt{looks\_\-like}}, then {\small\texttt{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 lamp shade), 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: 


{\small\begin{verbatim}
  #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
  }
\end{verbatim}}


   Now we add the light source: 


{\small\begin{verbatim}
  light_source {
    <0, 2, 0>
    color White
    looks_like { Lightbulb }
  }
\end{verbatim}}


   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: 


{\small\begin{verbatim}
  light_source {
    <0, 2, 0>
    color White
    area_light <1, 0, 0>, <0, 1, 0>, 2, 2
    adaptive 1
    jitter
    looks_like { Lightbulb }
  }
\end{verbatim}}


   We note that we have placed this area light in the x-\discretionary{}{}{}y-\discretionary{}{}{}plane instead of the x-\discretionary{}{}{}z-\discretionary{}{}{}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. 


\subsubsection{Using Light Fading}

% tutorial/000053.html

\index{Light Fading! using}\index{Fading Light}\index{light\_\-source! fade\_\-power, tutorial}

   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-\discretionary{}{}{}Ray allows us to use two keywords: {\small\texttt{fade\_\-distance}}, 
 which specifies the distance at which full illumination is achieved, and {\small\texttt{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 {\small\texttt{ Gray50}} to {\small\texttt{Gray75}}. Now we change that fill light as follows: 


{\small\begin{verbatim}
  light_source {
    <0, 20, 0>
    color Gray75
    fade_distance 5
    fade_power 1
    shadowless
  }
\end{verbatim}}


   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 off 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. 


\section{Simple Texture Options}

% tutorial/000054.html

\index{Texture Options! simple}

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


\subsection{Surface Finishes}

% tutorial/000055.html



   One of the main features of a ray-\discretionary{}{}{}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 {\small\texttt{finish}} keyword followed by a parameter. We change the definition 
 of the sphere to this: 


{\small\begin{verbatim}
  sphere {
    <0, 1, 2>, 2
    texture {
      pigment { color Yellow } //Yellow is pre-defined in COLORS.INC
      finish { phong 1 }
    }
  }
\end{verbatim}}


   We render the scene. The {\small\texttt{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). 


\subsection{Adding Bumpiness}

% tutorial/000056.html

\index{Bumpiness! adding}

   The highlight we have added illustrates how much of our perception depends on the reflective properties of an object. Ray-\discretionary{}{}{}tracing can exploit this by playing 
 tricks on our perception to make us see complex details that are not 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 \textit{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: 


{\small\begin{verbatim}
  sphere {
    <0, 1, 2>, 2
    texture {
      pigment { color Yellow }
      normal { bumps 0.4 scale 0.2 }
      finish { phong 1 }
    }
  }
\end{verbatim}}


   This tells POV-\discretionary{}{}{}Ray to use the {\small\texttt{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 does not work very well with a sphere of radius 2. The scale makes the bumps 1/5th as wide but does not affect their 
 depth. 


\subsection{Creating Color Patterns}

% tutorial/000057.html

\index{Color Patterns! creating}\index{Color Maps}\index{Patterns}\index{color\_\-map! tutorial}

   We can do more than assigning a solid color to an object. We can create complex patterns in the pigment block like in these examples: 


{\small\begin{verbatim}
  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 }
    }
  }

  sphere {
    <0, 1, 2>, 2
    texture {
      pigment {
        wood
        color_map {
          [0.0 color Red]
          [0.5 color Red]
          [0.5 color Blue]
          [1.0 color Blue]
        }
        scale <0.2, 0.3, 1>
      }
      finish { phong 1 }
    }
  }
\end{verbatim}}


   The keyword {\small\texttt{wood}} specifies a pigment pattern of concentric rings like rings in wood. For every position in POV-\discretionary{}{}{}space, a pattern returns a 
 float value in the range from zero to one. Values outside the zero to one range are ignored. The {\small\texttt{color\_\-map}} specifies what color vector is 
 assigned to that float value. In the first example the color of the wood blends from {\small\texttt{DarkTan}} to {\small\texttt{DarkBrown}} over the first 90\% 
 of the vein and from {\small\texttt{DarkBrown}} to {\small\texttt{VeryDarkBrown}} over the remaining 10\%. In the second example the colors do not blend from 
 one to an other, but change abrupt. The {\small\texttt{turbulence}} keyword slightly stirs up the pattern so the veins are not perfect circles and the {\small\texttt{scale}} 
 keyword adjusts the size of the pattern. 



   Most patterns are set up by default to give us one \textit{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 {\small\texttt{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. 


\subsection{Pre-\discretionary{}{}{}defined Textures}

% tutorial/000058.html

\index{Textures! pre-\discretionary{}{}{}defined}

   POV-\discretionary{}{}{}Ray has some very sophisticated textures pre-\discretionary{}{}{}defined in the standard include files {\small\texttt{\discretionary{glass.}{}{glass.}inc}}, {\small\texttt{\discretionary{metals.}{}{metals.}inc}}, {\small\texttt{\discretionary{stones.}{}{stones.}inc}} 
 and {\small\texttt{\discretionary{woods.}{}{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-\discretionary{}{}{}render it: 


{\small\begin{verbatim}
  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
    }
  }
\end{verbatim}}


   The pigment identifier {\small\texttt{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 {\small\texttt{\discretionary{textures.}{}{textures.}inc}} to see what pigments and finishes are defined and try them out. We just insert the name of the new 
 pigment where {\small\texttt{DMFWood4}} is now or try a different finish in place of {\small\texttt{Shiny}} and re-\discretionary{}{}{}render our file. 



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


{\small\begin{verbatim}
  sphere {
    <0, 1, 2>, 2
    texture { PinkAlabaster }
  }
\end{verbatim}}

\section{Using the Camera}

% tutorial/000059.html

\index{Camera! using the}
\subsection{Using Focal Blur}

% tutorial/000060.html

\index{Focal Blur! using}\index{focus}

   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 {\small\texttt{ \discretionary{focaldem.}{}{focaldem.}pov}} and enter the following text 


{\small\begin{verbatim}
  #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 }
\end{verbatim}}


   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: 


{\small\begin{verbatim}
  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
  }
\end{verbatim}}


   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 \textit{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-\discretionary{}{}{}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 need not specify anti-\discretionary{}{}{}aliasing because the focal blur code uses its own sampling method 
 that automatically takes care of anti-\discretionary{}{}{}aliasing. Focal blur can only be used with the perspective camera. 


\section{POV-\discretionary{}{}{}Ray Coordinate System}

% tutorial/000061.html



   Objects, lights and the camera are positioned using a typical 3D coordinate system. The usual coordinate system for POV-\discretionary{}{}{}Ray has the positive y-\discretionary{}{}{}axis pointing 
 up, the positive x-\discretionary{}{}{}axis pointing to the right and the positive z-\discretionary{}{}{}axis pointing into the screen. The negative values of the axes point the other direction as 
 shown in the images in section ``Understanding POV-\discretionary{}{}{}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 {\small\texttt{$<$\discretionary{1,}{}{1,}\discretionary{2,}{}{2,}3$>$}} means the point that is one unit to the right, two units up and three units in front of 
 the center of the universe at {\small\texttt{$<$\discretionary{0,}{}{0,}\discretionary{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 \textit{transformations}. The follow 
 sub-\discretionary{}{}{}sections describe the transformations and their usage. 


\subsection{Transformations}

% tutorial/000062.html



   The supported transformations are {\small\texttt{rotate}}, {\small\texttt{ scale}}, and {\small\texttt{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. 


{\small\begin{verbatim}
TRANSFORMATION:
    rotate <Rotate_Amt> | scale <Scale_Amt> | 
    translate <Translate_Amt> | transform TRANSFORM_IDENTIFIER | 
    transform { TRANSFORMATION_BLOCK...} |
    matrix <Val00, Val01, Val02,
        Val10, Val11, Val12,
        Val20, Val21, Val22,
        Val30, Val31, Val32>
TRANSFORMATION_BLOCK:
    TRANSFORM_IDENTIFIER | TRANSFORMATION | inverse
TRANSFORM_DECLARATION:
    #declare IDENTIFIER = transform { TRANSFORMATION_BLOCK...} |
    #local IDENTIFIER = transform { TRANSFORMATION_BLOCK...}
\end{verbatim}}

\subsubsection{Translate}

% tutorial/000063.html



   Items may be moved by adding a {\small\texttt{translate}} modifier. It consists of the keyword {\small\texttt{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 its current 
 position. For example 


{\small\begin{verbatim}
 sphere { <10, 10, 10>, 1
  pigment { Green }
  translate <-5, 2, 1>
 }
\end{verbatim}}


   will move the sphere from the location {\small\texttt{$<$\discretionary{10,}{}{10,}\discretionary{10,}{}{10,}10$>$}} to {\small\texttt{$<$\discretionary{5,}{}{5,}\discretionary{12,}{}{12,}11$>$}}. It does not move it to the absolute location {\small\texttt{$<$-\discretionary{5,}{}{5,}\discretionary{2,}{}{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: 


{\small\begin{verbatim}
 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
 }
\end{verbatim}}

\subsubsection{Scale}

% tutorial/000064.html



   You may change the size of an object or texture pattern by adding a {\small\texttt{ scale}} modifier. It consists of the keyword {\small\texttt{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 \textit{ stretch} or \textit{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-\discretionary{}{}{}sized using scale then scale will size 
 relative to the new size. Multiple scale values may used. 



   For example 


{\small\begin{verbatim}
 sphere { <0,0,0>, 1
  scale <2,1,0.5>
 }
\end{verbatim}}


   will stretch and smash the sphere into an ellipsoid shape that is twice the original size along the x-\discretionary{}{}{}direction, remains the same size in the y-\discretionary{}{}{}direction and 
 is half the original size in the z-\discretionary{}{}{}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: 


{\small\begin{verbatim}
 object {
  MyObject
  scale 5 // Evaluates as <5,5,5> so uniformly scale
      // by 5 in every direction.
 }
\end{verbatim}}


   When one of the scaling components is zero, POV-\discretionary{}{}{}Ray changes this component to 1 since it assumes that 0 means no scaling in this direction. A warning 
 ``Illegal Value: Scale X, Y or Z by 0.0. Changed to 1.0.'' is printed then. 


\subsubsection{Rotate}

% tutorial/000065.html



   You may change the orientation of an object or texture pattern by adding a {\small\texttt{rotate}} modifier. It consists of the keyword {\small\texttt{ 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-\discretionary{}{}{}axes. 



   \textbf{Note:} that the order of the rotations does matter. Rotations occur about the x-\discretionary{}{}{}axis first, then the y-\discretionary{}{}{}axis, then the z-\discretionary{}{}{}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. 


{\small\begin{verbatim}
 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.
\end{verbatim}}


   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 \textit{orbit} 
 about the axis as though it was swinging around on an invisible string. 



   POV-\discretionary{}{}{}Ray uses a left-\discretionary{}{}{}handed rotation system. Using the famous ``\textit{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-\discretionary{}{}{}Ray's Coordinate System'' 
 for an illustration. 


\subsubsection{Matrix}

% tutorial/000066.html



   The {\small\texttt{matrix}} keyword can be used to explicitly specify the transformation matrix to be used for objects or textures. Its syntax is: 


{\small\begin{verbatim}
MATRIX:
    matrix <Val00, Val01, Val02,
        Val10, Val11, Val12,
        Val20, Val21, Val22,
        Val30, Val31, Val32>
\end{verbatim}}


   Where \textit{{\small\texttt{Val00}}} through \textit{{\small\texttt{Val32}}} are float expressions enclosed in angle brackets and separated by commas. 



   \textbf{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 {\small\texttt{$<$\discretionary{0,}{}{0,}0,\discretionary{0,}{}{0,}1$>$}}. At any given point \textit{P, 
 P=$<$px, py, pz$>$}, is transformed into the point \textit{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 will not use the matrix keyword because it is less descriptive than the transformation commands and harder to visualize. However the matrix 
 command allows more general transformation effects like \textit{ shearing}. The following matrix causes an object to be sheared along the y-\discretionary{}{}{}axis. 


{\small\begin{verbatim}
 object {
  MyObject
  matrix < 1, 1, 0,
       0, 1, 0,
       0, 0, 1,
       0, 0, 0 >
 }
\end{verbatim}}

\subsection{Transformation Order}

% tutorial/000067.html



   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. \newline For 
 example 


{\small\begin{verbatim}
  translate <5, 6, 7>
  scale 4
\end{verbatim}}


   will translate to {\small\texttt{$<$\discretionary{20,}{}{20,}\discretionary{24,}{}{24,}28$>$}} instead of {\small\texttt{ $<$\discretionary{5,}{}{5,}\discretionary{6,}{}{6,}7$>$}}. Be careful when transforming to get the order correct for 
 your purposes. 


\subsection{Inverse Transform}

% tutorial/000068.html


{\small\begin{verbatim}
  transform { scale <20,24,28> translate y*3  inverse }
\end{verbatim}}


   An inverse transform does the opposite of what the transform would normally do, and can be used to ``undo'' transforms without messing around with 
 huge numbers of transformations. To do the same without this {\small\texttt{inverse}}, you would have to duplicate each transform, change them to do the 
 opposite of what they would normally do (for example {\small\texttt{translate -y*3}} instead of {\small\texttt{translate y*3}})and reverse their order. 


\subsection{Transform Identifiers}

% tutorial/000069.html



   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: 


{\small\begin{verbatim}
TRANSFORM_DECLARATION:
  #declare IDENTIFIER = transform{ TRANSFORMATION... } |
  #local IDENTIFIER = transform{ TRANSFORMATION... }
\end{verbatim}}


   Where \textit{IDENTIFIER} is the name of the identifier up to 40 characters long and \textit{TRANSFORMATION} is any valid transformation modifier. See ``\#declare 
 vs. \#local'' for information on identifier scope. Here is an example... 


{\small\begin{verbatim}
  #declare MyTrans =
    transform {
      rotate THISWAY
      scale SOMUCH
      rotate -THISWAY
      scale BIGGER
      translate OVERTHERE
      rotate WAYAROUND
    }
\end{verbatim}}


   A transform identifier is invoked by the {\small\texttt{transform}} keyword with or without brackets as shown here: 


{\small\begin{verbatim}
  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
  }
\end{verbatim}}


   On extremely complex CSG objects with lots of components it may speed up parsing if you apply a declared transformation rather than the individual {\small\texttt{translate}}, 
 {\small\texttt{rotate}}, {\small\texttt{scale}}, or {\small\texttt{ matrix}} modifiers. The {\small\texttt{transform}} is attached just once to each 
 component. Applying each individual {\small\texttt{translate}}, {\small\texttt{ rotate}}, {\small\texttt{scale}}, or {\small\texttt{matrix}} modifiers takes 
 longer. This only affects parsing - rendering works the same either way. 


\subsection{Transforming Textures and Objects}

% tutorial/000070.html



   When an object is transformed all textures attached to the object \textit{at that time} are transformed as well. This means that if you have a {\small\texttt{ 
 translate}}, {\small\texttt{rotate}}, {\small\texttt{scale}}, or {\small\texttt{ matrix}} modifier in an object \textit{before} a texture, then the texture 
 will not be transformed. If the transformation is \textit{after} the texture then the texture will be transformed with the object. If the transformation is \textit{inside} 
 the {\small\texttt{texture}} statement then \textit{only the texture} is affected. The shape remains the same. For example: 


{\small\begin{verbatim}
 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
  }
 }
\end{verbatim}}


   Transformations may also be independently applied to pigment patterns and surface normal patterns. 



   \textbf{Note:} scaling a normal pattern not only affects the width and spacing. It does also affect the apparent height or depth of the bumps, for how to 
 avoid this see Scaling normals. 



   For example: 


{\small\begin{verbatim}
 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
              // and also the height. Has no effect on
              // color pattern.
   }
   rotate y*45 // This affects the entire texture but
  }            // not the object.
 }
\end{verbatim}}

\section{Setting POV-\discretionary{}{}{}Ray Options}

% tutorial/000300.html

\index{Options! all versions}\index{Command-\discretionary{}{}{}line Options! all versions}\index{Command-\discretionary{}{}{}line Options}

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



   There are two distinct ways of setting POV-\discretionary{}{}{}Ray options (other than through the GUI interface, if applicable) : command line switches and INI file keywords. 
 Both are explained in detail in the following sections. 


\subsection{Command Line Switches}

% tutorial/000301.html

\index{Switches! command-\discretionary{}{}{}line}\index{Options! command-\discretionary{}{}{}line}

   Command line switches consist of a {\small\texttt{+}} (plus) or {\small\texttt{ -}} (minus) sign, followed by one or more alphabetic characters and possibly 
 a numeric value. Here is a typical command line with switches. 


{\small\begin{verbatim}
  POVRAY +Isimple.pov +V +W80 +H60
\end{verbatim}}


   {\small\texttt{povray}} is the name of the program and it is followed by several switches. Each switch begins with a plus or minus sign. The {\small\texttt{ 
 +I}} switch with the filename tells POV-\discretionary{}{}{}Ray what scene file it should use as input and {\small\texttt{+V}} tells the program to output its status to the text 
 screen as it is working. The {\small\texttt{+W}} and {\small\texttt{ +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 {\small\texttt{ +P}} turns on the \textit{pause for keypress 
 when finished} option while {\small\texttt{-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 {\small\texttt{+W320}} sets the width to 320 pixels. You could also use {\small\texttt{ -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 {\small\texttt{+L}} switch for setting library paths. 
 Up to ten unique paths may be specified. 



   Almost all {\small\texttt{ +}} or {\small\texttt{-}} 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. 


\subsection{Using INI Files}

% tutorial/000302.html

\index{Options! ini file}\index{INI files! using}

   \textbf{Note:} although the term 'INI file' is used by POV-\discretionary{}{}{}Ray, this was implemented before the widespread acceptance of Microsoft Windows, and while 
 POV-\discretionary{}{}{}Ray's INI files are almost identical to those of Windows, there are some minor differences (the foremost being that it is legal to 
 have multiple instances of the same item in a section). INI files are used on all platform versions of POV-\discretionary{}{}{}Ray, not just on the Windows platform. 



   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-\discretionary{}{}{}Ray called them default files or DEF files. You may still use 
 existing DEF files with this version of POV-\discretionary{}{}{}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 {\small\texttt{ \discretionary{povray.}{}{povray.}ini}} is automatically read if present. You may specify 
 additional INI files on the command-\discretionary{}{}{}line by simply typing the file name on the command line. For example: 


{\small\begin{verbatim}
  POVRAY MYOPTS.INI
\end{verbatim}}


   If no extension is given, then {\small\texttt{.ini}} is assumed. POV-\discretionary{}{}{}Ray knows this is not a switch because it is not preceded by a plus or minus. 



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


{\small\begin{verbatim}
  POVRAY MYOPTS +V OTHER
\end{verbatim}}


   This reads options from {\small\texttt{\discretionary{myopts.}{}{myopts.}ini}}, then sets the {\small\texttt{ +V}} switch, then reads options from {\small\texttt{\discretionary{other.}{}{other.}ini}}. 



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


{\small\begin{verbatim}
  Option_keyword=VALUE ; Text after semicolon is a comment
\end{verbatim}}


   For example the INI equivalent of the switch {\small\texttt{+\discretionary{Isimple.}{}{Isimple.}pov}} is... 


{\small\begin{verbatim}
  Input_File_Name=simple.pov
\end{verbatim}}


   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 {\small\texttt{Library\_\-Path=path}} options. Up to 25 unique paths may be 
 specified. 



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


{\small\begin{verbatim}
  ; 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!
\end{verbatim}}


   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: 


{\small\begin{verbatim}
  ; 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
\end{verbatim}}


   When you specify the INI file you should follow it with the section label in brackets. For example... 


{\small\begin{verbatim}
  POVRAY RES[Med] +Imyfile.pov
\end{verbatim}}


   POV-\discretionary{}{}{}Ray reads {\small\texttt{\discretionary{res.}{}{res.}ini}} and skips all options until it finds the label {\small\texttt{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. 



   If a file or path contains blanks the whole file and path specification has to be put in quotes. You may either use a double-\discretionary{}{}{}quote oir a single-\discretionary{}{}{}quote, but 
 you have to use the same at the beginning and end. For example: 


{\small\begin{verbatim}
 +I"my file.pov"
 +I'my file.pov'
 Input_File="my file.pov"
 Input_File='my file.pov'
\end{verbatim}}


   By using either single or double quotes it is possible to specify files whose name or path contains either as part of the name. For example: 


{\small\begin{verbatim}
 +I"file's.pov"
 +I'my "big" file.pov'
 Input_File="file's.pov"
 Input_File='my "big" file.pov'
\end{verbatim}}

\subsection{Using the POVINI Environment Variable}

% tutorial/000303.html

\index{Options! POVINI environment variable}\index{POVINI environment variable}\index{Environment variables! POVINI}\index{Environment variables! POVRAYOPT}\index{POVRAYOPT 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-\discretionary{}{}{}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-\discretionary{}{}{}DOS you might put the following line in your {\small\texttt{\discretionary{autoexec.}{}{autoexec.}bat}} file... 


{\small\begin{verbatim}
  set POVINI=c:\povray3\default.ini
\end{verbatim}}


   On most operating systems the sequence of reading options is as follows: 


\begin{enumerate}
 
 \item 
   Read options from default INI file specified by the POVINI environment variable or platform specific INI file. 
 

 \item 
   Read switches from command line (this includes reading any specified INI/DEF files). 
 

\end{enumerate}


   The POVRAYOPT environment variable supported by previous POV-\discretionary{}{}{}Ray versions is no longer available. 


\clearpage \chapter{Advanced Features}

% tutorial/000003.html


\section{Spline Based Shapes}

% tutorial/000006.html

\index{Shapes! spline based}

   After we have gained some experience with the simpler shapes available in POV-\discretionary{}{}{}Ray it is time to go on to the more advanced, thrilling shapes. 



   We should be aware that the shapes described in this and the following two chapters are not trivial to understand. We need not 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. 


\subsection{Lathe Object}

% tutorial/000007.html

\index{lathe! tutorial}

   In the real world, {\small\texttt{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 artefacts such as table legs, pottery, etc. In POV-\discretionary{}{}{}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. 


{\small\begin{verbatim}
  #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
    }
  }
\end{verbatim}}


   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/latheobj} \caption{A simple lathe object.} \end{figure} 



   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 is 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-\discretionary{}{}{}y-\discretionary{}{}{}plane, therefore it is as if all the z-\discretionary{}{}{}components were assumed to be zero. The use of a 
 two-\discretionary{}{}{}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-\discretionary{}{}{}tracer rotates this line around the y-\discretionary{}{}{}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 {\small\texttt{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-\discretionary{}{}{}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 does not allow the curve to double back over the same y-\discretionary{}{}{}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 $<$\discretionary{0,}{}{0,}0$>$ to 
 $<$\discretionary{2,}{}{2,}2$>$, then to dip back down to $<$\discretionary{4,}{}{4,}0$>$. Rotated around the y-\discretionary{}{}{}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-\discretionary{}{}{}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, it is 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. 


\subsubsection{Understanding The Concept of Splines}

% tutorial/000008.html

\index{Splines! understanding the concept of}

   It would be helpful, in order to understand splines, if we had a sort of \textit{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: 


{\small\begin{verbatim}
#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>;
  #declare Orange_Point = <1.75, 1.00>;
  #declare Yellow_Point = <2.50, 2.00>;
  #declare Green_Point  = <2.00, 3.00>;
  #declare Blue_Point   = <1.50, 4.00>;
  /* make the control points visible */
  cylinder { Red_Point, Red_Point - <0,0,20>, .1
    pigment { Red }
    finish { ambient 1 }
  }
  cylinder { Orange_Point, Orange_Point - <0,0,20>, .1
    pigment { Orange }
    finish { ambient 1 }
  }
  cylinder { Yellow_Point, Yellow_Point - <0,0,20>, .1
    pigment { Yellow }
    finish { ambient 1 }
  }
  cylinder { Green_Point, Green_Point - <0,0,20>, .1
    pigment { Green }
    finish { ambient 1 }
  }
  cylinder { Blue_Point, Blue_Point- <0,0,20>, .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 }
  }
\end{verbatim}}


   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/spline} \caption{A simple } \end{figure} 



   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 have not read up on that yet, a quick summary is: it renders the scene \textit{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\textit{ 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 {\small\texttt{ambient 1}} finish, which of course also eliminates the need for lighting. We have also positioned this particular side view so that 
 $<$\discretionary{0,}{}{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 is 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-\discretionary{}{}{}use those same vectors to determine the lathe. 



   Since trying to declare a 2D vector can have some odd results, and is not 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-\discretionary{}{}{}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 have declared looks, and the 
 circular ends of the cylinders show us where along the x-\discretionary{}{}{}y-\discretionary{}{}{}plane our control points are. In this case, it is very simple. The linear spline has been used so 
 our curve is just straight lines zig-\discretionary{}{}{}zagging between the points. We change the declarations of {\small\texttt{Red\_\-Point}} and {\small\texttt{Blue\_\-Point}} to 
 read as follows. 


{\small\begin{verbatim}
  #declare Red_Point  = <2.00, 0.00>;
  #declare Blue_Point = <0.00, 4.00>;
\end{verbatim}}


   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/mvspline} \caption{Moving some points of the spline.} \end{figure} 



   We re-\discretionary{}{}{}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. 


{\small\begin{verbatim}
  #declare Red_Point    = <1.00, 0.00>;
  #declare Orange_Point = <2.00, 1.00>;
  #declare Yellow_Point = <3.50, 2.00>;
  #declare Green_Point  = <2.00, 3.00>;
  #declare Blue_Point   = <1.50, 4.00>;
\end{verbatim}}


   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/quspline} \caption{A quadratic spline lathe.} \end{figure} 



   We then go down to the lathe declaration and change {\small\texttt{linear\_\-spline}} to {\small\texttt{quadratic\_\-spline}}. We re-\discretionary{}{}{}render and what do we have? 
 Well, there is 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, {\small\texttt{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-\discretionary{}{}{}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 \textit{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-\discretionary{}{}{}Ray can determine what curve to connect the first two points 
 with. It will not show up as part of the actual curve. 



   There is 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. Taking longer still is 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 {\small\texttt{quadratic\_\-spline}} with {\small\texttt{ 
 cubic\_\-spline}}. We render one more time, and take a look at what we have. 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/cuspline} \caption{A cubic spline lathe.} \end{figure} 



   While a quadratic spline takes three points to determine the curve, a cubic needs four. So, as we might expect, {\small\texttt{Blue\_\-Point}} has now dropped 
 out of the curve, just as {\small\texttt{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 {\small\texttt{ Orange\_\-Point}} to {\small\texttt{Yellow\_\-Point}} and then back to {\small\texttt{ 
 Green\_\-Point}}. Now, rather than looking mismatched, our curve segments look like one smoothly joined curve. 



   finally there is another kind of quadratic spline, the {\small\texttt{bezier\_\-spline}}. This one takes four points per section. The start point, the end 
 points and in between, two control points. To use it, we will have to make a few changes to our work shop. Delete the Yellow point, delete the Yellow 
 cylinder. Change the points to: 


{\small\begin{verbatim}
  #declare Red_Point    = <2.00, 1.00>;
  #declare Orange_Point = <3.00, 1.50>;
  #declare Green_Point  = <3.00, 3.50>;
  #declare Blue_Point   = <2.00, 4.00>;
\end{verbatim}}


   And change the lathe to: 


{\small\begin{verbatim}
  lathe {
    bezier_spline
    4,
    Red_Point,
    Orange_Point,
    Green_Point,
    Blue_Point
    pigment { White }
    finish { ambient 1 }
  }
\end{verbatim}}


   The, green and orange, control points are not connected to the curve. Move them around a bit, for example {\small\texttt{\#declare Orange\_\-Point = $<$1.00, 
 1.50$>$;}}. The line that can be drawn from the start point to its closest control point (red to orange) shows the tangent of the curve at the start point. 
 Same for the end point, blue to green. 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/bezspline1} \caption{a bezier\_\-spline lathe} \end{figure} 



   One spline segment is nice, two is nicer. So we will add another segment and connect it to the blue point. One segment has four points, so two segments have 
 eight. The first point of the second segment is the same as the last point of the first segment. The blue point. So we only have to declare three more points. 
 Also we have to move the camera a bit and add more cylinders. Here is the complete scene again: 


{\small\begin{verbatim}
#include "colors.inc"
  camera {
    orthographic
    up <0, 7, 0>
    right <7, 0, 0>
    location <3.5, 4, -100>
    look_at <3.5, 4, 0>
  }
  /* set the control points to be used */
  #declare Red_Point    = <2.00, 1.00>;
  #declare Orange_Point = <1.00, 1.50>;
  #declare Green_Point  = <3.00, 3.50>;
  #declare Blue_Point   = <2.00, 4.00>;
  #declare Green_Point2 = <3.00, 4.50>;
  #declare Orange_Point2= <1.00, 6.50>;
  #declare Red_Point2   = <2.00, 7.00>;
  /* make the control points visible */

  cylinder { Red_Point, Red_Point - <0,0,20>, .1
    pigment { Red } finish { ambient 1 }
  }
  cylinder { Orange_Point, Orange_Point - <0,0,20>, .1
    pigment { Orange } finish { ambient 1 }
  }
  cylinder { Green_Point, Green_Point - <0,0,20>, .1
    pigment { Green } finish { ambient 1 }
  }
  cylinder { Blue_Point, Blue_Point- <0,0,20>, .1
    pigment { Blue } finish { ambient 1 }
  }
  cylinder { Green_Point2, Green_Point2 - <0,0,20>, .1
    pigment { Green } finish { ambient 1 }
  }
  cylinder { Orange_Point2, Orange_Point2 - <0,0,20>, .1
    pigment { Orange } finish { ambient 1 }
  }
  cylinder { Red_Point2, Red_Point2 - <0,0,20>, .1
    pigment { Red } finish { ambient 1 }
  }  
  /* something to make the curve show up */
  lathe {
    bezier_spline
    8,
    Red_Point, Orange_Point, Green_Point, Blue_Point
    Blue_Point, Green_Point2, Orange_Point2, Red_Point2
    pigment { White }
    finish { ambient 1 }
  }
\end{verbatim}}


   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/bezspline2} \caption{two bezier\_\-spline segments, not smooth} \end{figure} 
 



   A nice curve, but what if we want a smooth curve? Let us have a look at the tangents on the Blue\_\-point, draw the lines Green\_\-Point, Blue\_\-point and 
 Green\_\-Point2, Blue\_\-point. Look at the angle they make, it is as sharp as the dent in the curve. What if we make the angle bigger? What if we make the angle 
 180°? Try a few positions for Green\_\-point2 and end with {\small\texttt{\#declare Green\_\-Point2 = $<$1.00, 4.50$>$;}}. A smooth curve. If we make sure that the 
 two control points and the connection point are on one line, the curve is perfectly smooth. In general this can be achieved by {\small\texttt{\#declare 
 Green\_\-Point2 = Blue\_\-Point+(Blue\_\-Point-\discretionary{}{}{}Green\_\-Point);}} 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/bezspline3} \caption{smooth bezier\_\-spline lathe} \end{figure} 



   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. 


\subsection{Surface of Revolution Object}

% tutorial/000011.html

\index{sor! tutorial}

   Bottles, vases and glasses make nice objects in ray-\discretionary{}{}{}traced scenes. We want to create a golden cup using the \textit{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-\discretionary{}{}{}Ray's surface of revolution object. If such a program is available we should take advantage of it. 



   \begin{figure} \centering\includegraphics[scale=0.30]{../final/tex/images/tutorial/ptcubobj} \caption{The point configuration of our cup object.} \end{figure} 
 



   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-\discretionary{}{}{}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 create a file called {\small\texttt{\discretionary{sordemo.}{}{sordemo.}pov}} and enter the following text. 


{\small\begin{verbatim}
  #include "colors.inc"
  #include "golds.inc"
  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>
    open
    texture { T_Gold_1B }
  }
\end{verbatim}}


   The scene contains our cup object resting on a checkered plane. Tracing this scene results in the image below. 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/sorobj} \caption{A surface of revolution object.} \end{figure} 



   The surface of revolution is described by starting with the number of points followed by the points. Points from second to last but one are listed with 
 ascending heights. Each of them determines the radius of the curve for a given height. E. g. the first valid point (second listed) tells POV-\discretionary{}{}{}Ray that at 
 height 0.0 the radius is 3. 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. First and last point from the list are used to determine slope at beginning and end of curve and can be defined for any height. 


\subsection{Prism Object}

% tutorial/000012.html

\index{prism! tutorial}

   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-\discretionary{}{}{}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 {\small\texttt{\discretionary{prismdm1.}{}{prismdm1.}pov}}). 
 


{\small\begin{verbatim}
  #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 }
  }
\end{verbatim}}


   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/hexprism} \caption{A hexagonal prism shape.} \end{figure} 



   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 did not do this, POV-\discretionary{}{}{}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 must not get too casual about those warning 
 messages! 


\subsubsection{Teaching An Old Spline New Tricks}

% tutorial/000010.html

\index{Spline! new tricks}\index{cubic\_\-spline! tutorial}

   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-\discretionary{}{}{}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 \textit{ control point} and will not 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 is 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 do not match the correct points on a quadratic or cubic shape, that is when we will get the ``too few 
 points in prism'' error. POV-\discretionary{}{}{}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 {\small\texttt{\discretionary{prismdm2.}{}{prismdm2.}pov}}). 


{\small\begin{verbatim}
  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 }
  }
\end{verbatim}}


   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/cubprism} \caption{A cubic, triangular prism shape.} \end{figure} 



   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 are not part 
 of the shape - they are just there to help compute what curves to use between the other points. 


\subsubsection{Smooth Transitions}

% tutorial/000014.html



   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 have made them, the curve transitions between points would not be as smooth. We change 
 points one and six to $<$\discretionary{4,}{}{4,}6$>$ and $<$\discretionary{0,}{}{0,}7$>$ respectively and re-\discretionary{}{}{}render to see how the back edge of the shape is altered (see file {\small\texttt{\discretionary{prismdm3.}{}{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. 


\subsubsection{Multiple Sub-\discretionary{}{}{}Shapes}

% tutorial/000013.html



   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-\discretionary{}{}{}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-\discretionary{}{}{}shapes overlap, 
 that region where they overlap behaves as though it has been cut away from both sub-\discretionary{}{}{}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 {\small\texttt{\discretionary{prismdm4.}{}{prismdm4.}pov}}). 


{\small\begin{verbatim}
  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 }
  }
\end{verbatim}}


   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/subshape} \caption{Using sub-\discretionary{}{}{}shapes to create a more complex shape.} \end{figure} 
 



   For readability purposes, we have started a new line every time we moved on to a new sub-\discretionary{}{}{}shape, but the ray-\discretionary{}{}{}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 have got. It is 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-\discretionary{}{}{}shape one exists, then the carved out part is where sub-\discretionary{}{}{}shapes one and two overlap. In the extreme center, the object 
 reappears because sub-\discretionary{}{}{}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! 


\subsubsection{Conic Sweeps And The Tapering Effect}

% tutorial/000009.html

\index{Tapering Conic Sweeps}

   In our original prism, the keyword {\small\texttt{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 {\small\texttt{\discretionary{prismdm4.}{}{prismdm4.}pov}}): 
 


{\small\begin{verbatim}
  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 }
  }
\end{verbatim}}


   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/pyrsweep} \caption{Creating a pyramid using conic sweeping.} \end{figure} 



   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, what have we 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 is 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 are making a pyramid. So we flip the shape 
 around the x-\discretionary{}{}{}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 
 have stretched it out a little. At this point, we are 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 is wrong with that, let's try and put it into practice (see file {\small\texttt{ \discretionary{prismdm5.}{}{prismdm5.}pov}}). 
 We must make sure to remove the scale statement, and then replace the line which reads 


{\small\begin{verbatim}
  1, // height 2
\end{verbatim}}


   with 


{\small\begin{verbatim}
  4, // height 2
\end{verbatim}}


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



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/imprswep} \caption{Choosing a second height larger than one for the conic sweep.} \end{figure} 
 



   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 do not 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 


{\small\begin{verbatim}
  0, // height 1
\end{verbatim}}


   to 


{\small\begin{verbatim}
  0.251, // height 1
\end{verbatim}}


   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/sweepinc} \caption{Increasing the first height for the conic sweep.} \end{figure} 
 



   When we re-\discretionary{}{}{}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. 


\subsection{Sphere Sweep Object}

% tutorial/000016.html

\index{sphere\_\-sweep! tutorial}

   A Sphere Sweep Object is the space a sphere occupies during its movement along a spline. \newline So we need to specify the kind of spline we want and a list 
 of control points to define that spline. To help POV-\discretionary{}{}{}Ray we tell how many control points will be used. In addition, we also define the radius the moving 
 sphere should have when passing through each of these control points. 



   The syntax of the sphere\_\-sweep object is: 


{\small\begin{verbatim}
  sphere_sweep {
    linear_spline | b_spline | cubic_spline
    NUM_OF_SPHERES,

    CENTER, RADIUS,
    CENTER, RADIUS,
    ...
    CENTER, RADIUS
    [tolerance DEPTH_TOLERANCE]
    [OBJECT_MODIFIERS]
  }
\end{verbatim}}


   An example for a linear Sphere Sweep would be: 


{\small\begin{verbatim}
  sphere_sweep {
    linear_spline
    4,
    <-5, -5, 0>, 1
    <-5,  5, 0>, 1
    < 5, -5, 0>, 1
    < 5,  5, 0>, 1
  }
\end{verbatim}}


   This object is described by four spheres. You can use as many spheres as you like to describe the object, but you will need at least two spheres for a linear 
 Sphere Sweep, and four spheres for one approximated with a cubic\_\-spline or b\_\-spline. 



   The example above would result in an object shaped like the letter ``N''. The sphere sweep goes through \textit{all} points which are connected with 
 straight cones. 



   Changing the kind of interpolation to a cubic\_\-spline produces a quite different, slightly bent, object. It then starts at the second sphere and ends at the 
 last but one. Since the first and last points are used to control the spline, you need two more points to get a shape that can be compared to the linear 
 sweep. Let's add them: 


{\small\begin{verbatim}
  sphere_sweep {
    cubic_spline
    6,
    <-4, -5, 0>, 1
    <-5, -5, 0>, 1
    <-5,  5, 0>, 0.5
    < 5, -5, 0>, 0.5
    < 5,  5, 0>, 1
    < 4,  5, 0>, 1
    tolerance 0.1
 }
\end{verbatim}}


   So the cubic sweep creates a smooth sphere sweep actually going through all points (except the first and last one). In this example the radius of the second 
 and third spheres have been changed. We also added the ``tolerance'' keyword, because dark spots appeared on the surface with the default value 
 (0.000001). 



   When using a b\_\-spline, the resulting object is somewhat similar to the cubic sweep, but does not actually go through the control points. It lies somewhere 
 between them. 


\subsection{Bicubic Patch Object}

% tutorial/000015.html

\index{bicubic\_\-patch! tutorial}

   Bicubic 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. POV-\discretionary{}{}{}Ray does not ray trace the patches directly, 
 they are approximated using triangles as described in the Scene Description Language section. 



   Bicubic patches are almost always created by using a third party modeler, but for this tutorial we will manipulate them by hand. Modelers that support 
 Bicubic patches and export to POV-\discretionary{}{}{}Ray can be found in the links collection on our server\footnote{ http://\discretionary{www.}{}{www.}\discretionary{povray.}{}{povray.}org/links/}\newline  
 Let's set up a basic scene and start exploring the Bicubic patch. 


{\small\begin{verbatim}
#version 3.5;
global_settings {assumed_gamma 1.0}
background {rgb <1,0.9,0.9>}
camera {location <1.6,5,-6> look_at <1.5,0,1.5> angle 40}
light_source {<500,500,-500> rgb 1 }

#declare B11=<0,0,3>; #declare B12=<1,0,3>; //
#declare B13=<2,0,3>; #declare B14=<3,0,3>; // row 1

#declare B21=<0,0,2>; #declare B22=<1,0,2>; //
#declare B23=<2,0,2>; #declare B24=<3,0,2>; // row 2

#declare B31=<0,0,1>; #declare B32=<1,0,1>; //
#declare B33=<2,0,1>; #declare B34=<3,0,1>; // row 3

#declare B41=<0,0,0>; #declare B42=<1,0,0>; //
#declare B43=<2,0,0>; #declare B44=<3,0,0>; // row 4

bicubic_patch {
   type 1 flatness 0.001
   u_steps 4 v_steps 4
   uv_vectors
   <0,0> <1,0> <1,1> <0,1>
   B11, B12, B13, B14
   B21, B22, B23, B24
   B31, B32, B33, B34
   B41, B42, B43, B44
   uv_mapping
   texture {
      pigment {
         checker 
         color rgbf <1,1,1,0.5> 
         color rgbf <0,0,1,0.7> 
         scale 1/3
      }
      finish {phong 0.6 phong_size 20}
   }
   no_shadow
}
\end{verbatim}}


   The points B11, B14, B41, B44 are the corner points of the patch. All other points are control points. The names of the declared points are as follows: B for 
 the colour of the patch, the first digit gives the row number, the second digit the column number. If you render the above scene, you will get a blue \& 
 white checkered square, not very exciting. First we will add some spheres to make the control points visible. As we do not want to type the code for 16 
 spheres, we will use an array and a while loop to construct the spheres. 


{\small\begin{verbatim}
#declare Points=array[16]{
   B11, B12, B13, B14
   B21, B22, B23, B24
   B31, B32, B33, B34
   B41, B42, B43, B44
}
#declare I=0;
#while (I<16)
   sphere {
      Points[I],0.1 
      no_shadow 
      pigment{
         #if (I=0|I=3|I=12|I=15)
            color rgb <1,0,0>
         #else
            color rgb <0,1,1>
         #end
      }
   }
   #declare I=I+1;
#end
\end{verbatim}}


   Rendering this scene will show the patch with its corner points in red and its control points in cyan. Now it is time to start exploring. \newline  Change 
 B41 to {\small\texttt{$<$-\discretionary{1,}{}{1,}\discretionary{0,}{}{0,}0$>$}} and render.\newline  Change B41 to {\small\texttt{$<$-\discretionary{1,}{}{1,}\discretionary{1,}{}{1,}0$>$}} and render.\newline  Change B41 to {\small\texttt{$<$ 
 \discretionary{1,}{}{1,}\discretionary{2,}{}{2,}1$>$}} and render.\newline  



   Let's do some exercise with the control points. Start with a flat patch again.\newline  Change B42 to {\small\texttt{$<$\discretionary{1,}{}{1,}\discretionary{2,}{}{2,}0$>$}} and B43 to {\small\texttt{$<$2,-\discretionary{2,}{}{2,}0$>$}} 
 and render.\newline  Change B42 and B43 back to their original positions and try B34 to {\small\texttt{$<$\discretionary{4,}{}{4,}\discretionary{2,}{}{2,}1$>$}} and B24 to {\small\texttt{$<$2,-\discretionary{2,}{}{2,}2$>$}} 
 and render. Move the points around some more, also try the control points in the middle. 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/bpatch01} \caption{Bicubic\_\-patch with control points} \end{figure} 



   After all this we notice two things: 


\begin{itemize}
 
 \item 
   The patch always goes through the corner points. 
 

 \item 
   In most situations the patch does not go through the control points. 
 

\end{itemize}


   Now go back to our spline work shop and have a look at the bezier\_\-spline again. Indeed, the points \discretionary{B11,}{}{B11,}B12,\discretionary{B13,}{}{B13,}B14, make up a bezier\_\-spline. So do the points 
 \discretionary{B11,}{}{B11,}B21,\discretionary{B31,}{}{B31,}B41 and \discretionary{B41,}{}{B41,}B42,\discretionary{B43,}{}{B43,}B44 and \discretionary{B14,}{}{B14,}B24,\discretionary{B34,}{}{B34,}B44. 



   So far we have only been looking at one single patch, but one of the strengths of the Bicubic patch lays in the fact that they can be connected smoothly, to 
 form bigger shapes. The process of connecting is relatively simple as there are actually only two rules to follow. It can be done by using a well set up set 
 of macros or by using a modeler. To give an idea what is needed we will do a simple example by hand. 



   First put the patch in our scene back to its flat position. Then change{\small\texttt{ \#declare B14 = $<$\discretionary{3,}{}{3,}\discretionary{0,}{}{0,}3$>$; \#declare B24 = $<$\discretionary{3,}{}{3,}\discretionary{2,}{}{2,}2$>$; \#declare 
 B34 = $<$3.\discretionary{5,}{}{5,}\discretionary{1,}{}{1,}1$>$ ; \#declare B44 = $<$3,-\discretionary{1,}{}{1,}0$>$; \#declare B41 = $<$0,-\discretionary{1,}{}{1,}0$>$;}} Move the camera a bit back {\small\texttt{camera \{ location 
 $<$3.\discretionary{1,}{}{1,}7,-8$>$ look\_\-at $<$3,-\discretionary{2,}{}{2,}1.5$>$ angle 40 \}}} and delete all the code for the spheres. We will now try and stitch a patch to the 
 right side of the current one. Off course the points on the left side (column 1) of the new patch have to be in the same position as the points on the right 
 side (column 4) of the blue one.\newline  Render the scene, including our new patch: 


{\small\begin{verbatim}
#declare R11=B14; #declare R12=<4,0,3>;     //
#declare R13=<5,0,3>; #declare R14=<6,0,3>; // row 1

#declare R21=B24; #declare R22=<4,0,2>;     //
#declare R23=<5,0,2>; #declare R24=<6,0,2>; // row 2

#declare R31=B34; #declare R32=<4,0,1>;     //
#declare R33=<5,0,1>; #declare R34=<6,0,1>; // row 3

#declare R41=B44; #declare R42=<4,0,0>;     //
#declare R43=<5,0,0>; #declare R44=<6,0,0>; // row 4

bicubic_patch {
   type 1 flatness 0.001
   u_steps 4 v_steps 4
   uv_vectors
   <0,0> <1,0> <1,1> <0,1>
   R11, R12, R13, R14
   R21, R22, R23, R24
   R31, R32, R33, R34
   R41, R42, R43, R44
   uv_mapping
   texture {
      pigment {
         checker 
         color rgbf <1,1,1,0.5> 
         color rgbf <1,0,0,0.7> 
         scale 1/3
      }
      finish {phong 0.6 phong_size 20}
   }
   no_shadow
}
\end{verbatim}}


   This is a rather disappointing result. The patches are connected, but not exactly smooth. In connecting patches the same principles apply as for connecting 
 two 2D bezier splines as we see in the spline workshop. Control point, connection point and the next control point should be on one line to give a smooth 
 result. Also it is preferred, not required, that the distances from both control points to the connection point are the same. For the Bicubic patch we have to 
 do the same, for all connection points involved in the joint. So, in our case, the following points should be on one line: 


\begin{itemize}
 
 \item 
   B13, B14=R11, R12 
 

 \item 
   B23, B24=R21, R22 
 

 \item 
   B33, B34=R31, R32 
 

 \item 
   B43, B44=R41, R42 
 

\end{itemize}


   To achieve this we do: 


{\small\begin{verbatim}
#declare R12=B14+(B14-B13); 
#declare R22=B24+(B24-B23); 
#declare R32=B34+(B34-B33); 
#declare R42=B44+(B44-B43); 
\end{verbatim}}


   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/bpatch02} \caption{patches, (un)smoothly connected} \end{figure} 



   This renders a smooth surface. Adding a third patch in front is relative simple now: 


{\small\begin{verbatim}
#declare G11=B41;      #declare G12=B42;                //
#declare G13=B43;      #declare G14=B44;                // row 1

#declare G21=B41+(B41-B31); #declare G22=B42+(B42-B32); //
#declare G23=B43+(B43-B33); #declare G24=B44+(B44-B34); // row 2

#declare G31=<0,0,-2>; #declare G32=<1,0,-2>;           //
#declare G33=<2,0,-2>; #declare G34=<3,2,-2>;           // row 3

#declare G41=<0,0,-3>; #declare G42=<1,0,-3>;           // 
#declare G43=<2,0,-3>; #declare G44=<3,0,-3>            // row 4

bicubic_patch {
   type 1 flatness 0.001
   u_steps 4 v_steps 4
   uv_vectors
   <0,0> <1,0> <1,1> <0,1>
   G11, G12, G13, G14
   G21, G22, G23, G24
   G31, G32, G33, G34
   G41, G42, G43, G44
   uv_mapping
   texture {
      pigment {
         checker 
         color rgbf <1,1,1,0.5> 
         color rgbf <0,1,0,0.7> 
         scale 1/3
      }
      finish {phong 0.6 phong_size 20}
   }
   no_shadow
}
\end{verbatim}}


   Finally, let's put a few spheres back in the scene and add some cylinders to visualize what is going on. See what happens if you move for example B44, B43, 
 B33 or B34. 


{\small\begin{verbatim}
#declare Points=array[8]{B33,B34,R32,B43,B44,R42,G23,G24}
#declare I=0;
#while (I<8)
   sphere {
      Points[I],0.1 
      no_shadow 
      pigment{
         #if (I=4)
            color rgb <1,0,0>
         #else
            color rgb <0,1,1>
         #end
      }
   }
   #declare I=I+1;
#end
union {
   cylinder {B33,B34,0.04} cylinder {B34,R32,0.04}
   cylinder {B43,B44,0.04} cylinder {B44,R42,0.04}
   cylinder {G23,G24,0.04} 
   cylinder {B33,B43,0.04} cylinder {B43,G23,0.04}
   cylinder {B34,B44,0.04} cylinder {B44,G24,0.04}
   cylinder {R32,R42,0.04}
   no_shadow 
   pigment {color rgb <1,1,0>}
}
\end{verbatim}}


   The hard part in using the Bicubic patch is not in connecting several patches. The difficulty is keeping control over the shape you want to build. As patches 
 are added, in order to keep the result smooth, control over the position of many points gets restrained. 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/bpatch03} \caption{3 patches, some control points} \end{figure} 


\subsection{Text Object}

% tutorial/000071.html

\index{text! tutorial}

   The {\small\texttt{text}} object is a primitive that can use TrueType fonts and TrueType Collections 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 {\small\texttt{ \discretionary{timrom.}{}{timrom.}ttf}} or {\small\texttt{\discretionary{cyrvetic.}{}{cyrvetic.}ttf}} which come bundled with POV-\discretionary{}{}{}Ray. 



   We create a file called {\small\texttt{\discretionary{textdemo.}{}{textdemo.}pov}} and edit it as follows: 


{\small\begin{verbatim}
  #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 }
  }
\end{verbatim}}


   Now let's add the text object. We will use the font {\small\texttt{ \discretionary{timrom.}{}{timrom.}ttf}} and we will create the string ``POV-\discretionary{}{}{}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. 


{\small\begin{verbatim}
  text {
    ttf "timrom.ttf" "POV-RAY 3.0" 1, 0
    pigment { Red }
  }
\end{verbatim}}


   Rendering this at 200x150 {\small\texttt{-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-\discretionary{}{}{}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-\discretionary{}{}{}axis. 


{\small\begin{verbatim}
  text {
    ttf "timrom.ttf" "POV-RAY 3.0" 1, 0
    pigment { Red }
    translate -3*x
  }
\end{verbatim}}


   That is 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! 


{\small\begin{verbatim}
  text {
    ttf "timrom.ttf" "POV-RAY 3.0" 25, 0
    pigment { Red }
    translate -2.25*x
  }
\end{verbatim}}


   Actually, that is 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-\discretionary{}{}{}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 {\small\texttt{0.1}} 
 with {\small\texttt{ 0.1*x}} and render it again. 



   That works! The letters are still in a straight line along the x-\discretionary{}{}{}axis, just a little further apart. Let's verify this and try to offset just in the y-\discretionary{}{}{}axis. 
 We replace {\small\texttt{ 0.1*x}} with {\small\texttt{ 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-\discretionary{}{}{}axis. Now let's try the z-\discretionary{}{}{}axis. We replace {\small\texttt{ 0.1*y}} with {\small\texttt{ 0.1*z}}. Rendering this yields a 
 disappointment. No offset occurs! The offset value can only be applied in the x- and y-\discretionary{}{}{}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-\discretionary{}{}{}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 {\small\texttt{ 
 +A0.2}}): 


{\small\begin{verbatim}
  #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 }
\end{verbatim}}


   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 {\small\texttt{\discretionary{textcsg.}{}{textcsg.}pov}} 
 and edit it as follows: 


{\small\begin{verbatim}
  #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 }
\end{verbatim}}


   Now let's create the block. We want it to be about eight units across because our text string ``POV-\discretionary{}{}{}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-\discretionary{}{}{}coordinate 0.1 instead of 0. Finally, we will give this block a nice stone texture. 


{\small\begin{verbatim}
  box {
    <-3.5, -1, 0.1>, <3.5, 1, 1>
    texture { T_Stone10 }
  }
\end{verbatim}}


   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. 


{\small\begin{verbatim}
  text {
    ttf "timrom.ttf" "POV-RAY 3.0" 0.15, 0
    pigment { BrightGold }
    finish { reflection .25 specular 1 }
    translate -3*x
  }
\end{verbatim}}


   We remember that the text object is placed by default so that its front surface lies directly on the x-\discretionary{}{}{}y-\discretionary{}{}{}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. 


{\small\begin{verbatim}
  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
    }
  }
\end{verbatim}}


   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/txtstone} \caption{Text carved from stone.} \end{figure} 



   We render this at 200x150 {\small\texttt{-A}}. We can see the inlay clearly and that it is indeed a bright gold color. We re-\discretionary{}{}{}render at 640x480 {\small\texttt{ 
 +A0.2}} to see the results more clearly, but be forewarned... this trace will take a little time. 


\section{Polygon Based Shapes}

% tutorial/000072.html

\index{Shapes! polygon based}
\subsection{Mesh Object}

% tutorial/000073.html

\index{mesh! tutorial}
\begin{description}
 
 \item 
   \textit{You know you have been raytracing too long when ...\newline  ... You think that the evolution theory was based on the triangular origin of the 
  wheel.} 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   \textit{-- Mark Kadela} 
 \end{list}

\end{description}


   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 {\small\texttt{\discretionary{meshdemo.}{}{meshdemo.}pov}} and add the 
 following lines. Note that a mesh is - not surprisingly - declared using the keyword {\small\texttt{mesh}}. 


{\small\begin{verbatim}
  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 }
  }
\end{verbatim}}


   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 \textit{ global} mesh texture. 


{\small\begin{verbatim}
  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 }
    }
  }
\end{verbatim}}


   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 {\small\texttt{ 
 \discretionary{chesmsh.}{}{chesmsh.}pov}}. 


\subsection{Mesh2 Object}

% tutorial/000074.html



   The {\small\texttt{mesh2}} is a representation of a mesh, that is much more like POV-\discretionary{}{}{}Ray's internal mesh representation than the standard {\small\texttt{mesh}}. 
 As a result, it parses faster and it file size is smaller. 



   Due to its nature, {\small\texttt{mesh2}} is not really suitable for building meshes by hand, it is intended for use by modelers and file format converters. 
 An other option is building the meshes by macros. Yet, to understand the format, we will do a small example by hand and go through all options. 



   \begin{figure} \centering\includegraphics[scale=0.30]{../final/tex/images/tutorial/mesh2} \caption{to be written as mesh2} \end{figure} 



   We will turn the mesh sketched above into a {\small\texttt{mesh2}} object. The mesh is made of 8 triangles, each with 3 vertices, many of these vertices are 
 shared among the triangles. This can later be used to optimize the mesh. First we will set it up straight forward. 



   In {\small\texttt{mesh2}} all the vertices are listed in a list named {\small\texttt{vertex\_\-vectors\{\}}}. A second list, {\small\texttt{face\_\-indices\{\}}}, 
 tells us how to put together three vertices to create one triangle, by pointing to the index number of a vertex. All lists in {\small\texttt{mesh2}} are zero 
 based, the number of the first vertex is 0. The very first item in a list is the amount of vertices, normals or uv\_\-vectors it contains. {\small\texttt{mesh2}} 
 has to be specified in the order \textit{VECTORS...}, \textit{LISTS...}, \textit{INDICES...}. 



   Lets go through the mesh above, we do it counter clockwise. The total amount of vertices is 24 (8 triangle * 3 vertices). 


{\small\begin{verbatim}
mesh2 {
   vertex_vectors {
      24,
      ...
\end{verbatim}}


   Now we can add the coordinates of the vertices of the first triangle: 


{\small\begin{verbatim}
mesh2 {
   vertex_vectors {
      24, 
      <0,0,0>, <0.5,0,0>, <0.5,0.5,0>
      ..
\end{verbatim}}


   Next step, is to tell the mesh how the triangle should be created; There will be a total of 8 face\_\-indices (8 triangles). The first point in the first face, 
 points to the first vertex\_\-vector (0: $<$\discretionary{0,}{}{0,}\discretionary{0,}{}{0,}0$>$), the second to the second (1: $<$0.\discretionary{5,}{}{5,}\discretionary{0,}{}{0,}0$>$), etc... 


{\small\begin{verbatim}
mesh2 {
   vertex_vectors {
      24, 
      <0,0,0>, <0.5,0,0>, <0.5,0.5,0>
      ...
   }
   face_indices {
      8, 
      <0,1,2> 
      ...
\end{verbatim}}


   The complete mesh: 


{\small\begin{verbatim}
mesh2 {
   vertex_vectors {
      24, 
      <0,0,0>, <0.5,0,0>, <0.5,0.5,0>, //1
      <0.5,0,0>, <1,0,0>, <0.5,0.5,0>, //2
      <1,0,0>, <1,0.5,0>, <0.5,0.5,0>, //3
      <1,0.5,0>, <1,1,0>, <0.5,0.5,0>, //4
      <1,1,0>, <0.5,1,0>, <0.5,0.5,0>, //5
      <0.5,1,0>, <0,1,0>, <0.5,0.5,0>, //6
      <0,1,0>, <0,0.5,0>, <0.5,0.5,0>, //7
      <0,0.5,0>, <0,0,0>, <0.5,0.5,0>  //8
   }
   face_indices {
      8, 
      <0,1,2>,    <3,4,5>,       //1 2
      <6,7,8>,    <9,10,11>,     //3 4
      <12,13,14>, <15,16,17>,    //5 6
      <18,19,20>, <21,22,23>     //7 8
   }
   pigment {rgb 1}
}
\end{verbatim}}


   As mentioned earlier, many vertices are shared by triangles. We can optimize the mesh by removing all duplicate vertices but one. In the example this reduces 
 the amount from 24 to 9. 


{\small\begin{verbatim}
mesh2 {
   vertex_vectors {
      9, 
      <0,0,0>, <0.5,0,0>, <0.5,0.5,0>,
      /*as 1*/ <1,0,0>,   /*as 2*/
      /*as 3*/ <1,0.5,0>, /*as 2*/
      /*as 4*/ <1,1,0>,   /*as 2*/
      /*as 5*/ <0.5,1,0>, /*as 2*/
      /*as 6*/ <0,1,0>,   /*as 2*/
      /*as 7*/ <0,0.5,0>, /*as 2*/
      /*as 8*/ /*as 0*/   /*as 2*/
   }
   ...
   ...
\end{verbatim}}


   Next step is to rebuild the list of face\_\-indices, as they now point to indices in the {\small\texttt{vertex\_\-vector\{\}}} list that do not exist anymore. 


{\small\begin{verbatim}
   ...
   ...
   face_indices {
      8, 
      <0,1,2>, <1,3,2>,
      <3,4,2>, <4,5,2>,
      <5,6,2>, <6,7,2>,
      <7,8,2>, <8,0,2>
   }
   pigment {rgb 1}
}
\end{verbatim}}

\subsubsection{Smooth triangles and mesh2}

% tutorial/000083.html



   In case we want a smooth mesh, the same steps we did also apply to the normals in a mesh. For each vertex there is one normal vector listed in {\small\texttt{normal\_\-vectors\{\}}}, 
 duplicates can be removed. If the number of normals equals the number of vertices then the {\small\texttt{normal\_\-indices\{\}}} list is optional and the indexes 
 from the {\small\texttt{face\_\-indices\{\}}} list are used instead. 


{\small\begin{verbatim}
mesh2 {
   vertex_vectors {
      9, 
      <0,0,0>, <0.5,0,0>, <0.5,0.5,0>,
      <1,0,0>, <1,0.5,0>, <1,1,0>,
      <0.5,1,0>, <0,1,0>, <0,0.5,0>   
   }
   normal_vectors {
      9,
     <-1,-1,0>,<0,-1,0>, <0,0,1>,
      /*as 1*/ <1,-1,0>, /*as 2*/
      /*as 3*/ <1,0,0>,  /*as 2*/
      /*as 4*/ <1,1,0>,  /*as 2*/
      /*as 5*/ <0,1,0>,  /*as 2*/
      /*as 6*/ <-1,1,0>, /*as 2*/
      /*as 7*/ <-1,0,0>, /*as 2*/
      /*as 8*/ /*as 0*/  /*as 2*/ 
   }
   face_indices {
      8, 
      <0,1,2>, <1,3,2>,
      <3,4,2>, <4,5,2>,
      <5,6,2>, <6,7,2>,
      <7,8,2>, <8,0,2>
   }
   pigment {rgb 1}
}
\end{verbatim}}


   When a mesh has a mix of smooth and flat triangles a list of {\small\texttt{normal\_\-indices\{\}}} has to be added, where each entry points to what vertices a 
 normal should be applied. In the example below only the first four normals are actually used. 


{\small\begin{verbatim}
mesh2 {
   vertex_vectors {
      9, 
      <0,0,0>, <0.5,0,0>, <0.5,0.5,0>,
      <1,0,0>, <1,0.5,0>, <1,1,0>,
      <0.5,1,0>, <0,1,0>,   <0,0.5,0>
   }
   normal_vectors {
      9,
      <-1,-1,0>, <0,-1,0>, <0,0,1>,
      <1,-1,0>, <1,0,0>, <1,1,0>,
      <0,1,0>, <-1,1,0>, <-1,0,0>
   }
   face_indices {
      8, 
      <0,1,2>, <1,3,2>,
      <3,4,2>, <4,5,2>,
      <5,6,2>, <6,7,2>,
      <7,8,2>, <8,0,2>
   }
   normal_indices {
      4, 
      <0,1,2>, <1,3,2>,
      <3,4,2>, <4,5,2>
   }
   pigment {rgb 1}
}
\end{verbatim}}

\subsubsection{UV mapping and mesh2}

% tutorial/000084.html



   uv\_\-mapping is a method of 'sticking' 2D textures on an object in such a way that it follows the form of the object. For uv\_\-mapping on triangles imagine it as 
 follows; First you cut out a triangular section of a texture form the xy-\discretionary{}{}{}plane. Then stretch, shrink and deform the piece of texture to fit to the triangle 
 and stick it on. 



   Now, in {\small\texttt{mesh2}} we first build a list of 2D-\discretionary{}{}{}vectors that are the coordinates of the triangular sections in the xy-\discretionary{}{}{}plane. This is the {\small\texttt{uv\_\-vectors\{\}}} 
 list. In the example we map the texture from the rectangular area {\small\texttt{$<$-0.5,-0.5$>$, $<$0.\discretionary{5,}{}{5,}0.5$>$}} to the triangles in the mesh. Again we 
 can omit all duplicate coordinates 


{\small\begin{verbatim}
mesh2 {
   vertex_vectors {
      9, 
      <0,0,0>, <0.5,0,0>, <0.5,0.5,0>,
      <1,0,0>, <1,0.5,0>, <1,1,0>,
      <0.5,1,0>, <0,1,0>,   <0,0.5,0>
   }
   uv_vectors {
      9
     <-0.5,-0.5>,<0,-0.5>,  <0,0>,
      /*as 1*/   <0.5,-0.5>,/*as 2*/
      /*as 3*/   <0.5,0>,   /*as 2*/
      /*as 4*/   <0.5,0.5>, /*as 2*/
      /*as 5*/   <0,0.5>,   /*as 2*/
      /*as 6*/   <-0.5,0.5>,/*as 2*/
      /*as 7*/   <-0.5,0>,  /*as 2*/
      /*as 8*/   /*as 0*/   /*as 2*/       
   }
   face_indices {
      8, 
      <0,1,2>, <1,3,2>,
      <3,4,2>, <4,5,2>,
      <5,6,2>, <6,7,2>,
      <7,8,2>, <8,0,2>
   }
   uv_mapping
   pigment {wood scale 0.2}
}
\end{verbatim}}


   Just as with the {\small\texttt{normal\_\-vectors}}, if the number of {\small\texttt{uv\_\-vectors}} equals the number of vertices then the {\small\texttt{uv\_\-indices\{\}}} 
 list is optional and the indices from the {\small\texttt{face\_\-indices\{\}}} list are used instead. 



   In contrary to the {\small\texttt{normal\_\-indices}} list, if the {\small\texttt{uv\_\-indices}} list is used, the amount of indices should be equal to the amount 
 of {\small\texttt{face\_\-indices}}. In the example below only 'one texture section' is specified and used on all triangles, using the {\small\texttt{uv\_\-indices}}. 
 


{\small\begin{verbatim}
mesh2 {
   vertex_vectors {
      9, 
      <0,0,0>, <0.5,0,0>, <0.5,0.5,0>,
      <1,0,0>, <1,0.5,0>, <1,1,0>,
      <0.5,1,0>, <0,1,0>,   <0,0.5,0>
   }
   uv_vectors {
      3
      <0,0>, <0.5,0>, <0.5,0.5>    
   }
   face_indices {
      8, 
      <0,1,2>, <1,3,2>,
      <3,4,2>, <4,5,2>,
      <5,6,2>, <6,7,2>,
      <7,8,2>, <8,0,2>
   }
   uv_indices {
      8, 
      <0,1,2>, <0,1,2>,
      <0,1,2>, <0,1,2>,
      <0,1,2>, <0,1,2>,
      <0,1,2>, <0,1,2>
   }
   uv_mapping
   pigment {gradient x scale 0.2}
}
\end{verbatim}}

\subsubsection{A separate texture per triangle}

% tutorial/000085.html



   By using the {\small\texttt{texture\_\-list}} it is possible to specify a texture per triangle or even per vertex in the mesh. In the latter case the three 
 textures per triangle will be interpolated. To let POV-\discretionary{}{}{}Ray know what texture to apply to a triangle, the index of a texture is added to the {\small\texttt{face\_\-indices}} 
 list, after the face index it belongs to. 


{\small\begin{verbatim}
mesh2 {
   vertex_vectors {
      9, 
      <0,0,0>, <0.5,0,0>, <0.5,0.5,0>,
      <1,0,0>, <1,0.5,0>, <1,1,0>   
      <0.5,1,0>, <0,1,0>, <0,0.5,0> 
   }
   texture_list {
      2,
      texture{pigment{rgb<0,0,1>}}
      texture{pigment{rgb<1,0,0>}}
   }
   face_indices {
      8, 
      <0,1,2>,0,  <1,3,2>,1,
      <3,4,2>,0,  <4,5,2>,1,
      <5,6,2>,0,  <6,7,2>,1,
      <7,8,2>,0,  <8,0,2>,1
   }
}
\end{verbatim}}


   To specify a texture per vertex, three {\small\texttt{texture\_\-list}} indices are added after the {\small\texttt{face\_\-indices}} 


{\small\begin{verbatim}
mesh2 {
   vertex_vectors {
      9, 
      <0,0,0>, <0.5,0,0>, <0.5,0.5,0>,
      <1,0,0>, <1,0.5,0>, <1,1,0>   
      <0.5,1,0>, <0,1,0>, <0,0.5,0> 
   }
   texture_list {
      3,
      texture{pigment{rgb <0,0,1>}}
      texture{pigment{rgb 1}}
      texture{pigment{rgb <1,0,0>}}
   }
   face_indices {
      8, 
      <0,1,2>,0,1,2,  <1,3,2>,1,0,2,
      <3,4,2>,0,1,2,  <4,5,2>,1,0,2,
      <5,6,2>,0,1,2,  <6,7,2>,1,0,2,
      <7,8,2>,0,1,2,  <8,0,2>,1,0,2
   }
}
\end{verbatim}}


   Assigning a texture based on the {\small\texttt{texture\_\-list}} and texture interpolation is done on a per triangle base. So it is possible to mix triangles 
 with just one texture and triangles with three textures in a mesh. It is even possible to mix in triangles without any texture indices, these will get their 
 texture from a general {\small\texttt{texture}} statement in the {\small\texttt{mesh2}}. uv\_\-mapping is supported for texturing using a {\small\texttt{texture\_\-list}}. 
 


\subsection{Polygon Object}

% tutorial/000075.html

\index{polygon! tutorial}

   The {\small\texttt{polygon}} object can be used to create any planar, n-\discretionary{}{}{}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-\discretionary{}{}{}y-\discretionary{}{}{}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): 


{\small\begin{verbatim}
    <-0.8, 0.0>, <-0.8, 1.0>,
    <-0.3, 1.0>, <-0.3, 0.5>,
    <-0.7, 0.5>, <-0.7, 0.0>
\end{verbatim}}


   Letter P (inner polygon): 


{\small\begin{verbatim}
    <-0.7, 0.6>, <-0.7, 0.9>,
    <-0.4, 0.9>, <-0.4, 0.6>
\end{verbatim}}


   Letter O (outer polygon): 


{\small\begin{verbatim}
    <-0.25, 0.0>, <-0.25, 1.0>,
    < 0.25, 1.0>, < 0.25, 0.0>
\end{verbatim}}


   Letter O (inner polygon): 


{\small\begin{verbatim}
    <-0.15, 0.1>, <-0.15, 0.9>,
    < 0.15, 0.9>, < 0.15, 0.1>
\end{verbatim}}


   Letter V: 


{\small\begin{verbatim}
    <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>
\end{verbatim}}


   Both letters P and O have a hole while the letter V consists of only one polygon. We will start with the letter V because it is easier to define than the 
 other two letters. 



   We create a new file called {\small\texttt{ \discretionary{polygdem.}{}{polygdem.}pov}} and add the following text. 


{\small\begin{verbatim}
  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> }
  }
\end{verbatim}}


   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 will 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 is all we have to do. There will be a hole where both polygons overlap. 



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



   The letter P consists of two sub-\discretionary{}{}{}polygons, one for the outer shape and one for the hole. Since the hole polygon overlaps the outer shape polygon we will get 
 a hole. 



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



   Finally, we get the complete word POV. 


{\small\begin{verbatim}
  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> }
  }
\end{verbatim}}


   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/polyword} \caption{The word } \end{figure} 


\section{Other Shapes}

% tutorial/000076.html

\index{Shapes! other}
\subsection{Blob Object}

% tutorial/000077.html



   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-\discretionary{}{}{}Ray code showing a basic camera, light, and a simple two 
 component blob: 


{\small\begin{verbatim}
  #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 }
  }
\end{verbatim}}


   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/simpblob} \caption{A simple, two-\discretionary{}{}{}part blob.} \end{figure} 
 



   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 \textit{outside} and those greater than are \textit{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-\discretionary{}{}{}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-\discretionary{}{}{}render. We note that these are meant to be entered as separate sphere objects, not more components in the blob. 


{\small\begin{verbatim}
  sphere { <.5,0,0>, .8
    pigment { Yellow transmit .75 }
  }
  sphere { <-.5,0,0>, .8
    pigment { Green transmit .75 }
  }
\end{verbatim}}


   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/sphblob} \caption{The spherical components made visible.} \end{figure} 



   Now the secrets of the kissing spheres are laid bare. These semi-\discretionary{}{}{}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. 


\subsubsection{Component Types and Other New Features}

% tutorial/000078.html

\index{New Features! component types}

   The shape shown so far is interesting, but limited. POV-\discretionary{}{}{}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-\discretionary{}{}{}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-\discretionary{}{}{}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-\discretionary{}{}{}render. We can get rid of the transparent spheres too, by the way. 


{\small\begin{verbatim}
  blob {
    threshold .65
    cylinder { <-.75,-.75,0>, <.75,.75,0>, .5, 1 }
    pigment { Blue }
    finish { phong 1 }
  }
\end{verbatim}}


   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 hemispheres. 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? 


\subsubsection{Complex Blob Constructs and Negative Strength}

% tutorial/000086.html

\index{Blob Constructs! complex}\index{Negative Strength! blob}

   Beginning a new POV-\discretionary{}{}{}Ray file, we enter this somewhat more complex example: 


{\small\begin{verbatim}
#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 }
}
\end{verbatim}}


   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/blobhand} \caption{A hand made with blobs.} \end{figure} 



   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. 


{\small\begin{verbatim}
sphere{<-.65,.28,-.05>, .26, -1} //counteract pinky knucklebulge
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
\end{verbatim}}


   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/imprhand} \caption{The hand without the swollen joints.} \end{figure} 



   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! 


\subsection{Height Field Object}

% tutorial/000079.html

\index{height\_\-field! tutorial}

   A {\small\texttt{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-\discretionary{}{}{}Ray is ideal for creating such an image. 



   We make a new file called {\small\texttt{\discretionary{image.}{}{image.}pov}} and edit it to contain the following: 


{\small\begin{verbatim}
  #include "colors.inc"
  global_settings {
    assumed_gamma 2.2
    hf_gray_16
  }
\end{verbatim}}


   The {\small\texttt{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-\discretionary{}{}{}axis at the origin. 


{\small\begin{verbatim}
  camera {
    location <0, 0, -10>
    look_at 0
  }
\end{verbatim}}


   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. 


{\small\begin{verbatim}
  plane { z, 10
    pigment {
      wrinkles
      color_map {
       [0 0.3*White]
       [1 White]
      }
    }
  }
\end{verbatim}}


   Finally, create a light source. 


{\small\begin{verbatim}
  light_source { <0, 20, -100> color White }
\end{verbatim}}


   We render this scene at 640x480 {\small\texttt{+A0.1}} {\small\texttt{+FT}}. We will get an image that will produce an excellent height field. We create a 
 new file called {\small\texttt{\discretionary{hfdemo.}{}{hfdemo.}pov}} and edit it as follows: 



   \textbf{Note:} Windows users, unless you specify {\small\texttt{+FT}} as above, you will get a .BMP file (which is the default Windows version output). In 
 this case you will need to use {\small\texttt{sys}} instead of {\small\texttt{tga}} in the {\small\texttt{height\_\-field}} statement below. 


{\small\begin{verbatim}
  #include "colors.inc"
\end{verbatim}}


   We add a camera that is two units above the origin and ten units back ... 


{\small\begin{verbatim}
  camera{
    location <0, 2, -10>
    look_at 0
    angle 30
  }
\end{verbatim}}


   ... and a light source. 


{\small\begin{verbatim}
  light_source{ <1000,1000,-1000> White }
\end{verbatim}}


   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. 


{\small\begin{verbatim}
  height_field {
    tga "image.tga"
    smooth
    pigment { White }
    translate <-.5, -.5, -.5>
    scale <17, 1.75, 17>
  }
\end{verbatim}}


   We save the file and render it at 320x240 {\small\texttt{-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-\discretionary{}{}{}aliasing. 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/pvhfield} \caption{A height field created completely with POV-\discretionary{}{}{}Ray.} \end{figure} 
 



   Wow! The Himalayas have come to our computer screen! 


\subsection{Isosurface Object}

% tutorial/000087.html

\index{isosurface! tutorial}
\begin{description}
 
 \item 
   \textit{You know you have been raytracing too long when ...\newline  ... You find yourself wishing you'd paid attention in math class to all those 
  formulae you thought you'd never have any use for in real life.} 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   \textit{-- Jeff Lee} 
 \end{list}

\end{description}


   Isosurfaces are shapes described by mathematical functions. 



   In contrast to the other mathematically based shapes in POV-\discretionary{}{}{}Ray, isosurfaces are approximated during rendering and therefore they are sometimes more 
 difficult to handle. However, they offer many interesting possibilities, like real deformations and surface displacements 



   Some knowledge about mathematical functions and geometry is useful, but not necessarily required to work with isosurfaces. 


\subsubsection{Simple functions}

% tutorial/000088.html



   For the start we will choose a most simple function: {\small\texttt{x}} The value of this function is exactly the current x-\discretionary{}{}{}coordinate. 



   The isosurface object takes this function as a user defined function: 


{\small\begin{verbatim}
  isosurface {
    function { x }
    contained_by { box { -2, 2 } }
  }
\end{verbatim}}


   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/iso_01} \caption{Isosurface sample (function \{ x \})} \end{figure} 



   the resulting shape is fairly simple: a box. 



   The fact that it is a box is only caused by the container object which is required for an isosurface. You can either use a box or a sphere for this purpose. 



   So only one side of the box is made by the function in fact. This surface is where the x-\discretionary{}{}{}coordinate is 0 since 0 is the default threshold. There usually is 
 no reason to change this, since it is the most common and most suggestive value, but you can specify something different by adding 



   {\small\texttt{ threshold 1}} 



   to the isosurface definition. 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/iso_02} \caption{Isosurface sample (function \{ x \}, threshold 1)} \end{figure} 
 



   As you can see, the surface is now at x-\discretionary{}{}{}coordinate 1. 



   We can also remove the visible surfaces of the container object by adding the word 'open' to the isosurface definition. 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/iso_03} \caption{Isosurface sample (function \{ x \}, open)} \end{figure} 



   For making it clearer what surfaces are the actual isosurface and what are caused by the container object, the color will be different in all the following 
 pictures. 



   Now we replace the used function with something different: 



   {\small\texttt{ function \{ x+y \}}} 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/iso_04} \caption{Isosurface sample (plane function)} \end{figure} 



   {\small\texttt{ function \{ x+y+z \}}} 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/iso_05} \caption{Isosurface sample (plane function)} \end{figure} 



   \textbf{Note:} 'max\_\-gradient 4' is added to the isosurface definition here, this will be explained later on. 



   All these functions describe planes going through the origin. The function just describes the normal vector of this plane. 


\subsubsection{Several surfaces}

% tutorial/000089.html



   The following two functions lead to identical results: 



   {\small\texttt{ function \{ abs(x)-1 \}}} 



   {\small\texttt{ function \{ sqrt(x*x)-1 \}}} 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/iso_06} \caption{Isosurface sample (function \{ abs(x)-1 \}, open)} \end{figure} 
 



   You can see that there are two planes now. The reason is that both formulas have the same two solutions (where the function value is 0), namely {\small\texttt{x=-1}} 
 and {\small\texttt{x=1}}. 



   We can now mix all these elements in different combinations, the results always consist of plane surfaces: 



   {\small\texttt{ function \{ abs(x)-1+y \}}} 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/iso_07} \caption{Isosurface sample (combined linear functions)} \end{figure} 
 



   {\small\texttt{ function \{ abs(x)+abs(y)+abs(z)-2 \}}} 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/iso_08} \caption{Isosurface sample (combined linear functions)} \end{figure} 
 


\subsubsection{Non-\discretionary{}{}{}linear functions}

% tutorial/000090.html



   Curved surfaces of many different kinds can be achieved with non-\discretionary{}{}{}linear functions. 



   {\small\texttt{ function \{ pow(\discretionary{x,}{}{x,}2) + y \}}} 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/iso_09} \caption{Isosurface sample (non-\discretionary{}{}{}linear function)} \end{figure} 
 



   You can see the parabolic shape caused by the square function. 



   To get a cylindrical surface we can use the following function. 



   {\small\texttt{ function \{ sqrt(pow(\discretionary{x,}{}{x,}2) + pow(\discretionary{z,}{}{z,}2)) - 1 \}}} 



   In 2 dimensions it describes a circle, since it is constant in the 3rd dimension, we get a cylinder: 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/iso_10} \caption{Isosurface sample (cylinder function)} \end{figure} 



   It is of course not difficult to change this into a cone, we just need to add a linear component in y-\discretionary{}{}{}direction: 



   {\small\texttt{ function \{ sqrt(pow(\discretionary{x,}{}{x,}2) + pow(\discretionary{z,}{}{z,}2)) + y \}}} 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/iso_11} \caption{Isosurface sample (cone function)} \end{figure} 



   And we of course can also make a sphere: 



   {\small\texttt{ function \{ sqrt(pow(\discretionary{x,}{}{x,}2) + pow(\discretionary{y,}{}{y,}2) + pow(\discretionary{z,}{}{z,}2)) - 2 \}}} 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/iso_12} \caption{Isosurface sample (sphere function)} \end{figure} 



   The {\small\texttt{2}} specifies the radius here. 


\subsubsection{Specifying functions}

% tutorial/000315.html



   As we have seen, the functions used to define the isosurface are written in the {\small\texttt{function \{...\}}} block. 



   Allowed are: 



   User defined functions (like equations). All float expressions and operators (see section ``User-\discretionary{}{}{}Defined Functions'') which are legal in POV-\discretionary{}{}{}Ray, can 
 be used. \newline With the equation of a sphere ``{\small\texttt{x\^{}2+y\^{}2+z\^{}2 = Threshold}}'' we get: 


{\small\begin{verbatim}
isosurface {
function {pow(x,2) + pow(y,2) + pow(z,2)}
  threshold Threshold
  ...
}
\end{verbatim}}


   Functions can be declared first (see section ``Declaring Functions'') and then used in the isosurface. 


{\small\begin{verbatim}
#declare Sphere = function {pow(x,2) + pow(y,2) + pow(z,2)}
isosurface {
  function { Sphere(x,y,z) }
  threshold Threshold
  ...
}
\end{verbatim}}


   By default a function takes three parameters (\discretionary{x,}{}{x,}\discretionary{y,}{}{y,}z) and you do not have to explicitly specify the parameter names when declaring it. \newline When \textit{using} 
 the identifier, the parameters \textit{must} be specified. \newline On the other hand, if you need more or less than three parameters when declaring a 
 function, you also have to explicitly specify the parameter names. 


{\small\begin{verbatim}
#declare Sphere = function(x,y,z,Radius) {
    pow(x,2) + pow(y,2) + pow(z,2) - pow(Radius,2) 
}
isosurface {
  function { Sphere(x,y,z,1) }
  ...
}
\end{verbatim}}

\subsubsection{Internal functions}

% tutorial/000091.html



   There are a lot of internal functions available in POV-\discretionary{}{}{}Ray. For example a sphere could also be generated with {\small\texttt{function \{ f\_\-sphere(x, y, z, 2) \}}} 
 These functions are declared in the {\small\texttt{\discretionary{functions.}{}{functions.}inc}} include file. Most of them are more complicated and it is usually faster to use them 
 instead of a hand coded equivalent. See the complete list for details. 



   The following makes a torus just like POV-\discretionary{}{}{}Ray's torus object: 


{\small\begin{verbatim}
  #include "functions.inc"

  isosurface {
    function { f_torus(x, y, z, 1.6, 0.4) }
    contained_by { box { -2, 2 } }
  }
\end{verbatim}}


   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/iso_13} \caption{Isosurface sample (torus function)} \end{figure} 



   The 4th and 5th parameter are the major and minor radius, just like the corresponding values in the {\small\texttt{torus\{\}}} object. 



   The parameters x, y and z are required, because it is a declared function. You can also declare functions yourself like it is explained in the reference 
 section. 


\subsubsection{Combining isosurface functions}

% tutorial/000092.html



   We can also simulate some Constructive Solid Geometry with isosurface functions. If you do not know about CSG we suggest you have a look at ``What is 
 CSG?'' or the corresponding part of the reference section first. 



   We will take two functions: a cylinder and a rotated box: 


{\small\begin{verbatim}
  #declare fn_A = function { sqrt(pow(y,2) + pow(z,2)) - 0.8 }
  #declare fn_B = function { abs(x)+abs(y)-1 }
\end{verbatim}}


   If we combine them the following way, we get a ``merge'': 



   {\small\texttt{function \{ min(fn\_\-A(x, y, z), fn\_\-B(x, y, z)) \}}} 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/iso_14} \caption{Isosurface sample (merge)} \end{figure} 



   An ``intersection'' can be obtained by using {\small\texttt{max()}} instead of {\small\texttt{min()}}: 



   {\small\texttt{function \{ max(fn\_\-A(x, y, z), fn\_\-B(x, y, z)) \}}} 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/iso_15} \caption{Isosurface sample (intersection)} \end{figure} 



   Of course also ``difference'' is possible, we just have to add a minus (-) before the second function: 



   {\small\texttt{function \{ max(fn\_\-A(x, y, z), -fn\_\-B(x, y, z)) \}}} 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/iso_16} \caption{Isosurface sample (difference)} \end{figure} 



   Apart from basic CSG you can also obtain smooth transits between the different surfaces (like with the blob object) 


{\small\begin{verbatim}
  #declare Blob_threshold=0.01;

  isosurface {
    function {
      (1+Blob_threshold)
      -pow(Blob_threshold, fn_A(x,y,z))
      -pow(Blob_threshold, fn_B(x,y,z))
    }
    max_gradient 4
    contained_by { box { -2, 2 } }
  }
\end{verbatim}}


   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/iso_17} \caption{Isosurface sample (blob)} \end{figure} 



   The {\small\texttt{Blob\_\-threshold}} value influences the smoothness of the transit between the shapes. a lower value leads to sharper edges. 



   The function for a negative blob looks like: 


{\small\begin{verbatim}
function{fn_A(x,y,z) + pow(Blob_threshold,(Fn_B(x,y,z) + Strength))}
\end{verbatim}}

\subsubsection{Noise and pigment functions}

% tutorial/000093.html



   Some of the internal functions have a random or noise-\discretionary{}{}{}like structure 



   Together with the pigment functions they are one of the most powerful tools for designing isosurfaces. We can add real surface displacement to the objects 
 rather than only normal perturbation known from the normal\{\} statement. 



   The relevant internal functions are: 


\begin{itemize}
 
 \item 
   {\small\texttt{f\_\-noise3d(\discretionary{x,}{}{x,}\discretionary{y,}{}{y,}z)}}\newline  uses the noise generator specified in {\small\texttt{global\_\-settings\{\}}} and generates structures like the 
  bozo pattern. 
 

 \item 
   {\small\texttt{f\_\-noise\_\-generator(x, y, z, noise\_\-generator)}}\newline  generates noise with a specified noise generator. 
 

 \item 
   {\small\texttt{f\_\-ridged\_\-mf(x, y, z, H, Lacunarity, Octaves, Offset, Gain, noise\_\-generator)}}\newline  generates a ridged multifractal pattern. 
 

 \item 
   {\small\texttt{f\_\-ridge(x, y, z, Lambda, Octaves, Omega, Offset, Ridge, noise\_\-generator)}}\newline  generates another noise with ridges. 
 

 \item 
   {\small\texttt{f\_\-hetero\_\-mf(x, y, z, H, Lacunarity, Octaves, Offset, T, noise\_\-generator)}}\newline  generates heterogenic multifractal noise. 
 

\end{itemize}


   Using pure noise3d as a function results in the following picture: 



   {\small\texttt{ function \{ f\_\-noise3d(x, y, z)-0.5 \}}} 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/iso_18} \caption{Isosurface sample (noise3d)} \end{figure} 



   \textbf{Note:} the {\small\texttt{-0.5}} is only there to make it match to the used threshold value of 0, the {\small\texttt{f\_\-noise3d}} function returns 
 values between 0 and 1. 



   With this and the other functions you can generate objects similar to heightfields, having the advantage that a high resolution can be achieved without high 
 memory requirements. 



   {\small\texttt{ function \{ x + f\_\-noise3d(0, y, z) \}}} 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/iso_19} \caption{Isosurface sample (noise3d 'heightfield')} \end{figure} 



   The noise function can of course also be subtracted which results in an 'inverted' version: 



   {\small\texttt{ function \{ x - f\_\-noise3d(0, y, z) \}}} 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/iso_20} \caption{Isosurface sample (noise3d 'heightfield' inverted)} \end{figure} 
 



   In the last two pictures we added the noise function to a plane function. The x-\discretionary{}{}{}parameter was set to 0 so the noise function is constant in x-\discretionary{}{}{}direction. This 
 way we achieve the typical heightfield structure. 



   Of course we can also add noise to any other function. If the noise function is very strong this can result in several separated surfaces. 



   {\small\texttt{ function \{ f\_\-sphere(x, y, z, 1.2) - f\_\-noise3d(x, y, z) \}}} 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/iso_21} \caption{Isosurface sample (noise3d on sphere)} \end{figure} 



   This is a noise function applied to a sphere surface, we can influence the intensity of the noise by multiplying it with a factor and change the scale by 
 multiplying the coordinate parameters: 



   {\small\texttt{ function \{ f\_\-sphere(x, y, z, 1.6) - f\_\-noise3d(x * 5, y * 5, z * 5) * 0.5 \}}} 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/iso_22} \caption{Isosurface sample (noise3d on sphere scaled)} \end{figure} 
 



   As alternative to noise functions we can also use any pigment in a function: 


{\small\begin{verbatim}
  #declare fn_Pigm=function {
    pigment {
      agate
      color_map {
        [0 color rgb 0]
        [1 color rgb 1]
      }
    }
  }
\end{verbatim}}


   This function is a vector function returning a (color) \discretionary{vector.}{}{vector.}For use in isosurface functions they \textit{must} be declared first. When using the 
 identifier, you have to specify which component of the color vector should be used. To do this, the dot notation is used: {\small\texttt{Function(\discretionary{x,}{}{x,}\discretionary{y,}{}{y,}z).red}}. 
 



   A color vector has five components. Supported dot types to access these components are: 


\begin{itemize}
 
 \item 
   F( ).{\small\texttt{x}} | F( ).{\small\texttt{u}} | F( ).{\small\texttt{red}} 
  \begin{itemize}
   
   \item 
     to get the red value of the color vector 
   

  \end{itemize}
   
 

 \item 
   F( ).{\small\texttt{y}} | F( ).{\small\texttt{v}} | F( ).{\small\texttt{green}} 
  \begin{itemize}
   
   \item 
     to get the green value of the color vector 
   

  \end{itemize}
   
 

 \item 
   F( ).{\small\texttt{z}} | F( ).{\small\texttt{blue}} 
  \begin{itemize}
   
   \item 
     to get the blue value of the color vector 
   

  \end{itemize}
   
 

 \item 
   F( ).{\small\texttt{filter}} | F( ).{\small\texttt{t}} 
  \begin{itemize}
   
   \item 
     to get the filter value of the color vector 
   

  \end{itemize}
   
 

 \item 
   F( ).{\small\texttt{transmit}} 
  \begin{itemize}
   
   \item 
     to get the transmit value of the color vector 
   

  \end{itemize}
   
 

 \item 
   F( ).{\small\texttt{gray}} 
  \begin{itemize}
   
   \item 
     to get the gray value of the color vector 
   

   \item 
     gray value = Red*29.7\% + Green*58.9\% + Blue*11.4\% 
   

  \end{itemize}
   
 

 \item 
   F( ).{\small\texttt{hf}} 
  \begin{itemize}
   
   \item 
     to get the height\_\-field value of the color vector 
   

   \item 
     hf value = (Red + Green/255)*0.996093 
   

   \item 
     the .hf operator is experimental and will generate a warning. 
   

  \end{itemize}
   
 

\end{itemize}


   {\small\texttt{ function \{ f\_\-sphere(x, y, z, 1.6)-fn\_\-Pigm(x/2, y/2, z/2).gray*0.5 \}}} 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/iso_23} \caption{Isosurface sample (pigment function)} \end{figure} 



   There are quite a lot of things possible with pigment functions, but you probably have recognized that this renders quite slow. 


\subsubsection{Conditional directives and loops}

% tutorial/000316.html



   Conditional directives are allowed in functions: 


{\small\begin{verbatim}
#declare Rough = yes;
#include "functions.inc"
isosurface {
  function { y #if(Rough=1)-f_noise3d(x/0.5,y/0.3,z/0.4)*0.8 #end }
  ...
}
\end{verbatim}}


   Loops can also be used in functions: 


{\small\begin{verbatim}
#include "functions.inc"
#declare Thr = 1/1000;
#declare Ang = radians(45);
#declare Offset = 1.5;
#declare Scale = 1.2;
#declare TrSph = function { f_sphere(x-Offset,y,z,0.7*Scale) }

function {
  (1-Thr)
  #declare A = 0;
  #while (A<8)
  -pow(Thr, TrSph(x*cos(A*Ang) + y*sin(A*Ang),
                  y*cos(A*Ang) -x*sin(A*Ang), z) )
    #declare A=A+1;
  #end
}
\end{verbatim}}


   \textbf{Note:} The loops and conditionals are evaluated at parse time, not at render time. 


\subsubsection{Transformations on functions}

% tutorial/000317.html



   Transforming an isosurface object is done like transforming any POV-\discretionary{}{}{}Ray object. Simply use the object modifiers (scale, translate, rotate, ...). 



   However, when you want to transform functions within the contained\_\-by object, you have to substitute parameters in the functions. 



   The results \textit{seem} inverted to what you would normally expect. Here is an explanation: \newline Take a Sphere(\discretionary{x,}{}{x,}\discretionary{y,}{}{y,}z). We know it sits at the origin 
 because x=0. When we want it at x=2 (translating 2 units to the right) we need to write the second equation in the same form: x-2=0 \newline Now that both 
 equations equal 0, we can replace parameter x with x-2 \newline So our Sphere(x-2, \discretionary{y,}{}{y,}z) moves two units to the \textit{right}. 



   Let's scale our Sphere 0.5 in the y direction. Default size is y=1 (one unit). We want y=0.5. \newline To get this equation in the same form as the first 
 one, we have to multiply both sides by two. y*2 = 0.5*2, which gives y*2=1 \newline Now we can replace the y parameter in our sphere: Sphere(x, y*2, z). This 
 squishes the y-\discretionary{}{}{}size of the sphere by half. \newline Well, this is the general idea of substitutions. 



   Here is an overview of some useful substitutions: \newline Using a declared object P(\discretionary{x,}{}{x,}\discretionary{y,}{}{y,}z) 



   \textbf{Scale}\newline  scale x : replace ``{\small\texttt{x}}'' with ``{\small\texttt{x/scale}}'' (idem other parameters) 


{\small\begin{verbatim}scale x*2   gives    P(x/2,y,z)\end{verbatim}}


   \textbf{Scale Infinitely}\newline  scale x infinitely : replace "{\small\texttt{x}}" with "{\small\texttt{0}}" (idem other parameters) 


{\small\begin{verbatim}scale y infinitely   gives    P(x,0,z)\end{verbatim}}


   \textbf{Translate}\newline  translate x : replace "{\small\texttt{x}}" with "{\small\texttt{x - translation}}" (idem other parameters) 


{\small\begin{verbatim}translate z*3   gives    P(x,y,z-3)\end{verbatim}}


   \textbf{Shear}\newline  shear in XY-\discretionary{}{}{}plane : replace "{\small\texttt{x}}" with "{\small\texttt{x + y*tan(radians(Angle))}}" (idem other 
 parameters) 


{\small\begin{verbatim}shear 45 degrees left   gives    P(x+y*tan(radians(45)), y, z)\end{verbatim}}


   \textbf{Rotate} 



   \textbf{Note:} these rotation substitutions work like normal POV-\discretionary{}{}{}rotations: they already compensate for the inverse working 



   rotate around X \newline : replace "{\small\texttt{y}}" with "{\small\texttt{z*sin(radians(Angle)) + y*cos(radians(Angle))}}" \newline : 
 replace "{\small\texttt{z}}" with "{\small\texttt{z*cos(radians(Angle)) - y*sin(radians(Angle))}}" 



   rotate around Y \newline : replace "{\small\texttt{x}}" with "{\small\texttt{x*cos(radians(Angle)) - z*sin(radians(Angle))}}" \newline : 
 replace "{\small\texttt{z}}" with "{\small\texttt{x*sin(radians(Angle)) + z*cos(radians(Angle))}}" 



   rotate around Z \newline : replace "{\small\texttt{x}}" with "{\small\texttt{x*cos(radians(Angle)) + y*sin(radians(Angle))}}" \newline : 
 replace "{\small\texttt{y}}" with "{\small\texttt{-x*sin(radians(Angle)) + y*cos(radians(Angle)) }}" 


{\small\begin{verbatim}
  rotate z*75   gives:
  P(x*cos(radians(75)) + y*sin(radians(75)),
    -x*sin(radians(75)) + y*cos(radians(75)), z)
 \end{verbatim}}


   \textbf{Flip}\newline  flip X - Y : replace "{\small\texttt{x}}" with "{\small\texttt{y}}" and replace "{\small\texttt{y}}" 
 with "{\small\texttt{-x}}" 



   flip Y - Z : replace "{\small\texttt{y}}" with "{\small\texttt{z}}" and replace "{\small\texttt{z}}" with "{\small\texttt{-y}}" 
 



   flip X - Z : replace "{\small\texttt{x}}" with "{\small\texttt{-z}}" and replace "{\small\texttt{z}}" with "{\small\texttt{x}}" 
 


{\small\begin{verbatim}flip x and y   gives    P(y, -x, z)\end{verbatim}}


   \textbf{Twist}\newline  twist N turns/unit around {\small\texttt{X}} \newline : replace "{\small\texttt{y}}" with "{\small\texttt{z*sin(x*2*pi*N) 
 + y*cos(x*2*pi*N)}}" \newline : replace "{\small\texttt{z}}" with "{\small\texttt{z*cos(x*2*pi*N) - y*sin(x*2*pi*N)}}" 


\subsubsection{Improving Isosurface Speed}

% tutorial/000094.html



   To optimize the approximation of the isosurface and to get maximum rendering speed it is important to adapt certain values; 



   {\small\texttt{accuracy}} 



   The accuracy value influences how accurate the surface geometry is calculated. Lower values lead to a more precise, but slower result. The default value of {\small\texttt{0.001}} 
 is fairly low. We used this value in all the previous samples, but often you can raise this quite a lot and thereby make things faster. 



   {\small\texttt{max\_\-gradient}} 



   For finding the actual surface it is important for POV-\discretionary{}{}{}Ray to know the maximum gradient of the function, meaning how fast the function value changes. We can 
 specify a value with the {\small\texttt{max\_\-gradient}} keyword. Lower max\_\-gradient values lead to faster rendering, but if the specified value is below the 
 actual maximum gradient of the function, there can be holes or other artefacts in the surface. 



   For the same reason functions with infinite gradient should not be used. This applies for pigment functions with brick or checker pattern for example. You 
 should also be careful when using {\small\texttt{select()}} in isosurface functions because of this. 



   If the real maximum gradient differs too much from the specified value POV-\discretionary{}{}{}Ray prints a warning together with the found maximum gradient. It is usually 
 sufficient to use this number for the {\small\texttt{max\_\-gradient}} parameter to get fast and correct results. 



   POV-\discretionary{}{}{}Ray can also dynamically change the {\small\texttt{max\_\-gradient}} when you specify {\small\texttt{evaluate}} with 3 parameters the isosurface definition. 
 Concerning the details on this and other things see the evaluate in the reference section. 



   {\small\texttt{contained\_\-by}} 



   Make sure your {\small\texttt{contained\_\-by}} 'object' fits as tightly as possible. An oversized container can sky-\discretionary{}{}{}rocket the render time. \newline When the 
 container has a lot of empty space around the actual isosurface, POV-\discretionary{}{}{}Ray has to do a lot of superfluous sampling: especially with complex functions this can 
 become very time consuming. On top of this, the {\small\texttt{max\_\-gradient}} needed to get a proper surface will also increase rapidly (almost proportional 
 to the oversize!). \newline You could use a transparent copy of the container (using exactly the same transformations) to check how it fits. Getting the {\small\texttt{min\_\-extent}} 
 and {\small\texttt{max\_\-extent}} of the {\small\texttt{isosurface}} is not useful because it only gives the extent of the container and not of the actual 
 isosurface. 


\subsection{Poly Object}

% tutorial/000080.html

\index{poly! tutorial}

   The polynomial object (and its "shortcut" versions: {\small\texttt{cubic}}, {\small\texttt{quartic}} and {\small\texttt{quadric}}) of POV-\discretionary{}{}{}Ray is 
 one of the most complex and mathematical primitives of the program. One could think that it is seldom used and more or less obsolete, but we have to remember 
 that for example the torus primitive is just a shortcut for the equivalent {\small\texttt{quartic}}, which is just a shortcut for the equivalent {\small\texttt{poly}} 
 object. Polys are, however, seldom used in scenes due to the fact that they are so difficult to define and it is far from trivial to get the desired shape 
 with just a polynomial equation. It is mostly used by the most mathematically oriented POV-\discretionary{}{}{}Ray users. 



   This tutorial explains the process of making a polynomial object in POV-\discretionary{}{}{}Ray. 



   \textbf{Note:}Since version 3.5, POV-\discretionary{}{}{}Ray includes the new {\small\texttt{isosurface}} object which makes the polynomial object more or less obsolete. The 
 isosurface is more versatile (you can specify any mathematical function, not just polynomials), easier to use. You can write the function as is, without 
 needing to put values in a gigantic vector. Isosurfaces often render considerably faster than equivalent polys. 



   However, the most mathematically oriented still like polys because isosurfaces are calculated just by approximating the right value, while the poly is 
 calculated in a mathematically exact way. Usually isosurfaces are more than good enough for most applications, though. 



   \textbf{Note:} at maximum a 15th degree polynomial can be represented with the poly object. If a higher degree polynomial or other non-\discretionary{}{}{}polynomial function 
 has to be represented, then it is necessary to use the isosurface object. 


\subsubsection{Creating the polynomial function}

% tutorial/000081.html



   The first step is to create the polynomial function to be represented. You will need some (high-\discretionary{}{}{}school level) mathematical knowledge for this. 



   \textbf{1)} Let's start with an easy example: A sphere. 



   The sphere function is: 



   
\begin{mathequ}
% FILE: polyfunc1
% ---------
\begin{displaymath}
  \sqrt{x^2+y^2+z^2} = r
\end{displaymath}

\caption{sphere function} \end{mathequ}
 



   Now we have to convert this to polynomial form: 



   
\begin{mathequ}
% FILE: polyfunc2
% ---------
\begin{displaymath}
  x^2+y^2+z^2-r = 0
\end{displaymath}

\caption{sphere polynomial} \end{mathequ}
 



   We will need a polynomial of the 2nd degree to represent this. 



   \textbf{2)} A more elaborated example: 



   Let's take the function: 



   
\begin{mathequ}
% FILE: polyfunc3
% ---------
\begin{displaymath}
  z = \frac{2xy^2}{x^2+y^4}
\end{displaymath}

\caption{function} \end{mathequ}
 



   Converting this to polynomial form we get: 



   
\begin{mathequ}
% FILE: polyfunc4
% ---------
\begin{displaymath}
  x^2z + y^4z - 2xy^2 = 0
\end{displaymath}

\caption{polynomial} \end{mathequ}
 



   Although the highest power is 4 we will need a 5th order polynomial to represent this function (because we cannot represent y$^{4}$z with a 4th order 
 polynomial). 



   \textbf{3)} And since we talked about the torus, let's also take it as an example. 



   A torus can be represented with the function: 



   
\begin{mathequ}
% FILE: polyfunc5
% ---------
\begin{displaymath}
  \sqrt{\left(\sqrt{x^2+z^2}-r_1\right)^2+y^2} = r_2
\end{displaymath}

\caption{torus function} \end{mathequ}
 



   where r$_{1}$ is the major radius and r$_{2}$ is the minor radius. 



   Now, this is tougher to convert to polynomial form, but finally we get: 



   
\begin{mathequ}
% FILE: polyfunc6
% ---------
\begin{displaymath}
  x^4+2x^2y^2+2x^2z^2-2(r_1^2+r_2^2)x^2+y^4+2y^2z^2+2(r_1^2-r_2^2)y^2+
  z^4-2(r_1^2+r_2^2)z^2+(r_1^2-r_2^2)^2 = 0
\end{displaymath}

\caption{torus polynomial} \end{mathequ}
 



   A 4th order polynomial is enough to represent this. 



   \textbf{Note:} not every function can be represented in polynomial form. Only functions that use addition (and substraction), multiplication (and division) 
 and scalar powers (including rational powers, eg. the square root) can be represented. Also, the poly primitive supports only polynomials of the 7th degree at 
 max. 



   Converting a function to polynomial form may be a very laborious task for certain functions. Some mathematical programs are very helpful in this matter. 


\subsubsection{Writing the polynomial vector}

% tutorial/000082.html



   Now that we have the function in polynomial form, we have to write it in POV-\discretionary{}{}{}Ray syntax. The syntax is specified in the in the chapters "Poly, Cubic and 
 Quartic" and "Quadric" of the SDL section. There is also a table in this chapter which we will be using to make the polynomial vector. It is 
 easier to have this table printed on paper. 



   \textbf{Note:} It is also possible to make a little program with your favorite programming language which will print the poly vector from the polynomial 
 function, but making a program like this is up to you. 



   \textbf{1)} Let's start with the easy one, ie. the sphere. 



   Since the sphere can be represented with a polynomial of 2nd degree, we look at the row titled "2nd" in the table. We see that it has 10 items, ie. 
 we need a vector of size 10. Each item of the vector will be the factor of the term listed in the table. 



   The polynomial was: 



   
\begin{mathequ}
% FILE: polyfunc2
% ---------
\begin{displaymath}
  x^2+y^2+z^2-r = 0
\end{displaymath}

\caption{sphere polynomial} \end{mathequ}
 



   Writing the poly in this way we get: 


{\small\begin{verbatim}
#declare Radius=1;
poly
{ 2,
  <1,0,0,0,1,
   0,0,1,0,-Radius*Radius>
}
\end{verbatim}}


   Put each group of factors (separated with lines in the table) in their own lines. 



   In the table we see that the first item is the factor for x$^{2}$, which is 1 in the function. The next item is xy. Since it is not in the function, its 
 factor is 0. Likewise the next item, which is xz. And so on. The last item is the scalar term, which is in this case -r$^{2}$. 



   If we make a proper scene and render it, we get: 


{\small\begin{verbatim}
camera { location y*4-z*5 look_at 0 angle 35 }
light_source { <100,200,-50> 1 }
background { rgb <0,.25,.5> }

#declare Radius=1;
poly
{ 2,
  <1,0,0,0,1,
   0,0,1,0,-Radius*Radius>
  pigment { rgb <1,.7,.3> } finish { specular .5 }
}
\end{verbatim}}


   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/polypic1} \caption{Sphere polynomial} \end{figure} 



   \textbf{Note:} there is a shortcut for 2nd degree polynomials: The {\small\texttt{quadric}} primitive. Using a shortcut version, whenever possible, can lead 
 to faster renderings. We can write the sphere code described above in the following way: 


{\small\begin{verbatim}
quadric
{ <1,1,1>, <0,0,0>, <0,0,0>, -Radius*Radius
  pigment { rgb <1,.7,.3> } finish { specular .5 }
}
\end{verbatim}}


   \textbf{2)} Now lets try the second one. We do it similarly, but this time we need to look at the row titled "5th" in the table. 



   The polynomial was: 



   
\begin{mathequ}
% FILE: polyfunc4
% ---------
\begin{displaymath}
  x^2z + y^4z - 2xy^2 = 0
\end{displaymath}

\caption{5th order polynomial} \end{mathequ}
 



   Writing the poly primitive we get: 


{\small\begin{verbatim}
poly
{ 5,
  <0,0,0,0,0,
   0,0,0,0,0,
   0,0,0,0,0,
   0,0,0,1,0,
   0,0,0,0,0,
   -2,0,0,0,0,
   0,0,0,0,0,
   0,1,0,0,0,
   0,0,0,0,0,
   0,0,0,0,0,
   0,0,0,0,0,0>
}
\end{verbatim}}


   With the proper scene we get: 


{\small\begin{verbatim}
camera { location <8,20,-10>*.7 look_at x*.01 angle 35 }
light_source { <100,200,20> 1 }
background { rgb <0,.25,.5> }

poly
{ 5,
  <0,0,0,0,0,
   0,0,0,0,0,
   0,0,0,0,0,
   0,0,0,1,0,
   0,0,0,0,0,
   -2,0,0,0,0,
   0,0,0,0,0,
   0,1,0,0,0,
   0,0,0,0,0,
   0,0,0,0,0,
   0,0,0,0,0,0>
  clipped_by { box { <-4,-4,-1><4,4,1> } }
  bounded_by { clipped_by }
  pigment { rgb <1,.7,.3> } finish { specular .5 }
  rotate <0,90,-90>
}
\end{verbatim}}


   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/polypic2} \caption{5th order polynomial example} \end{figure} 



   \textbf{3)} And finally the torus: 



   The polynomial was: 



   
\begin{mathequ}
% FILE: polyfunc6
% ---------
\begin{displaymath}
  x^4+2x^2y^2+2x^2z^2-2(r_1^2+r_2^2)x^2+y^4+2y^2z^2+2(r_1^2-r_2^2)y^2+
  z^4-2(r_1^2+r_2^2)z^2+(r_1^2-r_2^2)^2 = 0
\end{displaymath}

\caption{torus polynomial} \end{mathequ}
 



   And we get the proper 4th degree poly primitive: 


{\small\begin{verbatim}
camera { location y*4-z*5 look_at 0 angle 35 }
light_source { <100,200,-50> 1 }
background { rgb <0,.25,.5> }

#declare r1=1;
#declare r2=.5;
poly
{ 4,
  <1,0,0,0,2,
   0,0,2,0,-2*(r1*r1+r2*r2),
   0,0,0,0,0,
   0,0,0,0,0,
   1,0,0,2,0,
   2*(r1*r1-r2*r2),0,0,0,0,
   1,0,-2*(r1*r1+r2*r2),0,pow(r1,4)+pow(r2,4)-2*r1*r1*r2*r2>
  pigment { rgb <1,.7,.3> } finish { specular .5 }
}
\end{verbatim}}


   When rendered we get: 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/polypic3} \caption{Torus polynomial} \end{figure} 



   There is a shortcut for 4th order polynomials: The {\small\texttt{quartic}} primitive. We can write the torus like this: 


{\small\begin{verbatim}
quartic
{ <1,0,0,0,2,
   0,0,2,0,-2*(r1*r1+r2*r2),
   0,0,0,0,0,
   0,0,0,0,0,
   1,0,0,2,0,
   2*(r1*r1-r2*r2),0,0,0,0,
   1,0,-2*(r1*r1+r2*r2),0,pow(r1,4)+pow(r2,4)-2*r1*r1*r2*r2>
  pigment { rgb <1,.7,.3> } finish { specular .5 }
}
\end{verbatim}}

\subsection{Superquadric Ellipsoid Object}

% tutorial/000095.html

\index{superellipsoid! tutorial}

   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 {\small\texttt{superellipsoid}} 
 is a useful object. It is described by the simple syntax: 


{\small\begin{verbatim}
  superellipsoid { <Value_E, Value_N >}
\end{verbatim}}


   Where \textit{Value\_\-E} and \textit{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 \textit{Value\_\-E} and \textit{Value\_\-N} to see what kind of shapes we can make. We create a file called {\small\texttt{ \discretionary{supellps.}{}{supellps.}pov}} and edit it 
 as follows: 


{\small\begin{verbatim}
  #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 }
\end{verbatim}}


   The addition of a gray background makes it a little easier to see our object. We now type: 


{\small\begin{verbatim}
  superellipsoid { <.25, .25>
    pigment { Red }
  }
\end{verbatim}}


   We save the file and trace it at 200x150 {\small\texttt{-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 \textit{Value\_\-E} and \textit{ 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 do not know exactly what to call it, but it is interesting. Finally, let's 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 \textit{ Value\_\-E} nor \textit{ Value\_\-N}. 
 This will cause POV-\discretionary{}{}{}Ray to incorrectly make a black box instead of our desired shape. Second, very small values of \textit{Value\_\-E} and \textit{ 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-\discretionary{}{}{}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 {\small\texttt{ \discretionary{tiles.}{}{tiles.}pov}} and edit it so that it reads as follows: 


{\small\begin{verbatim}
  #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 }
\end{verbatim}}


   \textbf{Note:} we have added {\small\texttt{\#include "\discretionary{textures.}{}{textures.}inc"}} so we can use pre-\discretionary{}{}{}defined textures. Now we want to define the superellipsoid 
 which will be our tile. 


{\small\begin{verbatim}
  #declare Tile = superellipsoid { <0.5, 0.1>
    scale <1, .05, 1>
  }
\end{verbatim}}


   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 do not 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: 


{\small\begin{verbatim}
  #declare Offset = 2.1;
\end{verbatim}}


   We now want to lay down a row of tiles. Each tile will be offset from the original by an ever-\discretionary{}{}{}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 {\small\texttt{Row}} 
 like this: 


{\small\begin{verbatim}
  #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 }
  }
\end{verbatim}}


   This gives us a single row of 17 tiles, more than enough to fill the screen. Now we must make copies of the {\small\texttt{Row}} and translate them, again by 
 the offset value, in both the +x and -x directions in ever increasing amounts in the same manner. 


{\small\begin{verbatim}
  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 }
\end{verbatim}}


   Finally, our tiles are complete. But we need a texture for them. To do this we union all of the {\small\texttt{Rows}} together and apply a {\small\texttt{White 
 Marble}} pigment and a somewhat shiny reflective surface to it: 


{\small\begin{verbatim}
  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 }
  }
\end{verbatim}}


   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. 


{\small\begin{verbatim}
  plane {
    y, 0  //this is the grout
    pigment { color White }
    finish { ambient .4 diffuse .7 }
  }
\end{verbatim}}


   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. 


{\small\begin{verbatim}
  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
  }
\end{verbatim}}


   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/superell} \caption{Some superellipsoids hovering above a tiled floor.} \end{figure} 
 



   We trace the scene at 320x200 {\small\texttt{-A}} to see the result. If we are happy with that, we do a final trace at 640x480 {\small\texttt{+A0.2}}. 


\section{Advanced Texture Options}

% tutorial/000274.html

\index{Texture Options! advanced}

   The extremely powerful texturing ability is one thing that really sets POV-\discretionary{}{}{}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-\discretionary{}{}{}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. 



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


\subsection{Pigments}

% tutorial/000275.html

\index{pigment! tutorial}

   Every surface must have a color. In POV-\discretionary{}{}{}Ray this color is called a {\small\texttt{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 {\small\texttt{\discretionary{texdemo.}{}{texdemo.}pov}} and edit it as follows: 


{\small\begin{verbatim}
  #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 }
  }
\end{verbatim}}


   Giving this file a quick test render at 200x150 {\small\texttt{-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. 


\subsubsection{Using Color List Pigments}

% tutorial/000276.html

\index{Color List Pigments! using}

   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 three other kinds of color list pigments, {\small\texttt{brick}}, {\small\texttt{hexagon}} and the {\small\texttt{object}} 
 pattern. Let's quickly try each of these. First, we change the plane's pigment as follows: 


{\small\begin{verbatim}
  pigment { hexagon Green, White, Yellow }
\end{verbatim}}


   Rendering this we see a three-\discretionary{}{}{}color hexagonal pattern. Note that this pattern requires three colors. Now we change the pigment to... 


{\small\begin{verbatim}
  pigment { brick Gray75, Red rotate -90*x scale .25 }
\end{verbatim}}


   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. 


\subsubsection{Using Pigment and Patterns}

% tutorial/000277.html

\index{Pigment and Patterns! using}

   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. 


{\small\begin{verbatim}
  pigment {
    gradient x
    color_map {
      [0.00 color Red]
      [0.33 color Blue]
      [0.66 color Yellow]
      [1.00 color Red]
    }
  }
\end{verbatim}}


   Rendering this we see that the {\small\texttt{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. 


{\small\begin{verbatim}
  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
  }
\end{verbatim}}


   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 {\small\texttt{gradient x}} and render to see the result: {\small\texttt{bozo}}, {\small\texttt{marble}}, 
 {\small\texttt{agate}}, {\small\texttt{granite}}, {\small\texttt{leopard}}, {\small\texttt{spotted}} and {\small\texttt{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. 


\subsubsection{Using Pattern Modifiers}

% tutorial/000278.html

\index{Pattern Modifiers! using}\index{frequency! tutorial}\index{turbulence! tutorial}\index{omega! tutorial}\index{lambda! tutorial}\index{octaves! tutorial}

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


{\small\begin{verbatim}
  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
  }
\end{verbatim}}


   The {\small\texttt{frequency}} modifier determines the number of times the color map repeats itself per unit of size. This change makes the {\small\texttt{bozo}} 
 pattern we saw earlier have many more bands in it. Now we change the pattern type to {\small\texttt{marble}}. When we rendered this earlier, we saw a banded 
 pattern similar to {\small\texttt{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 {\small\texttt{turbulence}}. We change the line {\small\texttt{ frequency 3}} to {\small\texttt{turbulence 
 1}} and render again. That's better! Now let's put {\small\texttt{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 {\small\texttt{turbulence}} 
 keyword can be any value with higher values giving us more turbulence. Second, we can use the keywords {\small\texttt{omega}}, {\small\texttt{lambda}} and {\small\texttt{octaves}} 
 to change the turbulence parameters. 



   Let's try this now: 


{\small\begin{verbatim}
  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
  }
\end{verbatim}}


   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. 


\subsubsection{Using Transparent Pigments and Layered Textures}

% tutorial/000279.html

\index{Transparent Pigments! using}\index{Layered Textures! using}

   Pigments are described by numerical values that give the rgb value of the color to be used (like {\small\texttt{color rgb$<$\discretionary{1,}{}{1,}\discretionary{0,}{}{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: {\small\texttt{color 
 rgbf$<$\discretionary{1,}{}{1,}0,\discretionary{0,}{}{0,}1$>$}}. The \textit{f} stands for {\small\texttt{filter}}, POV-\discretionary{}{}{}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-\discretionary{}{}{}Ray. It is called \textit{transmittance} or non-\discretionary{}{}{}filtering transparency (the keyword is {\small\texttt{transmit}}; 
 see also {\small\texttt{rgbt}}). It is different from {\small\texttt{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: {\small\texttt{rgbt $<$\discretionary{1,}{}{1,}0,\discretionary{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. 


{\small\begin{verbatim}
  #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>]
        }
      }
    }
\end{verbatim}}


   This texture will be the land area. Now let's make the oceans by declaring the following. 


{\small\begin{verbatim}
  #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>]
        }
      }
    }
\end{verbatim}}


   \textbf{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. 


{\small\begin{verbatim}
  #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>]
      }
    }
  }
\end{verbatim}}


   Now apply all of these to our sphere. 


{\small\begin{verbatim}
  sphere {
    <0,0,0>, 1
    texture { LandArea }
    texture { OceanArea }
    texture { CloudArea }
  }
\end{verbatim}}


   We render this and have a pretty good rendition of a little planetoid. But it could be better. We do not particularly like the appearance of the clouds. 
 There is a way they could be done that would be much more realistic. 


\subsubsection{Using Pigment Maps}

% tutorial/000280.html

\index{Pigment Maps! using}\index{pigment\_\-map! tutorial}

   Pigments may be blended together in the same way as the colors in a color map using the same pattern keywords and a {\small\texttt{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. 


{\small\begin{verbatim}
  #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]
    }
  }
\end{verbatim}}


   Now we use these declared pigments in our cloud layer on our planetoid. We replace the declared cloud layer with. 


{\small\begin{verbatim}
  #declare CloudArea = texture {
    pigment {
      gradient y
      pigment_map {
        [0.00 Clouds1]
        [0.25 Clouds2]
        [0.50 Clouds3]
        [0.75 Clouds4]
        [1.00 Clouds1]
      }
    }
  }
\end{verbatim}}


   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. 


\subsection{Normals}

% tutorial/000281.html



   Objects in POV-\discretionary{}{}{}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. 


\subsubsection{Using Basic Normal Modifiers}

% tutorial/000282.html

\index{Normal Modifiers! using}

   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. 


{\small\begin{verbatim}
  sphere {
    <0,0,0>, 1
    pigment { Gray75 }
    normal { bumps 1 scale .2 }
  }
\end{verbatim}}


   Here we have added a {\small\texttt{normal}} block in addition to the {\small\texttt{ pigment}} block (note that these do not have to be included in a {\small\texttt{ 
 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 {\small\texttt{bumps}} the following keywords: {\small\texttt{dents}}, {\small\texttt{wrinkles}}, {\small\texttt{ripples}} 
 and {\small\texttt{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. 


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

\subsubsection{Blending Normals}

% tutorial/000283.html

\index{Normals! blending}\index{normal\_\-map! tutorial}

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


{\small\begin{verbatim}
  sphere {
    <0,0,0>, 1
    pigment { Gray75 }
      normal { radial frequency 10 }
      normal { gradient y scale .2 }
  }
\end{verbatim}}


   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-\discretionary{}{}{}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. 


{\small\begin{verbatim}
  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]
      }
    }
  }
\end{verbatim}}


   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 gives 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? Would not that make the land areas bumpy 
 while leaving the oceans smooth? Let's try it. First, let's render the two spheres side-\discretionary{}{}{}by-\discretionary{}{}{}side so we can see if the pattern is indeed the same. We un-\discretionary{}{}{}comment 
 the planetoid sphere and make the following changes. 


{\small\begin{verbatim}
  sphere {
    <0,0,0>, 1
    texture { LandArea }
    texture { OceanArea }
    //texture { CloudArea }  // <-comment this out
    translate -x             // <- add this transformation
  }
\end{verbatim}}


   Now we change the gray sphere as follows. 


{\small\begin{verbatim}
  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
  }
\end{verbatim}}


   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 {\small\texttt{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. 


{\small\begin{verbatim}
  #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]
      }
    }
  }
\end{verbatim}}


   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. 


\subsection{Finishes}

% tutorial/000284.html

\index{finish! tutorial}

   The final part of a POV-\discretionary{}{}{}Ray texture is the {\small\texttt{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-\discretionary{}{}{}than-\discretionary{}{}{}perfectly-\discretionary{}{}{}smooth surfaces and what happens to light that is reflected by surfaces with 
 thin-\discretionary{}{}{}film interference properties. There are twelve different properties available in POV-\discretionary{}{}{}Ray to specify the finish of a given object. 
 These are controlled by the following keywords: {\small\texttt{ambient}}, {\small\texttt{diffuse}}, {\small\texttt{brilliance}}, {\small\texttt{phong}}, {\small\texttt{specular}}, 
 {\small\texttt{metallic}}, {\small\texttt{reflection}}, {\small\texttt{crand}} and {\small\texttt{iridescence}}. Let's design a couple of textures that make 
 use of these parameters. 


\subsubsection{Using Ambient}

% tutorial/000285.html

\index{Ambient! using}

   Since objects in POV-\discretionary{}{}{}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, {\small\texttt{ambient}} and {\small\texttt{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. 


{\small\begin{verbatim}
  plane {
    y, -1.5
    pigment {checker Green, White}
  }
  sphere {
    <0,0,0>, 1
    pigment { Gray75 }
    finish {
      ambient .2
      diffuse .6
    }
  }
\end{verbatim}}


   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. 


{\small\begin{verbatim}
  ambient 0
  diffuse 0
\end{verbatim}}


   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 {\small\texttt{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 {\small\texttt{diffuse}} to 0.3 and {\small\texttt{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 {\small\texttt{ ambient}} and {\small\texttt{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: 


{\small\begin{verbatim}
sphere {
   <0,0,0>, 1
   pigment { White filter 1 }
   finish {
      ambient 0
      diffuse 0
      reflection .25
      specular 1
      roughness .001
   }
   interior { ior 1.33 }
}
\end{verbatim}}


   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 {\small\texttt{\discretionary{glass.}{}{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 {\small\texttt{ambient}} 
 value of 1 and a {\small\texttt{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. 


{\small\begin{verbatim}
  sphere {
     <0,0,0>, 1
     pigment { White }
     finish {
        ambient 1
        diffuse 0
     }
  }
\end{verbatim}}


   Rendering this we get a blinding white sphere with no visible highlights or shaded parts. It would make a pretty good street light. 


\subsubsection{Using Surface Highlights}

% tutorial/000286.html

\index{Surface Highlights! using}\index{Highlights}\index{phong! tutorial}

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


{\small\begin{verbatim}
  sphere {
    <0,0,0>, 1
    pigment { Gray50 }
    finish {
      ambient .2
      diffuse .6
      phong .75
      phong_size 25
    }
  }
\end{verbatim}}


   Rendering this we see a fairly broad, soft highlight that gives the sphere a kind of plastic appearance. Now let's change {\small\texttt{ 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 \textit{specular highlighting}. It is specified using the keyword {\small\texttt{specular}} 
 and operates in conjunction with another keyword called {\small\texttt{roughness}}. These two keywords work together in much the same way as {\small\texttt{phong}} 
 and {\small\texttt{phong\_\-size}} to create highlights that alter the apparent shininess of the surface. Let's try using specular in our sphere. 


{\small\begin{verbatim}
  sphere {
     <0,0,0>, 1
     pigment { Gray50 }
     finish {
        ambient .2
        diffuse .6
        specular .75
        roughness .1
    }
  }
\end{verbatim}}


   Looking at the result we see a broad, soft highlight similar to what we had when we used {\small\texttt{phong\_\-size}} of 25. Change {\small\texttt{roughness}} 
 to .001 and render again. Now we see a small, tight highlight similar to what we had when we used {\small\texttt{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. 


\subsubsection{Using Reflection, Metallic and Metallic}

% tutorial/000287.html

\index{Reflection! using}\index{Metallic! using}

   There is another surface parameter that goes hand in hand with highlights, {\small\texttt{reflection}}. Surfaces that are very shiny usually have a degree of 
 reflection to them. Let's take a look at an example. 


{\small\begin{verbatim}
  sphere {
     <0,0,0>, 1
     pigment { Gray50 }
     finish {
        ambient .2
        diffuse .6
        specular .75
        roughness .001
        reflection {
           .5
        }
     }
  }
\end{verbatim}}


   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 {\small\texttt{reflection}} is the lower {\small\texttt{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. 


{\small\begin{verbatim}
  sphere {
     <0,0,0>, 1
     pigment { BrightGold }
     finish {
        ambient .1
        diffuse .1
        specular 1
        roughness .001
        reflection {
           .75
        }
     }
   }
\end{verbatim}}


   That is close but there is something wrong, the colour of the reflection and the highlight. To make the surface appear more like metal the keyword {\small\texttt{metallic}} 
 is used. We add it now to see the difference. 


{\small\begin{verbatim}
  sphere {
     <0,0,0>, 1
     pigment { BrightGold }
     finish {
        ambient .1
        diffuse .1
        specular 1
        roughness .001
        reflection {
          .75
          metallic
        }
     }
  }
\end{verbatim}}


   The reflection has now more of the gold color than the color of its environment. Last detail, the highlight. We add another metallic statement, now to the 
 finish and not inside the reflection block. 


{\small\begin{verbatim}
  sphere {
     <0,0,0>, 1
     pigment { BrightGold }
     finish {
        ambient .1
        diffuse .1
        specular 1
        roughness .001
        metallic
        reflection {
          .75
          metallic
        }
     }
  }
\end{verbatim}}


   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. 


\subsubsection{Using Iridescence}

% tutorial/000288.html

\index{Irid! using}\index{Thin-\discretionary{}{}{}Film Interference}\index{Interference}

   \textit{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 \textit{thin-\discretionary{}{}{}film 
 interference} (read section "Iridescence" for details). For now let's just try using it. Iridescence is specified by the {\small\texttt{irid}} 
 statement and three values: amount, {\small\texttt{thickness}} and {\small\texttt{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 {\small\texttt{octaves}}, {\small\texttt{lambda}} or {\small\texttt{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. 


{\small\begin{verbatim}
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
     }
}
\end{verbatim}}


   We try to vary the values for amount, thickness and turbulence to see what changes they make. We also try to add a {\small\texttt{normal}} block to see what 
 happens. 


\subsection{Working With Pigment Maps}

% tutorial/000289.html

\index{Pigment Maps! working with}

   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 is not strictly necessary (we could put an entire 
 pigment description in each entry of the map) but it just makes the whole thing more readable. 


{\small\begin{verbatim}
  // simple Black on White checkerboard... 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 ]
      }
    }
  }
\end{verbatim}}


   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. 


{\small\begin{verbatim}
  pigment_map {
    [ 0.0 Pigment1 ]
    [ 0.5 Pigment1 ]
    [ 0.5 Pigment2 ]
    [ 1.0 Pigment2 ]
  }
\end{verbatim}}


   Blending individual pigment patterns is just the beginning. 


\subsection{Working With Normal Maps}

% tutorial/000290.html

\index{Normal Maps! working with}\index{normal\_\-map! using}

   For our next example, we replace the plane in the scene with this one. 


{\small\begin{verbatim}
  plane {
    -z, 0
    pigment { White }
    normal {
      gradient x
      normal_map {
        [ 0.0 bumps 1 scale .1]
        [ 1.0 ripples 1 scale .1]
      }
    }
  }
\end{verbatim}}


   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-\discretionary{}{}{}Ray 3, all patterns that work with pigments work as normals as well (and vice versa, except for facets) 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 {\small\texttt{ average}} function, 
 and we will return to it a little bit further down the page. 


\subsection{Working With Texture Maps}

% tutorial/000291.html

\index{Texture Maps! working with}\index{texture\_\-map! tutorial}

   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. 


{\small\begin{verbatim}
  #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
    }
  }
\end{verbatim}}


   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-\discretionary{}{}{}between point, POV-\discretionary{}{}{}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. 


\subsection{Working With List Textures}

% tutorial/000292.html

\index{List Textures! working with}

   If we have followed the corresponding tutorials on simple pigments, we know that there are three patterns called \textit{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 are talking about checker, 
 hexagon, the brick pattern and the object 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. 


{\small\begin{verbatim}
  #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
    }
  }
\end{verbatim}}


   We begin by declaring an example of each of the color list patterns as individual pigments. Then we use the hexagon pattern as a \textit{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-\discretionary{}{}{}direction, while hexagons align along the y-\discretionary{}{}{}direction, and we wanted everything to face toward the camera we originally declared out in 
 the -z-\discretionary{}{}{}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-\discretionary{}{}{}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 


{\small\begin{verbatim}
  normal {
    brick
    normal { granite .1 }
    normal { bumps 1 scale .1 }
  }
\end{verbatim}}


   or... 


{\small\begin{verbatim}
  texture {
    checker
    texture { Gold_Metal }
    texture { Silver_Metal }
  }
\end{verbatim}}

\subsection{What About Tiles?}

% tutorial/000293.html

\index{Tiles! what about}

   In earlier versions of POV-\discretionary{}{}{}Ray, there was a texture pattern called {\small\texttt{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-\discretionary{}{}{}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. 


\subsection{Average Function}

% tutorial/000294.html

\index{average! tutorial}

   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 {\small\texttt{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. 


{\small\begin{verbatim}
  plane { -z, 0
    pigment { White }
    normal {
      average
      normal_map {
        [1, gradient x ]
        [1, gradient y ]
      }
    }
  }
\end{verbatim}}


   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-\discretionary{}{}{}hand side of each map entry has a different meaning now. It 
 gives the weight factor per entry in the map. Try some different values for the 'gradient x' entry and see how the normal changes. 



   The weight factor can be omitted, the result then will be the same as if each entry had a weight factor of 1. 


\subsection{Working With Layered Textures}

% tutorial/000295.html

\index{Layered Textures! working with}

   With the multitudinous colors, patterns, and options for creating complex textures in POV-\discretionary{}{}{}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 \textit{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: \textit{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 will not receive a warning or an error - technically it is legal to do this: it just does not 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 {\small\texttt{\discretionary{LAYTEX.}{}{LAYTEX.}POV}} and add the following 
 lines. 


{\small\begin{verbatim}
  #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)
\end{verbatim}}


   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 do not 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 {\small\texttt{Silver\_\-Metal}} texture as declared in \discretionary{textures.}{}{textures.}inc (for bonus points, look up {\small\texttt{\discretionary{textures.}{}{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 {\small\texttt{bozo}} texture gradually fades from blackened centers to 
 semi-\discretionary{}{}{}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! 


\subsubsection{Declaring Layered Textures}

% tutorial/000296.html

\index{Layered Textures! declaring}

   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 will not repeat the 
 whole texture from above, but the general format would be something like this: 


{\small\begin{verbatim}
  #declare Abused_Metal =
    texture { /* insert your base texture here... */ }
    texture { /* and your rust flecks here... */ }
    texture { /* and of course, your sooty burn marks here */ }
\end{verbatim}}


   POV-\discretionary{}{}{}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-\discretionary{}{}{}Ray is concerned we can layer entire textures, but not individual 
 pieces of textures. For example 


{\small\begin{verbatim}
  #declare Bad_Texture =
    texture { /* insert your base texture here... */ }
    pigment { Red filter .5 }
    normal { bumps 1 }
\end{verbatim}}


   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. 


\subsubsection{Another Layered Textures Example}

% tutorial/000297.html

\index{Layered Textures! another 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 are 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 {\small\texttt{ \discretionary{layered1.}{}{layered1.}pov}}. 
 


{\small\begin{verbatim}
  #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>
  }
\end{verbatim}}


   We render this scene. It is not particularly interesting, is 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 the following box to the previous scene and re-\discretionary{}{}{}render (see file {\small\texttt{\discretionary{layered2.}{}{layered2.}pov}}). 


{\small\begin{verbatim}
  #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>
  }
\end{verbatim}}


   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-\discretionary{}{}{}render (see file {\small\texttt{\discretionary{layered3.}{}{layered3.}pov}}). 


{\small\begin{verbatim}
  #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>
  }
\end{verbatim}}


   Now there is 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-\discretionary{}{}{}render (see file {\small\texttt{ \discretionary{layered4.}{}{layered4.}pov}}) 


{\small\begin{verbatim}
  #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>
  }
\end{verbatim}}


   Well, this may not be the tablecloth we want at any picnic we are 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 \textit{lower} layer contains a specular finish and an \textit{upper} 
 layer does not, any place where the upper layer is transparent, the specular will show through. 


\subsection{When All Else Fails: Material Maps}

% tutorial/000298.html

\index{material\_\-map! tutor}

   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-\discretionary{}{}{}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-\discretionary{}{}{}Ray what texture 
 will go at that location). Now, if we have the complete package that comes with POV-\discretionary{}{}{}Ray, we have in our include files an image called {\small\texttt{\discretionary{povmap.}{}{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. 


{\small\begin{verbatim}
  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
    }
  }
\end{verbatim}}


   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 {\small\texttt{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-\discretionary{}{}{}paletted formats, such as 
 the TGA files that POV-\discretionary{}{}{}Ray itself outputs. That leads to an interesting consequence: We can use POV-\discretionary{}{}{}Ray to produce source maps for POV-\discretionary{}{}{}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-\discretionary{}{}{}Ray can make its own source maps. 



   To begin with, if using a non-\discretionary{}{}{}paletted image, POV-\discretionary{}{}{}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 


\begin{enumerate}
 
 \item 
   Using an rgb statement to choose our color such as rgb $<$N/\discretionary{255,}{}{255,}\discretionary{0,}{}{0,}0$>$, where "N" is the red value we want to assign that pigment, and 
  then... 
 

 \item 
   Use no light sources and apply a finish of {\small\texttt{finish \{ ambient 1 \}}} to all objects, to ensure that highlighting and shadowing will not 
  interfere. 
 

\end{enumerate}


   Confused? Alright, here is an example, which will generate a map very much like {\small\texttt{\discretionary{povmap.}{}{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-\discretionary{}{}{}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-\discretionary{}{}{}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 create the following code, name it {\small\texttt{\discretionary{povmap.}{}{povmap.}pov}}, then render it. This will create an output file called {\small\texttt{\discretionary{povmap.}{}{povmap.}tga}} (\textbf{{\small\texttt{\discretionary{povmap.}{}{povmap.}bmp}} 
 on Windows systems}). 


{\small\begin{verbatim}
  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 }
  }
\end{verbatim}}


   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 did not have to use an external paint program to generate 
 our source: POV-\discretionary{}{}{}Ray did it all! 


\subsection{Limitations Of Special Textures}

% tutorial/000299.html

\index{Special Textures! limitations of}

   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 does not actually prevent us from doing anything 
 we could not 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 {\small\texttt{ 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 would not 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 


{\small\begin{verbatim}
  // 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 ]
    }
  }
\end{verbatim}}


   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! 


\section{Using Atmospheric Effects}

% tutorial/000100.html

\index{Atmospheric Effects! using}
\begin{description}
 
 \item 
   \textit{You know you have been raytracing too long when ...\newline  ... You want to cheat and look at nature's source code.} 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   \textit{-- Mark Stock} 
 \end{list}

\end{description}


   POV-\discretionary{}{}{}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. 


\subsection{The Background}

% tutorial/000101.html

\index{Background! tutorial}

   The {\small\texttt{background}} feature is used to assign a color to all rays that do not hit any object. This is done in the following way. 


{\small\begin{verbatim}
  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> }
  }
\end{verbatim}}


   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. 


\subsection{The Sky Sphere}

% tutorial/000102.html

\index{Sky Sphere! the}\index{sky\_\-sphere! tutorial}

   The {\small\texttt{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 will start with a very simple sky sphere that will get more and more complex as we add new features to it. 


\subsubsection{Creating a Sky with a Color Gradient}

% tutorial/000103.html

\index{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 {\small\texttt{\discretionary{skysph1.}{}{skysph1.}pov}} below. 


{\small\begin{verbatim}
  #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
    }
  }
\end{verbatim}}


   The interesting part is the sky sphere statement. It contains a pigment that describes 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-\discretionary{}{}{}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 {\small\texttt{scale}} statement is used to avoid the repetition and the {\small\texttt{translate -1}} 
 statement moves the color at index zero to the bottom of the sky sphere (that is the point of the sky sphere you will 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. 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/skyspher} \caption{A simple gradient sky sphere.} \end{figure} 



   If you want to start one of the colors at a specific angle you will first have to convert the angle to a color map index. This is done by using the formula {\small\texttt{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-\discretionary{}{}{}Ray you first have to convert the degree value to {\small\texttt{radians}} as it is shown in the following example. 


{\small\begin{verbatim}
  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
    }
  }
\end{verbatim}}


   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. 


\subsubsection{Adding the Sun}

% tutorial/000105.html



   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 will 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 ({\small\texttt{\discretionary{skysph2.}{}{skysph2.}pov}}). 


{\small\begin{verbatim}
  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 }
  }
\end{verbatim}}


   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 do not 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 do not 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 {\small\texttt{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, \discretionary{i.}{}{i.}e. right below us. 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/redsun} \caption{A red sun descends into the night.} \end{figure} 



   Looking at the resulting image you will see what impressive effects you can achieve with the sky sphere. 


\subsubsection{Adding Some Clouds}

% tutorial/000104.html

\index{Clouds! adding}

   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). 


{\small\begin{verbatim}
  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
  }
\end{verbatim}}


   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/cloudsky} \caption{A cloudy sky with a setting sun.} \end{figure} 



   The sky sphere has one drawback as you might notice when looking at the final image ({\small\texttt{\discretionary{skysph3.}{}{skysph3.}pov}}). The sun does not emit any light and the 
 clouds will not cast any shadows. If you want to have clouds that cast shadows you will have to use a real, large sphere with an appropriate texture and a 
 light source somewhere outside the sphere. 


\subsection{The Fog}

% tutorial/000106.html

\index{Fog! adding}\index{fog! tutorial}

   You can use the {\small\texttt{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. 


\subsubsection{A Constant Fog}

% tutorial/000107.html

\index{Fog! constant}

   The simplest fog type is the constant fog that has a constant density in all locations. It is specified by a {\small\texttt{distance}} keyword which actually 
 describes the fog's density and a fog {\small\texttt{color}}. 



   The distance value determines the distance at which 36.8\% of the background is 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-\discretionary{}{}{}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 ({\small\texttt{\discretionary{fog1.}{}{fog1.}pov}}). 


{\small\begin{verbatim}
  #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>
  }
\end{verbatim}}


   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/smplfog} \caption{A foggy scene.} \end{figure} 



   According to their distance the spheres in this scene more or less vanish in the greenish fog we used, as does the checkerboard plane. 


\subsubsection{Setting a Minimum Translucency}

% tutorial/000113.html

\index{Fog! setting 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 


{\small\begin{verbatim}
  fog {
    distance 150
    color rgbt<0.3, 0.5, 0.2, 0.2>
  }
\end{verbatim}}


   the fog's translucency never drops below 20\% as you can see in the resulting image ({\small\texttt{\discretionary{fog2.}{}{fog2.}pov}}). 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/bgvisfog} \caption{Fog with translucency threshold added.} \end{figure} 


\subsubsection{Creating a Filtering Fog}

% tutorial/000112.html

\index{Fog! filtering}

   The greenish fog we have used so far does not filter the light passing through it. All it does is to diminish the light's intensity. We can change this by 
 using a non-\discretionary{}{}{}zero filter channel in the fog's color ({\small\texttt{\discretionary{fog3.}{}{fog3.}pov}}). 


{\small\begin{verbatim}
  fog {
    distance 150
    color rgbf<0.3, 0.5, 0.2, 1.0>
  }
\end{verbatim}}


   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. 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/filtfog} \caption{A filtering fog.} \end{figure} 



   You will 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. 


\subsubsection{Adding Some Turbulence to the Fog}

% tutorial/000111.html

\index{Fog! adding turbulence}

   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-\discretionary{}{}{}constant density ({\small\texttt{\discretionary{fog4.}{}{fog4.}pov}}). 
 


{\small\begin{verbatim}
  fog {
    distance 150
    color rgbf<0.3, 0.5, 0.2, 1.0>
    turbulence 0.2
    turb_depth 0.3
  }
\end{verbatim}}


   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/turbfog} \caption{Fog made more interesting with turbulence} \end{figure} 



   The {\small\texttt{turbulence}} keyword is used to specify the amount of turbulence used while the {\small\texttt{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 {\small\texttt{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-\discretionary{}{}{}based attenuation value of the fog is modified by the 
 turbulence value at a point along the viewing ray. 


\subsubsection{Using Ground Fog}

% tutorial/000110.html

\index{Ground Fog! using}\index{Fog! ground}

   The much more interesting and flexible fog type is the ground fog, which is selected with the {\small\texttt{fog\_\-type}} statement. Its appearance is 
 described with the {\small\texttt{fog\_\-offset}} and {\small\texttt{fog\_\-alt}} keywords. The {\small\texttt{fog\_\-offset}} specifies the height, i. e. y value, 
 below which the fog has a constant density of one. The {\small\texttt{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 ({\small\texttt{\discretionary{fog5.}{}{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. 


{\small\begin{verbatim}
  fog {
    distance 150
    color rgbf<0.3, 0.5, 0.2, 1.0>
    fog_type 2
    fog_offset 25
    fog_alt 1
  }
\end{verbatim}}


   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/lowfog} \caption{An example of ground fog.} \end{figure} 


\subsubsection{Using Multiple Layers of Fog}

% tutorial/000109.html

\index{Fog! using multiple layers of}

   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 ({\small\texttt{\discretionary{fog6.}{}{fog6.}pov}}). 


{\small\begin{verbatim}
  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
  }
\end{verbatim}}


   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/multifog} \caption{Using multiple layers of fog.} \end{figure} 



   You can combine constant density fogs, ground fogs, filtering fogs, non-\discretionary{}{}{}filtering fogs, fogs with a translucency threshold, etc. 


\subsubsection{Fog and Hollow Objects}

% tutorial/000108.html

\index{Fog! hollow objects}\index{Hollow Objects! fog inside}

   Whenever you use the fog feature and the camera is inside a non-\discretionary{}{}{}hollow object you will not 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 {\small\texttt{inverse}} 
 keyword) or by adding the {\small\texttt{hollow}} to them (which is much easier). 


\subsection{The Rainbow}

% tutorial/000114.html

\index{Rainbow! the}\index{rainbow! tutorial}

   The {\small\texttt{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-\discretionary{}{}{}like volume. 


\subsubsection{Starting With a Simple Rainbow}

% tutorial/000115.html

\index{Rainbow! simple}

   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-\discretionary{}{}{}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 {\small\texttt{angle}} and {\small\texttt{width}} keywords. The {\small\texttt{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-\discretionary{}{}{}width/2 and smaller than angle+width/2. 



   The incoming light is the virtual light source that is responsible for the rainbow. There need not be a real light source to create the rainbow effect. 



   The rainbow is a fog-\discretionary{}{}{}like effect, \discretionary{i.}{}{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 ({\small\texttt{\discretionary{rainbow1.}{}{rainbow1.}pov}}). 


{\small\begin{verbatim}
  #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]
    }
  }
\end{verbatim}}


   Some irregularity is added to the color bands using the {\small\texttt{jitter}} keyword. 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/crainbow} \caption{A colorful rainbow.} \end{figure} 



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


\subsubsection{Increasing the Rainbow's Translucency}

% tutorial/000117.html

\index{Rainbow! increasing translucency of}

   The result we have so far looks much too bright. Just reducing the rainbow's color helps but it is 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 ({\small\texttt{\discretionary{rainbow2.}{}{rainbow2.}pov}}). 


{\small\begin{verbatim}
  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]
    }
  }
\end{verbatim}}


   The transmittance values increase at the outer bands of the rainbow to make it softly blend into the background. 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/rrainbow} \caption{A much more realistic rainbow.} \end{figure} 



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


\subsubsection{Using a Rainbow Arc}

% tutorial/000116.html

\index{Rainbow! using an 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 {\small\texttt{arc\_\-angle}} 
 keyword with an angle below 360 degrees. 



   If you use {\small\texttt{arc\_\-angle 120}} for example you will get a rainbow arc that abruptly vanishes at the arc's ends. This does not look good. To avoid 
 this the {\small\texttt{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 {\small\texttt{falloff\_\-angle}} has to be smaller or equal 
 to the {\small\texttt{arc\_\-angle}}. 



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


{\small\begin{verbatim}
  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]
    }
  }
\end{verbatim}}


   The arc angles are measured against the rainbows up direction which can be specified using the {\small\texttt{up}} keyword. By default the up direction is 
 the y-\discretionary{}{}{}axis. 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/arainbow} \caption{A rainbow arc.} \end{figure} 



   We finally have a realistic looking rainbow arc. 


\section{Simple Media Tutorial}

% tutorial/000304.html

\index{media! tutorial}

   Media in POV-\discretionary{}{}{}Ray is a very versatile feature and can be used for a very diverse set of special effects such as glows, smoke, dust, fog, etc. However, due to 
 its versatility, media is not one of the easiest and simplest features of POV-\discretionary{}{}{}Ray and often requires experience for getting things to look good. 


\subsection{Types of media}

% tutorial/000305.html



   There are three types of media in POV-\discretionary{}{}{}Ray: Emitting, absorbing and scattering. They have the following properties: 


\begin{itemize}
 
 \item 
   Emitting: This is an additive media, which is handled as if it only emits light (note: it does not emit light to its surroundings like a {\small\texttt{light\_\-source}} 
  does; this just describes how it affects the rays going through it). That is, the color of the media is added to the color of the ray passing through it. 
  Light sources do not have any effect at all in it (ie. it does not affect shadows in any way). 
 

 \item 
   Absorbing: This is a substractive media. This media substracts (absorbs) its coloration from the ray passing through it. Light sources are taken into 
  account only in the shadow of the media (that is, absorbing media casts a shadow). 
 

 \item 
   Scattering: This is the most advanced media type as it fully takes into account light passing through it. That is, this media is lit by light sources 
  (and thus, for example, nearby objects can cast shadows into the scattering media). 
 

\end{itemize}


   Emitting and absorbing medias are the simplest and thus fastest ones. Emitting media can be used for things like glows, lasers, sparkles and similar 
 light-\discretionary{}{}{}emitting effects. Absorbing media can be used for things like smoke and fog (the difference between the {\small\texttt{fog}} feature 
 of POV-\discretionary{}{}{}Ray is that the density of an absorbing media can be modified by a pattern and the media can be contained inside an object). 



   Scattering media is the more advanced and slower type. It is somewhat similar to absorbing media except that it is fully lit by light sources. This can be 
 used for smoke or fog with visible lightbeams and shadows. 


\subsection{Some media concepts}

% tutorial/000306.html



   Media can be global to the whole universe, or it can be contained by an object. In the latter case the media is defined in the {\small\texttt{interior}} 
 block of the object definition. 



   For an object to be able to contain media (or to allow media from other objects or the global media inside itself) it has to be defined as {\small\texttt{hollow}} 
 (a common mistake is to forget adding this keyword). If an object with no media should not allow media inside itself (eg. a solid glass ball), then {\small\texttt{hollow}} 
 should not be defined for that object. 



   If media is defined in the {\small\texttt{interior}} of an object or as a global media it will have a constant density throughout the object/universe. 
 However, a density pattern can be specified for non-\discretionary{}{}{}uniform media. Also all kinds of transformations can be applied to the media. This is specially useful for 
 various effects (such as smoke with certain shape). 


\subsection{Simple media examples}

% tutorial/000307.html


\subsubsection{Emitting media}

% tutorial/000308.html



   Let's start with a very simple scene showing an emitting media using a spherical density map. Emitting media is used with the {\small\texttt{emission}} 
 keyword followed by a color value. This color value tells the overall color of the media: 


{\small\begin{verbatim}
 global_settings { assumed_gamma 1 }
 background { rgb 1 }
 camera { location <3,4,-5>*.8 look_at 0 angle 35 }
 light_source { <20,40,10>, 1 }

 box // floor
 { <-1.5,-1.01,-1.5>, <1.5,-1.2,1.5>
   pigment { checker rgb 0.75, rgb 0.25 scale 0.2 }
 }

 sphere // transparent sphere containing media
 { 0,1 pigment { rgbt 1 } hollow
   interior
   { media
     { emission 1
       density
       { spherical density_map
         { [0 rgb 0]
           [0.4 rgb <1,0,0>]
           [0.8 rgb <1,1,0>]
           [1 rgb 1]
         }
       }
     }
  }
 }
\end{verbatim}}


   Note that the {\small\texttt{spherical}} pattern gets values from 0 in the outer surface of a unit sphere to 1 in the origin (that is, the density with the 
 index value 1 will be the density at the center of the media). 



   The color values in the density map tell what color the media is emitting at a certain point in the pattern. That is, for example when the pattern gets the 
 value 0.4, the media will be completely red at that place. If the color is {\small\texttt{$<$\discretionary{0,}{}{0,}\discretionary{0,}{}{0,}0$>$}}, it means that the media does not emit any light at 
 all in that location. 



   Note that the density map colors are multiplied by the color given with the {\small\texttt{emission}} keyword; since 1 is used in this case, the density map 
 colors are not affected. 



   Thus, this will give us a media with a bright white center which fades to yellow and red at the outer limits of the unit sphere: 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/mediatut1} \caption{Simple emitting media example} \end{figure} 



   As you can see from the image, the emitting media is invisible against white background. This is due to its additive nature (any color added to pure white 
 gives pure white). In fact, emitting media gives usually best results for dark backgrounds. 


\subsubsection{Absorbing media}

% tutorial/000309.html



   Modifying the previous example to use absorbing media is rather simple: Simply change the {\small\texttt{emission}} keyword for {\small\texttt{absorption}}. 
 However, the colors we used above are not very illustrative for absorbing media, so let's change them a bit like this: 


{\small\begin{verbatim}
    media
    { absorption 1
      density
      { spherical density_map
        { [0 rgb 0]
          [0.4 rgb 0]
          [0.5 rgb <0,0.5,1>]
          [1 rgb <0,1,1>]
        }
      }
    }
\end{verbatim}}


   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/mediatut2} \caption{Simple absorbing media example} \end{figure} 



   The feature which we immediately notice in the image is that the media seems to be inverted from the colors specified in the density map: Blueish colors were 
 specified in the map, but the image shows a reddish media. This is perfectly normal and to be expected from the substractive nature of absorbing media: The 
 media actually absorbs the colors we specified in the density map. This means that for example specifying a white color ({\small\texttt{$<$\discretionary{1,}{}{1,}\discretionary{1,}{}{1,}1$>$}}) in 
 the density map will absorb all colors, thus resulting in a dark media. 



   Note how this media has a shadow: light rays passing through the media are absorbed. 



   Because of its substractive nature, absorbing media works well with light backgrounds and not very well with dark ones. 


\subsubsection{Scattering media}

% tutorial/000310.html



   Since scattering media fully takes light sources into account we need to make a slightly more complex scene to see this. Let's modify the above example by 
 replacing the sphere with a box containing evenly distributed scattering media, and a cylinder which will cast a shadow onto the media: 


{\small\begin{verbatim}
 box
 { -1,1 pigment { rgbt 1 } hollow
   interior
   { media
     { scattering { 1, 0.5 }
     }
   }
 }
 cylinder
 { <0.9, -1, 0.7>, <0.9, 0.9, 0.7>, 0.5
   pigment { rgb <1, 0.8, 0.5> }
 }
\end{verbatim}}


   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/mediatut3} \caption{Simple scattering media example} \end{figure} 



   (The effect may look a bit unnatural for a fog effect because the media is contained inside a box and the cylinder is partially out of this box, but this is 
 done to better visualize what is happening.) 



   The {\small\texttt{scattering}} keyword takes more parameters than the other two. The first number inside the curly brackets is the scattering media type. In 
 this example we used scattering media type 1. A full list of scattering media types is given in the section {\small\texttt{ scattering }} of the Media 
 reference. 



   The second parameter is the overall color of the media, similar to the parameter of the other two media types. 



   An optional third parameter can be given with the {\small\texttt{extinction}} keyword inside the curly brackets. This keyword controls how fast the 
 scattering media absorbs light and has to be used sometimes to get the desired effect, such as when the media absorbs too much light. 



   Tip: If you are getting a really dense or dark scattering media, try different values for the color and the extinction value (usually values between 0 and 
 1). It is usually enough to play with these two values to get the desired effect. 


\subsection{Multiple medias inside the same object}

% tutorial/000311.html



   Emitting media works well with dark backgrounds. Absorbing media works well for light backgrounds. But what if we want a media which works with both type of 
 backgrounds? 



   One solution for this is to use both types of medias inside the same object. This is possible in POV-\discretionary{}{}{}Ray. 



   Let's take the very first example, which did not work well with the white background, and add a slightly absorbing media to the sphere: 


{\small\begin{verbatim}
 sphere
 { 0,1 pigment { rgbt 1 } hollow
   interior
   { media
     { emission 1
       density
       { spherical density_map
         { [0 rgb 0]
           [0.4 rgb <1,0,0>]
           [0.8 rgb <1,1,0>]
           [1 rgb 1]
         }
       }
     }
     media
     { absorption 0.2
     }
   }
 }
\end{verbatim}}


   This will make the sphere not only add light to the rays passing through it, but also substract. 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/mediatut4} \caption{Emitting and absorbing media example} \end{figure} 



   Multiple medias in the same object can be used for several other effects as well. 


\subsection{Media and transformations}

% tutorial/000312.html



   The density of a media can be modified with any pattern modifier, such as turbulence, scale, etc. This is a very powerful tool for making diverse effects. 



   As an example, let's make an absorbing media which looks like smoke. For this we take the absorbing media example and modify the sphere like this: 


{\small\begin{verbatim}
 sphere
 { 0,1.5 pigment { rgbt 1 } hollow
   interior
   { media
     { absorption 7
       density
       { spherical density_map
         { [0 rgb 0]
           [0.5 rgb 0]
           [0.7 rgb .5]
           [1 rgb 1]
         }
         scale 1/2
         warp { turbulence 0.5 }
         scale 2
       }
     }
   }
   scale <1.5,6,1.5> translate y
 }
\end{verbatim}}


   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/mediatut5} \caption{Media transformation example} \end{figure} 



   A couple of notes: 



   The radius of the sphere is now a bit bigger than 1 because the turbulented pattern tends to take more space. 



   The absorption color can be larger than 1, making the absorption stronger and the smoke darker. 



   \textbf{Note:} When you scale an object containing media the media density is not scaled accordingly. This means that if you for example scale a container 
 object larger the rays will pass through more media than before, giving a stronger result. If you want to keep the same media effect with the larger object, 
 you will need to divide the color of the media by the scaling amount. 



   The question of whether the program should scale the density of the media with the object is a question of interpretation: For example, if you have a glass 
 of colored water, a larger glass of colored water will be more colored because the light travels a larger distance. This is how POV-\discretionary{}{}{}Ray behaves. Sometimes, 
 however, the object needs to be scaled so that the media does not change; in this case the media color needs to be scaled inversely. 


\subsection{A more advanced example of scattering media}

% tutorial/000313.html



   For a bit more advanced example of scattering media, let's make a room with a window and a light source illuminating from outside the room. The room contains 
 scattering media, thus making the light beam coming through the window visible. 


{\small\begin{verbatim}
 global_settings { assumed_gamma 1 }
 camera { location <14.9, 1, -8> look_at -z angle 70 }
 light_source { <10,100,150>, 1 }
 background { rgb <0.3, 0.6, 0.9> }

 // A dim light source inside the room which does not
 // interact with media so that we can see the room:
 light_source { <14, -5, 2>, 0.5 media_interaction off }

 // Room
 union
 { difference
   { box { <-11, -7, -11>, <16, 7, 10.5> }
     box { <-10, -6, -10>, <15, 6, 10> }
     box { <-4, -2, 9.9>, <2, 3, 10.6> }
   }
   box { <-1.25, -2, 10>, <-0.75, 3, 10.5> }
   box { <-4, 0.25, 10>, <2, 0.75, 10.5> }
   pigment { rgb 1 }
 }
 
 // Scattering media box:
 box
 { <-5, -6.5, -10.5>, <3, 6.5, 10.25>
   pigment { rgbt 1 } hollow
   interior
   { media
     { scattering { 1, 0.07 extinction 0.01 }
       samples 30,100
     }
   }
 }
\end{verbatim}}


   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/mediatut6} \caption{More advanced scattering media example} \end{figure} 



   As suggested previously, the scattering color and extinction values were adjusted until the image looked good. In this kind of scene usually very small 
 values are needed. 



   Note how the container box is quite smaller than the room itself. Container boxes should always be sized as minimally as possible. If the box were as big as 
 the room much higher values for {\small\texttt{samples}} would be needed for a good result, thus resulting in a much slower rendering. 


\subsection{Media and photons}

% tutorial/000314.html



   The photon mapping technique can be used in POV-\discretionary{}{}{}Ray for making stunningly beautiful images with light reflecting and refracting from objects. By default, 
 however, reflected and refracted light does not affect media. Making photons interact with media can be turned on with the {\small\texttt{media}} keyword in 
 the {\small\texttt{photons}} block inside {\small\texttt{global\_\-settings}}. 



   To visualize this, let's make the floor of our room reflective so that it will reflect the beam of light coming from the window. 



   Firstly, due to how photons work, we need to specify {\small\texttt{photons \{ pass\_\-through \}}} in our scattering media container box so that photons will 
 pass through its surfaces. 



   Secondly, we will want to turn photons off for our fill-\discretionary{}{}{}light since it's there only for us to see the interior of the room and not for the actual lighting 
 effect. This can be done by specifying {\small\texttt{photons \{ reflection off \}}} in that light source. 



   Thirdly, we need to set up the photons and add a reflective floor to the room. Let's make the reflection colored for extra effect: 


{\small\begin{verbatim}
 global_settings
 { photons
   { count 20000
     media 100
   }
 }
 
 // Reflective floor:
 box
 { <-10, -5.99, -10>, <15, -6, 10>
   pigment { rgb 1 }
   finish { reflection <0.5, 0.4, 0.2> }
   photons { target reflection on }
 }
\end{verbatim}}


   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/mediatut7} \caption{Scattering media with photons example} \end{figure} 



   With all these fancy effects the render times start becoming quite high, but unfortunately this is a price which has to be paid for such effects. 


\section{Radiosity}

% tutorial/000124.html

\index{Radiosity! tutorial}
\subsection{Introduction}

% tutorial/000159.html



   Radiosity is a lighting technique to simulate the diffuse exchange of radiation between the objects of a scene. With a raytracer like POV-\discretionary{}{}{}Ray, normally only 
 the direct influence of light sources on the objects can be calculated, all shadowed parts look totally flat. Radiosity can help to overcome this limitation. 
 More details on the technical aspects can be found in the reference section. 



   To enable radiosity, you have to add a radiosity block to the global\_\-settings in your POV-\discretionary{}{}{}Ray scene file. Radiosity is more accurate than simplistic ambient 
 light but it takes much longer to compute, so it can be useful to switch off radiosity during scene development. You can use a declared constant or an INI-\discretionary{}{}{}file 
 constant and an {\small\texttt{\#if}} statement to do this: 


{\small\begin{verbatim}
  #declare RAD = off;

  global_settings {
     #if(RAD)
        radiosity {
           ...
        }
     #end
  }
\end{verbatim}}


   Most important for radiosity are the ambient and diffuse finish components of the objects. Their effect differs quite much from a conventionally lit scene. 


\begin{itemize}
 
 \item 
   {\small\texttt{ambient}}: specifies the amount of light emitted by the object. This is the basis for radiosity without conventional lighting but also 
  in scenes with light sources this can be important. Since most materials do not actually emit light, the default value of {\small\texttt{0.1}} is too high in 
  most cases. You can also change ambient\_\-light to influence this. 
 

 \item 
   {\small\texttt{diffuse}}: influences the amount of diffuse reflection of incoming light. In a radiosity scene this does not only mean the direct 
  appearance of the surface but also how much other objects are illuminated by indirect light from this surface. 
 

\end{itemize}

\subsection{Radiosity with conventional lighting}

% tutorial/000163.html

\index{Radiosity! with conventional lighting}

   The pictures here introduce combined conventional/radiosity lighting. Later on you can also find examples for pure radiosity illumination. 



   The following settings are default, the result will be the same with an empty radiosity block: 


{\small\begin{verbatim}
  global_settings {
    radiosity {
      pretrace_start 0.08
      pretrace_end   0.04
      count 35

      nearest_count 5
      error_bound 1.8
      recursion_limit 3

      low_error_factor 0.5
      gray_threshold 0.0
      minimum_reuse 0.015
      brightness 1

      adc_bailout 0.01/2
    }
  }
\end{verbatim}}


   The following pictures are rendered with default settings and are made to introduce the sample scene. 



   All objects except the sky have an ambient finish of 0. 



   The {\small\texttt{ambient 1}} finish of the blue sky makes it functioning as some kind of diffuse light source. This leads to a bluish touch of the whole 
 scene in the radiosity version. 


\begin{center} \begin{tabular*}{402pt}[t]{@{} p{133pt}@{} p{133pt}@{} p{133pt}@{} }
 
 
  
  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_01} \newline no radiosity 
  } & 

  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_03} \newline radiosity (default settings) 
  } & 
{\raggedleft  \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_03a} \newline difference w/o radiosity } \\ 
 

\end{tabular*} \end{center}


   You can see that radiosity much affects the shadowed parts when applied combined with conventional lighting. 



   Changing {\small\texttt{brightness}} changes the intensity of radiosity effects. {\small\texttt{brightness 0}} would be the same as without radiosity. {\small\texttt{brightness 
 1}} should work correctly in most cases, if effects are too strong you can reduce this. Larger values lead to quite strange results in most cases. 


\begin{center} \begin{tabular*}{402pt}[t]{@{} p{133pt}@{} p{133pt}@{} p{133pt}@{} }
 
 
  
  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_04} \newline brightness 0.5 
  } & 

  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_03} \newline brightness 1.0 
  } & 
{\raggedleft  \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_05} \newline brightness 2.0 } \\ 
 

\end{tabular*} \end{center}


   Changing the {\small\texttt{recursion\_\-limit}} value leads to the following results, second line are difference to default ({\small\texttt{recursion\_\-limit 3}}): 
 


\begin{center} \begin{tabular*}{402pt}[t]{@{} p{133pt}@{} p{133pt}@{} p{133pt}@{} }
 
 
  
  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_06} \newline recursion\_\-limit 1 
  } & 

  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_07} \newline recursion\_\-limit 2 
  } & 
{\raggedleft  \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_08} \newline recursion\_\-limit 5 } \\ 
 

\end{tabular*} \end{center}

\begin{center} \begin{tabular*}{402pt}[t]{@{} p{133pt}@{} p{133pt}@{} p{133pt}@{} }
 
 
  
  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_06a} \newline recursion\_\-limit 1 (difference) 
  } & 

  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_07a} \newline recursion\_\-limit 2 (difference) 
  } & 
{\raggedleft  \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_08a} \newline recursion\_\-limit 5 (difference) } \\ 
 

\end{tabular*} \end{center}


   You can see that higher values than the default of 3 do not lead to much better results in such a quite simple scene. In most cases values of 1 or 2 are 
 sufficient. 



   The {\small\texttt{error\_\-bound}} value mainly affects the structures of the shadows. Values larger than the default of 1.8 do not have much effects, they 
 make the shadows even flatter. Extremely low values can lead to very good results, but the rendering time can become very long. For the following samples {\small\texttt{recursion\_\-limit 
 1}} is used. 


\begin{center} \begin{tabular*}{402pt}[t]{@{} p{133pt}@{} p{133pt}@{} p{133pt}@{} }
 
 
  
  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_09} \newline error\_\-bound 0.01 
  } & 

  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_10} \newline error\_\-bound 0.5 
  } & 
{\raggedleft  \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_11} \newline error\_\-bound 1.0 } \\ 
 

\end{tabular*} \end{center}

\begin{center} \begin{tabular*}{402pt}[t]{@{} p{133pt}@{} p{133pt}@{} p{133pt}@{} }
 
 
  
  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_09a} \newline error\_\-bound 0.01 (difference) 
  } & 

  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_10a} \newline error\_\-bound 0.5 (difference) 
  } & 
{\raggedleft  \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_11a} \newline error\_\-bound 1.0 (difference) } \\ 
 

\end{tabular*} \end{center}


   Somewhat related to {\small\texttt{error\_\-bound}} is {\small\texttt{low\_\-error\_\-factor}}. It reduces error\_\-bound during the last pretrace step. Changing this 
 can be useful to eliminate artefacts. 


\begin{center} \begin{tabular*}{402pt}[t]{@{} p{133pt}@{} p{133pt}@{} p{133pt}@{} }
 
 
  
  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_12} \newline low\_\-error\_\-factor 0.01 
  } & 

  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_13} \newline low\_\-error\_\-factor 0.5 
  } & 
{\raggedleft  \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_14} \newline low\_\-error\_\-factor 1.0 } \\ 
 

\end{tabular*} \end{center}

\begin{center} \begin{tabular*}{402pt}[t]{@{} p{133pt}@{} p{133pt}@{} p{133pt}@{} }
 
 
  
  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_12a} \newline low\_\-error\_\-factor 0.01 (difference) 
  } & 

  {\raggedleft 
      
  } & 
{\raggedleft  \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_14a} \newline low\_\-error\_\-factor 1.0 (difference) } \\ 
 

\end{tabular*} \end{center}


   The next samples use {\small\texttt{recursion\_\-limit 1}} and {\small\texttt{error\_\-bound 0.2}}. These 3 pictures illustrate the effect of {\small\texttt{count}}. 
 It is a general quality and accuracy parameter leading to higher quality and slower rendering at higher values. 


\begin{center} \begin{tabular*}{402pt}[t]{@{} p{133pt}@{} p{133pt}@{} p{133pt}@{} }
 
 
  
  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_15} \newline count 2 
  } & 

  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_13a} \newline count 35 (default) 
  } & 
{\raggedleft  \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_16} \newline count 300 } \\ 
 

\end{tabular*} \end{center}


   Another parameter that affects quality is {\small\texttt{nearest\_\-count}}. You can use values from 1 to 20, default is 5: 


\begin{center} \begin{tabular*}{402pt}[t]{@{} p{133pt}@{} p{133pt}@{} p{133pt}@{} }
 
 
  
  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_17} \newline nearest\_\-count 1 
  } & 

  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_13a} \newline nearest\_\-count 5 
  } & 
{\raggedleft  \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_18} \newline nearest\_\-count 10 } \\ 
 

\end{tabular*} \end{center}


   Again higher values lead to less artefacts and smoother appearance but slower rendering. 



   {\small\texttt{minimum\_\-reuse}} influences whether previous radiosity samples are reused during calculation. It also affects quality and smoothness. 


\begin{center} \begin{tabular*}{402pt}[t]{@{} p{133pt}@{} p{133pt}@{} p{133pt}@{} }
 
 
  
  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_19} \newline minimum\_\-reuse 0.2 
  } & 

  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_13a} \newline minimum\_\-reuse 0.015 
  } & 
{\raggedleft  \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_20} \newline minimum\_\-reuse 0.005 } \\ 
 

\end{tabular*} \end{center}

\begin{center} \begin{tabular*}{402pt}[t]{@{} p{133pt}@{} p{133pt}@{} p{133pt}@{} }
 
 
  
  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_19a} \newline minimum\_\-reuse 0.2 (difference) 
  } & 

  {\raggedleft 
      
  } & 
{\raggedleft  \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_20a} \newline minimum\_\-reuse 0.005 (difference) } \\ 
 

\end{tabular*} \end{center}


   Another important value is {\small\texttt{pretrace\_\-end}}. It specifies how many pretrace steps are calculated and thereby strongly influences the speed. 
 Usually lower values lead to better quality, but it is important to keep this in good relation to {\small\texttt{error\_\-bound}}. 


\begin{center} \begin{tabular*}{402pt}[t]{@{} p{133pt}@{} p{133pt}@{} p{133pt}@{} }
 
 
  
  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_21} \newline pretrace\_\-end 0.2 
  } & 

  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_13a} \newline pretrace\_\-end 0.04 
  } & 
{\raggedleft  \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_22} \newline pretrace\_\-end 0.002 } \\ 
 

\end{tabular*} \end{center}


   Strongly related to {\small\texttt{pretrace\_\-end}} is {\small\texttt{always\_\-sample}}. Normally even in the final trace additional radiosity samples are taken. 
 You can avoid this by adding {\small\texttt{always\_\-sample off}}. That is especially useful if you load previously calculated radiosity data with {\small\texttt{load\_\-file}}. 
 


\begin{center} \begin{tabular*}{402pt}[t]{@{} p{133pt}@{} p{133pt}@{} p{133pt}@{} }
 
 
  
  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_13a} \newline always\_\-sample on 
  } & 

  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_23} \newline always\_\-sample off 
  } & 
{\raggedleft  \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_23a} \newline always\_\-sample off (difference) } \\ 
 

\end{tabular*} \end{center}


   The effect of {\small\texttt{max\_\-sample}} is similar to {\small\texttt{brightness}}. It does not reduce the radiosity effect in general but weakens samples 
 with brightness above the specified value. 


\begin{center} \begin{tabular*}{402pt}[t]{@{} p{133pt}@{} p{133pt}@{} p{133pt}@{} }
 
 
  
  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_24} \newline max\_\-sample 0.5 
  } & 

  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_25} \newline max\_\-sample 0.8 
  } & 
{\raggedleft  \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_13a} \newline default } \\ 
 

\end{tabular*} \end{center}


   You can strongly affect things with the objects' finishes. In fact that is the most important thing about radiosity. Normal objects should have ambient 
 finish 0 which is not default in POV-\discretionary{}{}{}Ray and therefore needs to be specified. Objects with ambient $>$ 0 actually emit light. 



   Default finish values used until now are {\small\texttt{diffuse 0.65 ambient 0}}. 


\begin{center} \begin{tabular*}{402pt}[t]{@{} p{133pt}@{} p{133pt}@{} p{133pt}@{} }
 
 
  
  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_29} \newline diffuse 0.65 ambient 0.2 
  } & 

  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_30} \newline diffuse 0.4 ambient 0 
  } & 
{\raggedleft  \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_31} \newline diffuse 1.0 ambient 0 } \\ 
 

\end{tabular*} \end{center}


   Finally you can vary the sky in outdoor radiosity scenes. In all these examples it is implemented with a sphere object. {\small\texttt{finish \{ ambient 1 
 diffuse 0 \}}} was used until now. The following pictures show some variations: 


\begin{center} \begin{tabular*}{402pt}[t]{@{} p{133pt}@{} p{133pt}@{} p{133pt}@{} }
 
 
  
  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_27} \newline ambient 0 diffuse 1 
  } & 

  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_26} \newline ambient 0 diffuse 0 (no sky) 
  } & 
{\raggedleft  \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_28} \newline yellow-\discretionary{}{}{}blue gradient } \\ 
 

\end{tabular*} \end{center}

\subsection{Radiosity without conventional lighting}

% tutorial/000162.html

\index{Radiosity! without conventional lighting}

   You can also leave out all light sources and have pure radiosity lighting. The situation then is similar to a cloudy day outside, when the light comes from 
 no specific direction but from the whole sky. 



   The following 2 pictures show what changes with the scene used in part 1, when the light source is removed. (default radiosity, but {\small\texttt{recursion\_\-limit 
 1}} and {\small\texttt{error\_\-bound 0.2}}) 


\begin{center} \begin{tabular*}{410pt}[t]{@{} p{205pt}@{} p{205pt}@{} }
 
 
  
  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radA_10} \newline with light source 
  } & 
{\raggedleft  \includegraphics[scale=0.40]{../final/tex/images/tutorial/radB_01} \newline without light source } \\ 
 

\end{tabular*} \end{center}


   You can see that when the light source is removed the whole picture becomes very blue, because the scene is illuminated by a blue sky, while on a cloudy day, 
 the color of the sky should be somewhere between grey and white. 



   The following pictures show the sample scene used in this part with different settings for {\small\texttt{recursion\_\-limit}} (everything else default 
 settings). 


\begin{center} \begin{tabular*}{402pt}[t]{@{} p{133pt}@{} p{133pt}@{} p{133pt}@{} }
 
 
  
  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radB_02} \newline recursion\_\-limit 1 
  } & 

  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radB_03} \newline recursion\_\-limit 2 
  } & 
{\raggedleft  \includegraphics[scale=0.40]{../final/tex/images/tutorial/radB_04} \newline recursion\_\-limit 3 } \\ 
 

\end{tabular*} \end{center}


   This looks much worse than in the first part, because the default settings are mainly selected for use with conventional light sources. 



   The next three pictures show the effect of {\small\texttt{error\_\-bound}}. ({\small\texttt{recursion\_\-limit}} is 1 here) Without light sources, this is even 
 more important than with, good values much depend on the scenery and the other settings, lower values do not necessarily lead to better results. 


\begin{center} \begin{tabular*}{402pt}[t]{@{} p{133pt}@{} p{133pt}@{} p{133pt}@{} }
 
 
  
  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radB_02} \newline error\_\-bound 1.8 
  } & 

  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radB_05} \newline error\_\-bound 0.4 
  } & 
{\raggedleft  \includegraphics[scale=0.40]{../final/tex/images/tutorial/radB_06} \newline error\_\-bound 0.02 } \\ 
 

\end{tabular*} \end{center}


   If there are artefacts it often helps to increase {\small\texttt{count}}, it does affect quality in general and often helps removing them (the following 
 three pictures use {\small\texttt{error\_\-bound 0.02}}). 


\begin{center} \begin{tabular*}{402pt}[t]{@{} p{133pt}@{} p{133pt}@{} p{133pt}@{} }
 
 
  
  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radB_07} \newline count 2 
  } & 

  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radB_08} \newline count 50 
  } & 
{\raggedleft  \includegraphics[scale=0.40]{../final/tex/images/tutorial/radB_09} \newline count 200 } \\ 
 

\end{tabular*} \end{center}


   The next sequence shows the effect of {\small\texttt{nearest\_\-count}}, the difference is not very strong, but larger values always lead to better results 
 (maximum is 20). From now on all the pictures use {\small\texttt{error\_\-bound 0.2}} 


\begin{center} \begin{tabular*}{402pt}[t]{@{} p{133pt}@{} p{133pt}@{} p{133pt}@{} }
 
 
  
  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radB_11} \newline nearest\_\-count 2 
  } & 

  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radB_10} \newline nearest\_\-count 5 (default) 
  } & 
{\raggedleft  \includegraphics[scale=0.40]{../final/tex/images/tutorial/radB_12} \newline nearest\_\-count 10 } \\ 
 

\end{tabular*} \end{center}


   The {\small\texttt{minimum\_\-reuse}} is a geometric value related to the size of the render in pixel and affects whether previous radiosity calculations are 
 reused at a new point. Lower values lead to more often and therefore more accurate calculations. 


\begin{center} \begin{tabular*}{402pt}[t]{@{} p{133pt}@{} p{133pt}@{} p{133pt}@{} }
 
 
  
  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radB_13} \newline minimum\_\-reuse 0.001 
  } & 

  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radB_10} \newline minimum\_\-reuse 0.015 (default) 
  } & 
{\raggedleft  \includegraphics[scale=0.40]{../final/tex/images/tutorial/radB_14} \newline minimum\_\-reuse 0.1 } \\ 
 

\end{tabular*} \end{center}


   In most cases it is not necessary to change the {\small\texttt{low\_\-error\_\-factor}}. This factor reduces the error\_\-bound value during the final pretrace step. {\small\texttt{pretrace\_\-end}} 
 was lowered to {\small\texttt{0.01}} in these pictures, the second line shows the difference to default. Changing this value can sometimes help to remove 
 persistent artefacts. 


\begin{center} \begin{tabular*}{402pt}[t]{@{} p{133pt}@{} p{133pt}@{} p{133pt}@{} }
 
 
  
  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radB_15} \newline low\_\-error\_\-factor 0.01 
  } & 

  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radB_16} \newline low\_\-error\_\-factor 0.5 (default) 
  } & 
{\raggedleft  \includegraphics[scale=0.40]{../final/tex/images/tutorial/radB_17} \newline low\_\-error\_\-factor 1.0 } \\ 
 

\end{tabular*} \end{center}

\begin{center} \begin{tabular*}{402pt}[t]{@{} p{133pt}@{} p{133pt}@{} p{133pt}@{} }
 
 
  
  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radB_15a} \newline low\_\-error\_\-factor 0.01 
  } & 

  {\raggedleft 
      
  } & 
{\raggedleft  \includegraphics[scale=0.40]{../final/tex/images/tutorial/radB_17a} \newline low\_\-error\_\-factor 1.0 } \\ 
 

\end{tabular*} \end{center}


   {\small\texttt{gray\_\-threshold}} reduces the color in the radiosity calculations. as mentioned above the blue sky affects the color of the whole scene when 
 radiosity is calculated. To reduce this coloring effect without affecting radiosity in general you can increase {\small\texttt{gray\_\-threshold}}. 1.0 means no 
 color in radiosity at all. 


\begin{center} \begin{tabular*}{402pt}[t]{@{} p{133pt}@{} p{133pt}@{} p{133pt}@{} }
 
 
  
  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radB_10} \newline gray\_\-threshold 0.0 (default) 
  } & 

  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radB_18} \newline gray\_\-threshold 0.5 
  } & 
{\raggedleft  \includegraphics[scale=0.40]{../final/tex/images/tutorial/radB_19} \newline gray\_\-threshold 1.0 } \\ 
 

\end{tabular*} \end{center}


   Another important parameter is {\small\texttt{pretrace\_\-end}}. Together with pretrace\_\-start it specifies the pretrace steps that are done. Lower values lead 
 to more pretrace steps and more accurate results but also to significantly slower rendering. 


\begin{center} \begin{tabular*}{402pt}[t]{@{} p{133pt}@{} p{133pt}@{} p{133pt}@{} }
 
 
  
  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radB_26} \newline pretrace\_\-end 0.2 
  } & 

  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radB_27} \newline pretrace\_\-end 0.02 
  } & 
{\raggedleft  \includegraphics[scale=0.40]{../final/tex/images/tutorial/radB_28} \newline pretrace\_\-end 0.004 } \\ 
 

\end{tabular*} \end{center}


   It is worth experimenting with the things affecting radiosity to get some feeling for how things work. The next 3 images show some more experiments. 


\begin{center} \begin{tabular*}{402pt}[t]{@{} p{133pt}@{} p{133pt}@{} p{133pt}@{} }
 
 
  
  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radB_23} \newline ambient 3 instead of ambient 0 for one object 
  } & 

  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radB_24} \newline ambient 0.5 instead of ambient 0 for all objects sky: ambient 0 
  } & 
{\raggedleft  \includegraphics[scale=0.40]{../final/tex/images/tutorial/radB_25} \newline error\_\-bound 0.04 recursion\_\-limit 2 } \\ 
 

\end{tabular*} \end{center}


   Finally you can strongly change the appearance of the whole scene with the sky's texture. The following pictures give some example. 


\begin{center} \begin{tabular*}{402pt}[t]{@{} p{133pt}@{} p{133pt}@{} p{133pt}@{} }
 
 
  
  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radB_20} \newline yellow-\discretionary{}{}{}blue gradient from left to right 
  } & 

  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radB_21} \newline light-\discretionary{}{}{}dark gradient from left to right 
  } & 
{\raggedleft  \includegraphics[scale=0.40]{../final/tex/images/tutorial/radB_22} \newline light-\discretionary{}{}{}dark gradient from bottom to top } \\ 
 

\end{tabular*} \end{center}


   Really good results much depend on the single situation and how the scene is meant to look. Here is some "higher quality" render of this particular 
 scene, but requirements can be much different in other situations. 


{\small\begin{verbatim}
  global_settings {
    radiosity {
      pretrace_start 0.08
      pretrace_end   0.01
      count 500

      nearest_count 10
      error_bound 0.02
      recursion_limit 1

      low_error_factor 0.2
      gray_threshold 0.0
      minimum_reuse 0.015
      brightness 1

      adc_bailout 0.01/2
    }
  }
\end{verbatim}}


   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/radB_X} \caption{Higher quality radiosity scene} \end{figure} 


\subsection{Normals and Radiosity}

% tutorial/000161.html

\index{Normals and Radiosity}

   When using a normal statement in combination with radiosity lighting, you will see that the shadowed parts of the objects are totally smooth, no matter how 
 strong the normals are made. 



   The reason is that POV-\discretionary{}{}{}Ray by default does not take the normal into account when calculating radiosity. You can change this by adding {\small\texttt{normal on}} 
 to the radiosity block. This can slow things down quite a lot, but usually leads to more realistic results if normals are used. 



   When using normals you should also remember that they are only faked irregularities and do not generate real geometric disturbances of the surface. A more 
 realistic approach is using an isosurface with a pigment function, but this usually leads to very slow renders, especially if radiosity is involved. 


\begin{center} \begin{tabular*}{402pt}[t]{@{} p{133pt}@{} p{133pt}@{} p{133pt}@{} }
 
 
  
  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radC_01} \newline normal off (default) 
  } & 

  {\raggedleft 
    \includegraphics[scale=0.40]{../final/tex/images/tutorial/radC_02} \newline normal on 
  } & 
{\raggedleft  \includegraphics[scale=0.40]{../final/tex/images/tutorial/radC_03} \newline isosurface } \\ 
 

\end{tabular*} \end{center}


   You can see that the isosurface version does not have a natural smooth circumference and a more realistic shadowline. 


\subsection{Performance considerations}

% tutorial/000160.html

\index{Radiosity performance considerations}

   Radiosity can be very slow. To some extend this is the price to pay for realistic lighting, but there are a lot of things that can be done to improve speed. 



   The radiosity settings should be set as fast as possible. In most cases this is a quality vs. speed compromise. Especially {\small\texttt{recursion\_\-limit}} 
 should be kept as low as possible. Sometimes {\small\texttt{1}} is sufficient, if not {\small\texttt{2}} or {\small\texttt{3}} should often be enough. 



   With high quality settings, radiosity data can take quite a lot of memory. Apart from that the other scene data is also used much more intensive than in a 
 conventional scene. Therefore insufficient memory and swapping can slow down things even more. 



   Finally the scene geometry and textures are important too. Objects not visible in the camera usually only increase parsing time and memory use, but in a 
 radiosity scene, also objects behind the camera can slow down the rendering process. 


\section{Making Animations}

% tutorial/000118.html



   There are a number of programs available that will take a series of still image files (such as POV-\discretionary{}{}{}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-\discretionary{}{}{}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-\discretionary{}{}{}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-\discretionary{}{}{}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 have already worked with animation in previous versions of POV-\discretionary{}{}{}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. 


\subsection{The Clock Variable: Key To It All}

% tutorial/000119.html

\index{Animation! clock variable}

   POV-\discretionary{}{}{}Ray supports an automatically declared floating point variable identified as {\small\texttt{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 {\small\texttt{+k}} switch. For example, {\small\texttt{ +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 {\small\texttt{Clock=3.4}} in an INI file. 



   If we do not 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 is 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-\discretionary{}{}{}axis. We would have 
 the statement 


{\small\begin{verbatim}
  translate <clock, 0, 0>
\end{verbatim}}


   in our object's declaration, and then have the animation loop assign progressively higher values to clock. And that is 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 
 are 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 


{\small\begin{verbatim}
  #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>
  }
\end{verbatim}}


   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: 


\begin{enumerate}
 
 \item 
   Translate the ball from point A to point B, and, 
 

 \item 
   Rotate the ball in exactly the right proportion to its linear movement to imply that it is rolling -- not gliding -- to its final position. 
 

\end{enumerate}


   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, {\small\texttt{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 could not 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-\discretionary{}{}{}translate the sphere by a clock relative distance, causing it to move relative to the starting point. We have 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 have 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. 


\subsection{Clock Dependant Variables And Multi-\discretionary{}{}{}Stage Animations}

% tutorial/000123.html

\index{Animation! multi-\discretionary{}{}{}stage}

   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-\discretionary{}{}{}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... 


{\small\begin{verbatim}
  #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
\end{verbatim}}


   If we spotted the fact that this will cause the ball to do an unrealistic \textit{snap turn} when changing direction, bonus points for us - we are 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 {\small\texttt{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 {\small\texttt{ 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. 


\subsection{The Phase Keyword}

% tutorial/000122.html

\index{phase! tutorial}

   There is another keyword we should know for purposes of animations: the {\small\texttt{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: 


{\small\begin{verbatim}
  color_map {
    [0.00 White ]
    [0.25 Blue ]
    [0.76 Green ]
    [1.00 Red ]
  }
\end{verbatim}}


   The floating point value to the left inside each set of brackets helps POV-\discretionary{}{}{}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 {\small\texttt{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 


{\small\begin{verbatim}
  #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 }
  }
\end{verbatim}}


   Now, here we have created a simple blue flag with a gradient normal pattern on it. We have forced the gradient to use a sine-\discretionary{}{}{}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 has been set to take the clock 
 variable as a floating point value which, as the clock increments slowly toward 1.0, will cause the crests and troughs of the flag's wave to shift along the 
 x-\discretionary{}{}{}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. 


\subsection{Do Not Use Jitter Or Crand}

% tutorial/000121.html

\index{Animation! not using jitter or crand with}\index{jitter! in animations}\index{crand! in animations}

   One last piece of basic information to save frustration. Because jitter is an element of anti-\discretionary{}{}{}aliasing, we could just as easily have mentioned this under the 
 INI file settings section, but there are also forms of anti-\discretionary{}{}{}aliasing used in area lights, and the new atmospheric effects of POV-\discretionary{}{}{}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-\discretionary{}{}{}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 (\discretionary{e.}{}{e.}g., where an infinite plane disappears 
 into the distance). 



   For this reason, we should always set jitter to {\small\texttt{off}} in area lights and anti-\discretionary{}{}{}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 {\small\texttt{crand}}. 


\subsection{INI File Settings}

% tutorial/000120.html

\index{Animation! INI file settings for}\index{initial\_\-frame! ini-\discretionary{}{}{}option, tutorial}\index{final\_\-frame! ini-\discretionary{}{}{}option, tutorial}\index{initial\_\-clock! ini-\discretionary{}{}{}option, tutorial}\index{final\_\-clock! ini-\discretionary{}{}{}option, tutorial}

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



   The first concept we will need to know is the INI file settings, {\small\texttt{Initial\_\-Frame}} and {\small\texttt{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 is an example anyway. We just add the following lines to our favorite INI file 
 settings 


{\small\begin{verbatim}
  Initial_Frame = 1
  Final_Frame = 20
\end{verbatim}}


   and we will 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 is 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{\small\texttt{ Initial\_\-Clock = 0.0\newline  Final\_\-Clock = 2.0\newline  }} 



   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 have fixed it. We would like to render just those 25 frames instead of redoing the whole sequence from the beginning. What do we change? 



   If we said make {\small\texttt{Initial\_\-Frame = 51}}, and {\small\texttt{Final\_\-Frame = 75}}, we are wrong. Even though this would re-\discretionary{}{}{}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 {\small\texttt{Initial\_\-Frame}} and {\small\texttt{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{\small\texttt{ Subset\_\-Start\_\-Frame = 51\newline  Subset\_\-End\_\-Frame 
 = 75\newline  }} 



   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 does not 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-\discretionary{}{}{}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-\discretionary{}{}{}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 do not 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-\discretionary{}{}{}Ray is capable of. Adventure awaits! 


\section{While-\discretionary{}{}{}loop tutorial}

% tutorial/000165.html



   Usually people who have never programmed have great difficulties understanding how simple while-\discretionary{}{}{}loops work and how they should be used. When you get into 
 nested loops, the problem is even worse. 



   Sometimes even people who have programmed a bit with some language get confused with POV-\discretionary{}{}{}Ray's while-\discretionary{}{}{}loops. This usually happens when they have only used a 
 for-\discretionary{}{}{}loop which in itself has an index variable (which is often even incremented automatically). 


\subsection{What a while-\discretionary{}{}{}loop is and what it is not}

% tutorial/000134.html



   A while-\discretionary{}{}{}loop in POV-\discretionary{}{}{}Ray is just a control structure which tells POV-\discretionary{}{}{}Ray to loop a command block while the specified condition is true (ie. until it gets 
 false). 



   That is, a while-\discretionary{}{}{}loop is like this: 


{\small\begin{verbatim}
#while(condition)
  ...
#end
\end{verbatim}}


   The commands between {\small\texttt{\#while}} and {\small\texttt{\#end}} are run over and over as long as the condition evaluates to true. 



   A while-\discretionary{}{}{}loop \textbf{is not} a for-\discretionary{}{}{}loop nor any kind of loop which has an index variable by itself (which may be incremented automatically in each loop). 



   The while-\discretionary{}{}{}loop \textbf{does not} care what the conditions are between the parentheses (as long as they evaluate to some value) or what does the block between {\small\texttt{\#while}} 
 and {\small\texttt{\#end}} contain. It will just execute that block until the condition becomes false. 



   The while-\discretionary{}{}{}loop does not do anything else. You can think about it as a kind of "dumb" loop, which does not do anything automatically (and this is 
 not necessarily a bad thing). 


\subsection{How does a single while-\discretionary{}{}{}loop work?}

% tutorial/000203.html



   The while-\discretionary{}{}{}loop works like this: 


\begin{enumerate}
 
 \item 
   If the condition between the parentheses evaluates to false, jump to the command after the {\small\texttt{\#end}} statement. If the condition evaluates 
  to true, just continue normally. 
 

 \item 
   At the {\small\texttt{\#end}} statement jump to the {\small\texttt{\#while}} statement and start again. 
 

\end{enumerate}


   That is: 


\begin{itemize}
 
 \item 
   When POV-\discretionary{}{}{}Ray gets to the {\small\texttt{\#while}} statement it evaluates the condition between parentheses. 
 

 \item 
   If the statement evaluated to true then it will just continue normally with the next command. 
 

 \item 
   However, if the statement evaluated to false, POV-\discretionary{}{}{}Ray will skip the entire body of the loop and continue from the command after the {\small\texttt{\#end}} 
  statement. 
 

 \item 
   At an {\small\texttt{\#end}} statement POV-\discretionary{}{}{}Ray will just jump back to the corresponding {\small\texttt{\#while}}-statement and then continue normally 
  (ie. testing the condition and so on). 
 

\end{itemize}


   Note that nowhere there is any mention about any index variable or anything else that could be used to automatically end the loop or whatever. As said, it is 
 just a "dumb" loop that continues forever if necessary, only testing the statement between the parentheses (but it is not interested in what it is, 
 only in its evaluated value). 



   Although one could easily think that this kind of "dumb" loop is bad and it should be more "intelligent" and better, the fact is that 
 this kind of "dumb" loop is actually a lot more flexible and versatile. It allows you to make things not possible or very difficult to do with an 
 "intelligent" for-\discretionary{}{}{}loop with automatic index variables. 


\subsection{How do I make a while-\discretionary{}{}{}loop?}

% tutorial/000202.html



   It depends on what you are trying to make. 



   The most common usage is to use it as a simple for-\discretionary{}{}{}loop, that is, a loop which loops a certain number of times (for example 10 times) with an index value 
 getting successive values (for example 1, 2, 3, ..., 10). 



   For this you need to first declare your index identifier with the first value. For example: 


{\small\begin{verbatim}
#declare Index = 1;
\end{verbatim}}


   Now you want to loop 10 times. Remember how the condition worked: The while-\discretionary{}{}{}loop loops as long as the condition is true. So it should loop as long as our 
 'Index' identifier is less or equal to 10: 


{\small\begin{verbatim}
#while(Index <= 10)
\end{verbatim}}


   When the 'Index' gets the value 11 the loop ends, as it should. 



   Now we only have to add 1 to 'Index' at each loop, so we should do it at the end of the loop, thus getting: 


{\small\begin{verbatim}
#declare Index = 1;
#while(Index <= 10)

  (some commands here)

  #declare Index = Index + 1;
#end
\end{verbatim}}


   The incrementation before the {\small\texttt{\#end}} is important. If we do not do it, 'Index' would always have the value 1 and the loop would go forever 
 since 1 is always less or equal to 10. 



   What happens here? 


\begin{enumerate}
 
 \item 
   First POV-\discretionary{}{}{}Ray sets the value 1 to 'Index'. 
 

 \item 
   Then it sees the {\small\texttt{\#while}} statement and evaluates what is between the parentheses: Index $<$= 10 
 

 \item 
   As 'Index' has the value of 1 and 1 $<$= 10, the condition evaluates to true. 
 

 \item 
   So, it just continues normally. It executes the commands following the {\small\texttt{\#while}} statement (denoted in the above example as "(some 
  commands here)"). 
 

 \item 
   Then it arrives normally to the last \#declare command in the block. This causes the value 2 to be assigned to 'Index'. 
 

 \item 
   Now it arrives the the {\small\texttt{\#end}} command and so it just jumps to the {\small\texttt{\#while}}. 
 

 \item 
   After that it executes the steps 2-6 again because also 2 is less or equal to 10. 
 

 \item 
   After this has been done 10 times, the value 11 is assigned to 'Index' in the last command of the block. 
 

 \item 
   Now, when POV-\discretionary{}{}{}Ray evaluates the condition it sees that it is false (because 11 is not less or equal to 10). This causes POV-\discretionary{}{}{}Ray to jump to the command 
  after the {\small\texttt{\#end}} statement. 
 

 \item 
   The net effect of all this is that POV-\discretionary{}{}{}Ray looped 10 times and the 'Index' variable got successive values from 1 to 10 along the way. 
 

\end{enumerate}


   If you read carefully the above description you will notice that the looping is done in a quite "dumb" way, that is, there is no higher logic 
 hidden inside the loop structure. In fact, POV-\discretionary{}{}{}Ray does not have the slightest idea how many times the loop is executed and what variable is used to count the 
 loops. It just follows orders. 



   The higher logic in this type of loop is in the combination of commands we wrote. The effect of this combination is that the loop works like a simple 
 for-\discretionary{}{}{}loop in most programming languages (like BASIC, etc). 


\subsection{What is a condition and how do I make one?}

% tutorial/000201.html



   A condition is an expression that evaluates to a boolean value (ie. true or false) and is used in POV-\discretionary{}{}{}Ray in {\small\texttt{\#while}}-loops and {\small\texttt{\#if}}-statements. 
 



   A condition is mainly a comparison between two values (although there are also some other ways of making a condition, but that is not important now). For 
 example: 


{\small\begin{verbatim}
1 < 2  is true
1 > 2  is false
1 = 1  is true
1 = 2  is false

and so on.
\end{verbatim}}


   Usually it makes no sense to make comparisons like those. However, when comparing identifiers with some value or two identifiers together it starts to be 
 very useful. Consider this: 


{\small\begin{verbatim}
#if(version < 3.1)
  #error "Wrong version!"
#end
\end{verbatim}}


   If the identifier called 'version' has a value which is less than 3.1 the {\small\texttt{\#error}} line will be executed. If 'version' has a value which is 
 3.1 or greater, the {\small\texttt{\#error}} line is just skipped. 



   You can combine conditions together with the boolean operators \& (and) and | (or). You can also invert the value of a condition with ! (not). 



   For example, if you want something to be done when 'a' is less than 10 \textbf{and} 'b' is greater or equal to 20, the condition would be: 


{\small\begin{verbatim}
a<10 \& b>=20
\end{verbatim}}


   For more information about these comparison operators, see the 'Float operators' section of the POV-\discretionary{}{}{}Ray documentation. 


\subsection{What about loop types other than simple for-\discretionary{}{}{}loops?}

% tutorial/000200.html



   As POV-\discretionary{}{}{}Ray does not care what the condition is and what we are using to make that condition, we can use the while-\discretionary{}{}{}loop in many other ways. 



   For example, this is a typical use of the while-\discretionary{}{}{}loop which is not a simple for-\discretionary{}{}{}loop: 


{\small\begin{verbatim}
#declare S = seed(0);
#declare Point = <2*rand(S)-1, 2*rand(S)-1, 2*rand(S)-1>;
#while(vlength(Point) > 1)
  #declare Point = <2*rand(S)-1, 2*rand(S)-1, 2*rand(S)-1>;
#end
\end{verbatim}}


   What we are doing here is this: Take a random point between $<$-1, -1, -1$>$ and $<$1, 1, 1$>$ and if it is not inside the unit sphere take another 
 random point in that range. Do this until we get a point inside the unit sphere. 



   This is not an unrealistic example since it is very handy. 



   As we see, this has nothing to do with an ordinary for-\discretionary{}{}{}loop: 


\begin{itemize}
 
 \item 
   It does not have any "index" value which gets consecutive values during the loop. 
 

 \item 
   We do not know how many times it will loop. In this case it loops a random number of times. 
 

 \item 
   For-\discretionary{}{}{}loops are usually used to get a series of things (eg. objects). At each loop another instance of that thing is created. Here, however, we are only 
  interested in the value that results \textbf{after} the loop, not the values inside it. 
 

\end{itemize}


   As we can see, a while-\discretionary{}{}{}loop can also be used for a task of type "calculate a value or some values until the result is inside a specified range" 
 (among many other tasks). 



   By the way, there is a variant of this kind of loop where the task is: "Calculate a value until the result is inside a specified range, but make only a 
 certain number of tries. If the value does not get inside that range after that number of tries, stop trying". This is used when there is a possibility 
 for the loop for going on forever. 



   In the above example about the point inside the unit sphere we do not need this because the random point will surely hit the inside of the sphere at some 
 time. In some other situations, however, we cannot be so sure. 



   In this case we need a regular index variable to count the number of loops. If we have made that amount of loops then we stop. 



   Suppose that we wanted to modify our point searching program to be completely safe and to try only up to 10 times. If the point does not hit the inside of 
 the sphere after 10 tries, we just give up and take the point $<$\discretionary{0,}{}{0,}\discretionary{0,}{}{0,}0$>$. 


{\small\begin{verbatim}
#declare S = seed(0);
#declare Point = <2*rand(S)-1, 2*rand(S)-1, 2*rand(S)-1>;
#declare Index = 1;
#while(Index <= 10 \& vlength(Point) > 1)
  #declare Point = <2*rand(S)-1, 2*rand(S)-1, 2*rand(S)-1>;
  #declare Index = Index + 1;
#end

#if(vlength(Point) > 1)
  #declare Point = <0,0,0>
#end
\end{verbatim}}


   What did we do? 


\begin{itemize}
 
 \item 
   We added an 'Index' value which counts the amount of loops gone so far. It is quite similar to the index loop of a simple for-\discretionary{}{}{}loop. 
 

 \item 
   We added an extra condition to the while-\discretionary{}{}{}loop: Besides testing that the point is outside the unit sphere it also tests that our index variable has not 
  bailed out. So now there are two conditions for the loop to continue: The 'Index' value must be less or equal to 10 \textbf{and} the 'Point' has to be 
  outside the unit sphere. If either one of them fails, the loop is ended. 
 

 \item 
   Then we check if the point is still outside the unit sphere. If it is, we just take $<$\discretionary{0,}{}{0,}\discretionary{0,}{}{0,}0$>$. 
 

\end{itemize}


   Btw, sometimes it is not convenient to make the test again in the {\small\texttt{\#if}} statement. There is another way of determining whether the loop bailed 
 out without successful termination or not: Since the loop ends when the 'Index' gets the value 11, we can use this to test the successfulness of the loop: 


{\small\begin{verbatim}
#if(Index = 11)
  (loop was not successful)
#end
\end{verbatim}}

\subsection{What about nested loops?}

% tutorial/000199.html



   Even when one masters simple loops, nested loops can be a frightening thing (or at least hard to understand). 



   Nested loops are used for example for creating a 2D array of objects (with rows and columns of objects), etc. For example if you want to create a 10x20 array 
 of spheres in your scene, a nested loop is the tool for it. 



   There is nothing special about nested loops. You only have to pay attention to where you initialize and update your index variables. 



   Let's recall the form of a simple for-\discretionary{}{}{}loop: 


{\small\begin{verbatim}
#declare Index = initial_value;
#while(Index <= final_value)

  [Something here]

  #declare Index = Index + index_step;
#end
\end{verbatim}}


   The [Something here] part can be anything. If it is another while-\discretionary{}{}{}loop, then we have nested loops. The inner loop should have the same structure as the outer 
 one. 



   Note that proper indentation helps us distinguishing between the loops. It is always a good idea to use a good indentation scheme: 


{\small\begin{verbatim}
#declare Index1 = initial_value1;
#while(Index1 <= final_value1)

   #declare Index2 = initial_value2;
   #while(Index2 <= final_value2)

      [Something here]

      #declare Index2 = Index2 + index2_step;
   #end

   #declare Index1 = Index1 + index1_step;
#end
\end{verbatim}}


   It is a common mistake for beginners to break this structure. For example it is common to declare the 'Index2' before the first {\small\texttt{\#while}}. This 
 breaks the for-\discretionary{}{}{}loop structure and thus does not work. If you follow step by step what POV-\discretionary{}{}{}Ray does, as explained earlier, you will see why it does not work. 
 Do not mix the structures of the inner and the outer loops together or your code will simply not work as expected. 



   So, if we want to make our 10x20 array of spheres, it will look like this: 


{\small\begin{verbatim}
#declare Index1 = 0;
#while(Index1 <= 9)

   #declare Index2 = 0;
   #while(Index2 <= 19)

      sphere { <Index1, Index2, 0>, .5 }

      #declare Index2 = Index2 + 1;
   #end

   #declare Index1 = Index1 + 1;
#end
\end{verbatim}}


   Note how we now start from 0 and continue to 9 in the outer loop and from 0 to 19 in the inner loop. This has been done to get the sphere array start from 
 the origin (instead of starting from $<$1, 1, 0$>$). Of course we could have made the 'Index1' and 'Index2' go from 1 to 10 and from 1 to 20 respectively 
 and then created the sphere in this way: 


{\small\begin{verbatim}
  sphere { <Index1-1, Index2-1, 0>, .5 }
\end{verbatim}}


   Although you should not mix the loop structures together, you can perfectly use the values of the outer loop in the inner loop (eg. in its condition). For 
 example, if we wanted to create a triangular array of spheres instead of a rectangular one (that is, we create only half of the spheres), we could have made 
 the inner {\small\texttt{\#while}} like this: 


{\small\begin{verbatim}
  #while(Index2 < Index1*2)
\end{verbatim}}


   ('Index2' will go from 0 to the value of 'Index1' multiplied by 2.) 



   There is no reason why we should limit ourselves to just two nested loops. There is virtually no limit how many loops you can nest. For example, if we wanted 
 to create a box-\discretionary{}{}{}shape filled by spheres rows, colums and depth, we just make three nested loops, one for the x-\discretionary{}{}{}axis, another for the y-\discretionary{}{}{}axis and the third for 
 the z-\discretionary{}{}{}axis. 


\subsection{Mixed-\discretionary{}{}{}type nested loops}

% tutorial/000198.html



   It is perfectly possible to put a for-\discretionary{}{}{}loop inside a non-\discretionary{}{}{}for-\discretionary{}{}{}loop or vice-\discretionary{}{}{}versa. Again, you just have to be careful (with experience it gets easier). 



   For example, suppose that we want to create 50 spheres which are randomly placed inside the unit sphere. 



   So the distinction is clear: First we need a loop to create 50 spheres (a for-\discretionary{}{}{}loop type suffices) and then we need another loop inside it to calculate the 
 location of the sphere. It will look like this: 


{\small\begin{verbatim}
#declare S = seed(0);
#declare Index = 1;
#while(Index <= 50)

   #declare Point = <2*rand(S)-1, 2*rand(S)-1, 2*rand(S)-1>;
   #while(vlength(Point) > 1)
      #declare Point = <2*rand(S)-1, 2*rand(S)-1, 2*rand(S)-1>;
   #end

   sphere { Point, .1 }

   #declare Index = Index + 1;
#end
\end{verbatim}}


   There are some important things to note in this specific example: 


\begin{itemize}
 
 \item 
   Although this is a nested loop, the sphere is not created in the inner loop but in the outer one. The reason is clear: We want to create 50 spheres, so 
  the sphere creation has to be inside the loop that counts to 50. The inner loop just calculates an appropriate location. 
 

 \item 
   The seed value 'S' is declared outside all the loops although it is used only in the inner loop. Can you guess why? (Putting it inside the outer loop 
  would have caused an undesired result: Which one?) 
 

\end{itemize}

\subsection{Other things to note}

% tutorial/000197.html



   There is no reason why the index value in your simple for-\discretionary{}{}{}loop should step one unit at a time. Since the while-\discretionary{}{}{}loop does not care how the index changes, you 
 can change it in whichever way you want. Eg: 


{\small\begin{verbatim}
#declare Index = Index - 1;  Decrements the index (be careful with the
                             while loop condition)

#declare Index = Index + 0.2;  Increases by steps of 0.2

#declare Index = Index * 2;  Doubles the value of the index at each step.

etc.
\end{verbatim}}


   - Be careful \textbf{where} you put your while-\discretionary{}{}{}loop. 



   I have seen this kind of mistake more than once: 


{\small\begin{verbatim}
#declare Index = 1;
#while(Index <= 10)
   blob
   {  threshold 0.6
      sphere { <Index, 0, 0>, 2, 1 }
   }
   #declare Index = Index + 1;
#end
\end{verbatim}}


   You will probably see immediately the problem. 



   This code creates 10 blobs with one component each. It does not seem to make much sense. Most probably the user wanted to make one blob with 10 components. 



   Why did this mistake happen? It may be that the user (more or less subconsciously) thought that the while-\discretionary{}{}{}loop must be the outermost control structure and 
 does not realize that while-\discretionary{}{}{}loops can be anywhere, also inside objects (creating subcomponents or whatever). 



   The correct code is, of course: 


{\small\begin{verbatim}
blob
{  threshold 0.6

   #declare Index = 1;
   #while(Index <= 10)

      sphere { <Index, 0, 0>, 2, 1 }

      #declare Index = Index + 1;
   #end
}
\end{verbatim}}


   The essential difference here is that it is only the sphere code which is run 10 times instead of the whole blob code. The net result is the same as if we 
 had written the sphere code 10 times with proper values of 'Index'. 



   Be also careful with the placement of the braces. If you put them in the wrong place you can end up accidentally repeating an opening or a closing brace 10 
 times. Again, a proper indentation usually helps a lot with this (as seen in the above example). 



   - Tip: You can use while-\discretionary{}{}{}loops in conjunction with arrays to automatize the creation of long lists of elements with differing data. 



   Imagine that you are making something like this: 


{\small\begin{verbatim}
  color_map
  {  [0.00 rgb <.1,1,.6>]
     [0.05 rgb <.8,.3,.6>]
     [0.10 rgb <.3,.7,.9>]
     [0.15 rgb <1,.7,.3>]
     ...
     and so on
\end{verbatim}}


   It is tedious to have to write the same things over and over just changing the index value and the values in the vector (even if you use copy-\discretionary{}{}{}paste to copy 
 the lines). 



   There is also one very big problem here: If you ever want to add a new color to the color map or remove a color, you would have to renumber all the indices 
 again, which can be extremely tedious and frustrating. 



   Would not it be nice to automatize the creation of the color map so that you only have to write the vectors and that is it? 



   Well, you can. Using a while-\discretionary{}{}{}loop which reads an array of vectors: 


{\small\begin{verbatim}
#declare MyColors = array[20]
   {  <.1,1,.6>, <.8,.3,.6>, <.3,.7,.9>,
      <1,.7,.3>, ...
   }

...

   color_map
   {  #declare LastIndex = dimension_size(MyColors, 1)-1;
      #declare Index = 0;
      #while(Index <= LastIndex)

         [Index/LastIndex rgb MyColors[Index]]

         #declare Index = Index + 1;
      #end
   }
\end{verbatim}}


   Now it is easy to add, remove or modify colors in your color map. Just edit the vector array (remembering to change its size number accordingly) and the 
 while-\discretionary{}{}{}loop will automatically calculate the right values and create the color map for you. 


\section{SDL tutorial: A raytracer}

% tutorial/000158.html


\begin{description}
 
 \item 
   \textit{You know you have been raytracing too long when ...\newline  ... You've been asked how you did that thing you did, by the author of the 
  raytracer you used to do it.} 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   \textit{-- Alex McLeod} 
 \end{list}

\end{description}

\subsection{Introduction}

% tutorial/000125.html



   A raytracer made with POV-\discretionary{}{}{}Ray sounds really weird, doesn't it? What is it anyways? POV-\discretionary{}{}{}Ray is already a raytracer in itself, how can we use it to make a 
 raytracer? What the...? 



   The idea is to make a simple sphere raytracer which supports colored spheres (with diffuse and specular lighting), colored light sources, reflections and 
 shadows with the POV-\discretionary{}{}{}Ray SDL (Scene Description Language), then just render the image created this way. That is, we do not use POV-\discretionary{}{}{}Ray itself to raytrace the 
 spheres, but we make our own raytracer with its SDL and use POV-\discretionary{}{}{}Ray's raytracing part to just get the image on screen. 



   What obscure idea could be behind this weirdness (besides a very serious case of YHBRFTLW...)? Why do not just use POV-\discretionary{}{}{}Ray itself to raytrace the spheres a 
 lot faster and that is it? 



   The idea is not speed nor quality, but to show the power of the POV-\discretionary{}{}{}Ray SDL. If you know how to make such a thing as a raytracer with it, we can really grasp 
 the expressive power of the SDL. 



   The idea of this document is to make a different approach to POV-\discretionary{}{}{}Ray SDL teaching. It is intended to be a different type of tutorial: Instead of starting 
 from the basics and give simple and dumb examples, we jump right into a high-\discretionary{}{}{}end SDL code and see how it is done. However, this is done in a way that even 
 beginners can learn something from it. 



   Another advantage is that you will learn how a simple sphere raytracer is done by reading this tutorial. There are lots of misconceptions about raytracing 
 out there, and knowing how to make one helps clear most of them. 



   Although this tutorial tries to start from basics, it will go quite fast to very "high-\discretionary{}{}{}end" scripting, so it might not be the best tutorial to read 
 for a completely new user, but it should be enough to have some basic knowledge. Also more advanced users may get some new info from it. 



   \textbf{Note:} in some places some mathematics is needed, so you would better not be afraid of math. 



   If some specific POV-\discretionary{}{}{}Ray SDL syntax is unclear you should consult the POV-\discretionary{}{}{}Ray documentation for more help. This tutorial explains how they can be used, not 
 so much what is their syntax. 


\subsection{The idea and the code}

% tutorial/000129.html



   The idea is to raytrace a simple scene consisting of spheres and light sources into a 2-dimensional array containing color vectors which represents our 
 "screen". 



   After this we just have to put those colors on the actual scene for POV-\discretionary{}{}{}Ray to show them. This is made by creating a flat colored triangle mesh. The mesh is 
 just flat like a plane with a color map on it. We could as well have written the result to a format like PPM and then read it and apply it as an image map to 
 a plane, but this way we avoid a temporary file. 



   The following image is done with the raytracer SDL. It calculated the image at a resolution of 160x120 pixels and then raytraced an 512x384 image from it. 
 This causes the image to be blurred and jagged (because it is practically "zoomed in" by a factor of 3.2). Calculating the image at 320x240 gives a 
 much nicer result, but it is also much slower: 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/raytracer} \caption{Some spheres raytraced by the SDL at 160x120} \end{figure} 
 



   \textbf{Note:} there are no real spheres nor light sources here ("real" from the point of view of POV-\discretionary{}{}{}Ray), just a flat colored triangle mesh (like 
 a plane with a pigment on it) and a camera, nothing else. 



   Here is the source code of the raytracer; we will look it part by part through this tutorial. 


{\small\begin{verbatim}
#declare ImageWidth = 160;
#declare ImageHeight = 120;
#declare MaxRecLev = 5;
#declare AmbientLight = <.2,.2,.2>;
#declare BGColor = <0,0,0>;

// Sphere information.
// Values are:
// Center, <Radius, Reflection, 0>, Color, <phong_size, amount, 0>
#declare Coord = array[5][4]
{ {<-1.05,0,4>, <1,.5,0>, <1,.5,.25>, <40, .8, 0>}
  {<1.05,0,4>, <1,.5,0>, <.5,1,.5>, <40, .8, 0>}
  {<0,-3,5>, <2,.5,0>, <.25,.5,1>, <30, .4, 0>}
  {<-1,2.3,9>, <2,.5,0>, <.5,.3,.1>, <30, .4, 0>}
  {<1.3,2.6,9>, <1.8,.5,0>, <.1,.3,.5>, <30, .4, 0>}
}

// Light source directions and colors:
#declare LVect = array[3][2]
{ {<-1, 0, -.5>, <.8,.4,.1>}
  {<1, 1, -.5>, <1,1,1>}
  {<0,1,0>, <.1,.2,.5>}
}



//==================================================================
// Raytracing calculations:
//==================================================================
#declare MaxDist = 1e5;
#declare ObjAmnt = dimension_size(Coord, 1);
#declare LightAmnt = dimension_size(LVect, 1);

#declare Ind = 0;
#while(Ind < LightAmnt)
  #declare LVect[Ind][0] = vnormalize(LVect[Ind][0]);
  #declare Ind = Ind+1;
#end

#macro calcRaySphereIntersection(P, D, sphereInd)
  #local V = P-Coord[sphereInd][0];
  #local R = Coord[sphereInd][1].x;

  #local DV = vdot(D, V);
  #local D2 = vdot(D, D);
  #local SQ = DV*DV-D2*(vdot(V, V)-R*R);
  #if(SQ < 0) #local Result = -1;
  #else
    #local SQ = sqrt(SQ);
    #local T1 = (-DV+SQ)/D2;
    #local T2 = (-DV-SQ)/D2;
    #local Result = (T1<T2 ? T1 : T2);
  #end
  Result
#end

#macro Trace(P, D, recLev)
  #local minT = MaxDist;
  #local closest = ObjAmnt;

  // Find closest intersection:
  #local Ind = 0;
  #while(Ind < ObjAmnt)
    #local T = calcRaySphereIntersection(P, D, Ind);
    #if(T>0 \& T<minT) 
      #local minT = T;
      #local closest = Ind;
    #end
    #local Ind = Ind+1;
  #end

  // If not found, return background color:
  #if(closest = ObjAmnt)
    #local Pixel = BGColor;
  #else
    // Else calculate the color of the intersection point:
    #local IP = P+minT*D;
    #local R = Coord[closest][1].x;
    #local Normal = (IP-Coord[closest][0])/R;

    #local V = P-IP;
    #local Refl = 2*Normal*(vdot(Normal, V)) - V;

    // Lighting:
    #local Pixel = AmbientLight;
    #local Ind = 0;
    #while(Ind < LightAmnt)
      #local L = LVect[Ind][0];

      // Shadowtest:
      #local Shadowed = false;
      #local Ind2 = 0;
      #while(Ind2 < ObjAmnt)
        #if(Ind2!=closest \& calcRaySphereIntersection(IP,L,Ind2)>0)
          #local Shadowed = true;
          #local Ind2 = ObjAmnt;
        #end
        #local Ind2 = Ind2+1;
      #end
      
      #if(!Shadowed)
        // Diffuse:
        #local Factor = vdot(Normal, L);
        #if(Factor > 0)
          #local Pixel=Pixel+LVect[Ind][1]*Coord[closest][2]*Factor;
        #end

        // Specular:
        #local Factor = vdot(vnormalize(Refl), L);
        #if(Factor > 0)
          #local Pixel = 
             Pixel +
             LVect[Ind][1]*pow(Factor, Coord[closest][3].x)*
             Coord[closest][3].y;
        #end
      #end
      #local Ind = Ind+1;
    #end

    // Reflection:
    #if(recLev < MaxRecLev \& Coord[closest][1].y > 0)
      #local Pixel = 
	    Pixel + Trace(IP, Refl, recLev+1)*Coord[closest][1].y;
    #end
  #end

  Pixel
#end


#debug "Rendering...\n\n"
#declare Image = array[ImageWidth][ImageHeight]
#declare IndY = 0;
#while(IndY < ImageHeight)
  #declare CoordY = IndY/(ImageHeight-1)*2-1;
  #declare IndX = 0;
  #while(IndX < ImageWidth)
    #declare CoordX = 
      (IndX/(ImageWidth-1)-.5)*2*ImageWidth/ImageHeight;
    #declare Image[IndX][IndY] =
      Trace(-z*3, <CoordX, CoordY, 3>, 1);
    #declare IndX = IndX+1;
  #end
  #declare IndY = IndY+1;
  #debug concat("\rDone ", str(100*IndY/ImageHeight, 0, 1),
    "\%  (line ",str(IndY,0,0)," out of ",str(ImageHeight,0,0),")")
#end
#debug "\n"


//==================================================================
// Image creation (colored mesh):
//==================================================================
#default { finish { ambient 1 } }

#debug "Creating colored mesh to show image...\n"
mesh2
{ vertex_vectors
  { ImageWidth*ImageHeight*2,
    #declare IndY = 0;
    #while(IndY < ImageHeight)
      #declare IndX = 0;
      #while(IndX < ImageWidth)
        <(IndX/(ImageWidth-1)-.5)*ImageWidth/ImageHeight*2,
         IndY/(ImageHeight-1)*2-1, 0>,
        <((IndX+.5)/(ImageWidth-1)-.5)*ImageWidth/ImageHeight*2,
         (IndY+.5)/(ImageHeight-1)*2-1, 0>
        #declare IndX = IndX+1;
      #end
      #declare IndY = IndY+1;
    #end
  }
  texture_list
  { ImageWidth*ImageHeight*2,
    #declare IndY = 0;
    #while(IndY < ImageHeight)
      #declare IndX = 0;
      #while(IndX < ImageWidth)
        texture { pigment { rgb Image[IndX][IndY] } }
        #if(IndX < ImageWidth-1 \& IndY < ImageHeight-1)
          texture { pigment { rgb
            (Image[IndX][IndY]+Image[IndX+1][IndY]+
             Image[IndX][IndY+1]+Image[IndX+1][IndY+1])/4 } }
        #else
          texture { pigment { rgb 0 } }
        #end
        #declare IndX = IndX+1;
      #end
      #declare IndY = IndY+1;
    #end
  }
  face_indices
  { (ImageWidth-1)*(ImageHeight-1)*4,
    #declare IndY = 0;
    #while(IndY < ImageHeight-1)
      #declare IndX = 0;
      #while(IndX < ImageWidth-1)
        <IndX*2+  IndY    *(ImageWidth*2),
         IndX*2+2+IndY    *(ImageWidth*2),
         IndX*2+1+IndY    *(ImageWidth*2)>,
         IndX*2+  IndY    *(ImageWidth*2),
         IndX*2+2+IndY    *(ImageWidth*2),
         IndX*2+1+IndY    *(ImageWidth*2),

        <IndX*2+  IndY    *(ImageWidth*2),
         IndX*2+  (IndY+1)*(ImageWidth*2),
         IndX*2+1+IndY    *(ImageWidth*2)>,
         IndX*2+  IndY    *(ImageWidth*2),
         IndX*2+  (IndY+1)*(ImageWidth*2),
         IndX*2+1+IndY    *(ImageWidth*2),

        <IndX*2+  (IndY+1)*(ImageWidth*2),
         IndX*2+2+(IndY+1)*(ImageWidth*2),
         IndX*2+1+IndY    *(ImageWidth*2)>,
         IndX*2+  (IndY+1)*(ImageWidth*2),
         IndX*2+2+(IndY+1)*(ImageWidth*2),
         IndX*2+1+IndY    *(ImageWidth*2),

        <IndX*2+2+IndY    *(ImageWidth*2),
         IndX*2+2+(IndY+1)*(ImageWidth*2),
         IndX*2+1+IndY    *(ImageWidth*2)>,
         IndX*2+2+IndY    *(ImageWidth*2),
         IndX*2+2+(IndY+1)*(ImageWidth*2),
         IndX*2+1+IndY    *(ImageWidth*2)
        #declare IndX = IndX+1;
      #end
      #declare IndY = IndY+1;
    #end
  }
}

camera { orthographic location -z*2 look_at 0 }
\end{verbatim}}

\subsection{Short introduction to raytracing}

% tutorial/000128.html



   Before we start looking at the code, let's look briefly how raytracing works. This will help you understand what the script is doing. 



   The basic idea of raytracing is to "shoot" rays from the camera towards the scene and see what does the ray hit. If the ray hits the surface of an 
 object then lighting calculations are performed in order to get the color of the surface at that place. 



   The following image shows this graphically: 



   \begin{figure} \centering\includegraphics[scale=0.30]{../final/tex/images/tutorial/raytracing} \caption{The basic raytracing algorithm} \end{figure} 



   First a ray is "shot" in a specified direction to see if there is something there. As this is solved mathematically, we need to know the 
 mathematical representation of the ray and the objects in the scene so that we can calculate where does the ray intersect the objects. Once we get all the 
 intersection points, we choose the closest one. 



   After this we have to calculate the lighting (ie. the illumination) of the object at the intersection point. In the most basic lighting model (as the one 
 used in the script) there are three main things that affect the lighting of the surface: 


\begin{itemize}
 
 \item 
   The shadow test ray, which determines whether a light source illuminates the intersection point or not. 
 

 \item 
   The normal vector, which is a vector perpendicular (ie. at 90 degrees) to the object surface at the intersection point. It determines the diffuse 
  component of the lighting as well as the direction of the reflected ray (in conjunction with the incoming ray; that is, the angle alpha determines the 
  direction of the reflected ray). 
 

 \item 
   The reflected ray, which determines the specular component of the lighting and of course the color of the reflection (if the object is reflective). 
 

\end{itemize}


   Do not worry if these things sound a bit confusing. Full details of all these things will be given through this tutorial, as we look what does the raytracing 
 script do. The most important thing at this stage is to understand how the basic raytracing algorithm works at theoretical level (the image above should say 
 most of it). 



   Let's just look at the raytracer source code line by line and look what does it do 


\subsection{Global settings}

% tutorial/000127.html


{\small\begin{verbatim}
#declare ImageWidth = 160;
#declare ImageHeight = 120;
#declare MaxRecLev = 5;
#declare AmbientLight = <.2,.2,.2>;
#declare BGColor = <0,0,0>;
\end{verbatim}}


   These lines just declare some identifiers defining some general values which will be used later in the code. The keyword we use here is {\small\texttt{\#declare}} 
 and it means that we are declaring a global identifier, which will be seen in the whole code. 



   As you can see, we declare some identifiers to be of float type and others to be of vector type. The vector type identifiers are, in fact, used later for 
 color definition (as their name implies). 



   The {\small\texttt{ImageWidth}} and {\small\texttt{ImageHeight}} define the resolution of the image we are going to render. 



   \textbf{Note:} this only defines the resolution of the image we are going to render in our SDL (ie. into the array we will define later); it does not set the 
 resolution of the image which POV-\discretionary{}{}{}Ray will render. 



   The {\small\texttt{MaxRecLev}} limits the maximum number of recursive reflections the code will calculate. It is equivalent to the {\small\texttt{max\_\-trace\_\-level}} 
 value in {\small\texttt{global\_\-settings}} which POV-\discretionary{}{}{}Ray uses to raytrace. 



   The {\small\texttt{AmbientLight}} defines a color which is added to all surfaces. This is used to "lighten up" shadowed parts so that they are not 
 completely dark. It is equivalent to the {\small\texttt{ambient\_\-light}} value in {\small\texttt{global\_\-settings}}. 



   Finally, {\small\texttt{BGColor}} defines the color of the rays which do not hit anything. It is equivalent to the {\small\texttt{background}} block of 
 POV-\discretionary{}{}{}Ray. 


\subsection{Scene definition}

% tutorial/000126.html


{\small\begin{verbatim}
// Sphere information.
// Values are:
// Center, <Radius, Reflection, 0>, Color, <phong_size, amount, 0>
#declare Coord = array[5][4]
{ {<-1.05,0,4>, <1,.5,0>, <1,.5,.25>, <40, .8, 0>}
  {<1.05,0,4>, <1,.5,0>, <.5,1,.5>, <40, .8, 0>}
  {<0,-3,5>, <2,.5,0>, <.25,.5,1>, <30, .4, 0>}
  {<-1,2.3,9>, <2,.5,0>, <.5,.3,.1>, <30, .4, 0>}
  {<1.3,2.6,9>, <1.8,.5,0>, <.1,.3,.5>, <30, .4, 0>}
}

// Light source directions and colors:
#declare LVect = array[3][2]
{ {<-1, 0, -.5>, <.8,.4,.1>}
  {<1, 1, -.5>, <1,1,1>}
  {<0,1,0>, <.1,.2,.5>}
}
\end{verbatim}}


   Here we use a bit more complex declarations: Array declarations. 



   In fact, they are even more complex than simple arrays, as we are declaring two-\discretionary{}{}{}dimensional arrays. 



   A simple one-\discretionary{}{}{}dimensional array can be declared like: 


{\small\begin{verbatim}
#declare MyArray = array[4] { 1, 2, 3, 4 }
\end{verbatim}}


   and then values can be read from inside it with for example: {\small\texttt{MyArray[2]}} (which will return {\small\texttt{3}} in this case as the indexing 
 starts from 0, ie. the index 0 gets the first value in the array). 



   A two-\discretionary{}{}{}dimensional array can be thought as an array containing arrays. That is, if you say {\small\texttt{array[3][2]}}, that means "an array which has 3 
 elements; each one of those elements is an array with 2 elements". When you want to read a value from it, for example {\small\texttt{MyArray[1][3]}}, you 
 can think about it as "get the fourth value from the second array" (as indexing starts from 0, then the index value 3 actually means "fourth 
 value"). 



   \textbf{Note:} although you can put almost anything inside an array (floats, vectors, objects and so on) you can only put one type of things inside an array. 
 That is, you cannot mix float values and objects inside the same array. (One nice feature is that all POV-\discretionary{}{}{}Ray objects are considered equivalent, which means 
 that an object array can contain any objects inside it.) 



   What we are doing here is to define the information for our spheres and light sources. The first array (called {\small\texttt{Coord}}) defines the 
 information for the spheres and the second ({\small\texttt{LVect}}) defines the light sources. 



   For spheres we define their center as the first vector. The second vector has both the radius of the sphere and its reflection amount (which is equivalent to 
 the {\small\texttt{reflection}} value in the {\small\texttt{finish}} block of an object). This is a trick we use to not to waste so much space, so we use two 
 values of the same vector for defining two different things. 



   The third vector defines the color of the sphere and the fourth the specular component of the lighting (equivalent to {\small\texttt{phong\_\-size}} and {\small\texttt{phong}} 
 values in the {\small\texttt{finish}} block of an object). 



   The light source definition array contains direction vectors and colors. This means that the light sources are directional, that is, they just say which 
 direction the light is coming from. It could have been equally easy to make point lights, though. 



   We will use the information inside these arrays later in order to raytrace the scene they define. 


\subsection{Initializing the raytracer}

% tutorial/000130.html


{\small\begin{verbatim}
#declare MaxDist = 1e5;
#declare ObjAmnt = dimension_size(Coord, 1);
#declare LightAmnt = dimension_size(LVect, 1);

#declare Ind = 0;
#while(Ind < LightAmnt)
  #declare LVect[Ind][0] = vnormalize(LVect[Ind][0]);
  #declare Ind = Ind+1;
#end
\end{verbatim}}


   Before being able to start the raytracing, we have to intialize a couple of things. 



   The {\small\texttt{MaxDist}} defines the maximum distance a surface can be from the starting point of a ray. This means that if a surface is farther away 
 from the starting point of the ray than this value, it will not be seen. Strictly speaking this value is unnecessary and we can make the raytracer so that 
 there is no such a limitation, but we save one extra step when we do it this way, and for scenes sized like ours it does not really matter. (If you really, 
 really want to get rid of the limitation, I am sure you will figure out yourself how to do it after this tutorial.) 



   The {\small\texttt{ObjAmnt}} and {\small\texttt{LightAmnt}} identifiers are declared just to make it easier for us to see how many objects and lights are 
 there (we need this info to loop through all the objects and lights). Calling the {\small\texttt{dimension\_\-size()}} function is a really nice way of getting 
 the number of items in an array. 



   All right, now we are getting to a bit more advanced stuff: What does the while-\discretionary{}{}{}loop do there? 



   The {\small\texttt{\#while}}-loop uses the {\small\texttt{Ind}} identifier as an index value going from {\small\texttt{0}} to {\small\texttt{LightAmnt-1}} 
 (yes, {\small\texttt{-1}}; when {\small\texttt{Ind}} gets the value {\small\texttt{LightAmnt}} the loop is ended right away). We also see that we are indexing 
 the {\small\texttt{LVect}} array; thus, it is clear we are going through all the light sources (specifically through their direction vectors, as we only use 
 the {\small\texttt{[0]}} part) and we assign something to them. 



   What we are doing is to assign a normalized version of each light source direction onto themselves, that is, just normalizing them. 



   Normalize is a synonym for "convert to unit vector", that is, convert to a vector with the same direction as the original but with length 1. 



   Why? We will later see that for illumination calculations we will be needing unit vectors. It is more efficient to convert the light source directions to 
 unit vectors once at the beginning than every time for each pixel later. 


\subsection{Ray-\discretionary{}{}{}sphere intersection}

% tutorial/000131.html


{\small\begin{verbatim}
#macro calcRaySphereIntersection(P, D, sphereInd)
  #local V = P-Coord[sphereInd][0];
  #local R = Coord[sphereInd][1].x;

  #local DV = vdot(D, V);
  #local D2 = vdot(D, D);
  #local SQ = DV*DV-D2*(vdot(V, V)-R*R);
  #if(SQ < 0) #local Result = -1;
  #else
    #local SQ = sqrt(SQ);
    #local T1 = (-DV+SQ)/D2;
    #local T2 = (-DV-SQ)/D2;
    #local Result = (T1<T2 ? T1 : T2);
  #end
  Result
#end
\end{verbatim}}


   This is the core of the whole raytracing process. 



   First let's see how a macro works (if you know it, just skip the following section): 


\subsubsection{Inner workings of a \#macro}

% tutorial/000150.html



   A macro works like a substitution command (similar to the \#define macros in the C programming language). The body of the macro is in practice inserted in the 
 place where the macro is called. For example you can use a macro like this: 


{\small\begin{verbatim}
#macro UnitSphere()
  sphere { 0,1 }
#end

object { UnitSphere() pigment { rgb 1 } }
\end{verbatim}}


   The result of this code is, in effect, as if you had written: 


{\small\begin{verbatim}
object { sphere { 0,1 } pigment { rgb 1 } }
\end{verbatim}}


   Of course there is no reason in making this, as you could have just \#declared the {\small\texttt{UnitSphere}} as a sphere of radius 1. However, the power of 
 macros kick in when you start using macro parameters. For example: 


{\small\begin{verbatim}
#macro Sphere(Radius)
  sphere { 0, Radius }
#end

object { Sphere(3) pigment { rgb 1 } }
\end{verbatim}}


   Now you can use the macro {\small\texttt{Sphere}} to create a sphere with the specified radius. Of course this does not make much sense either, as you could 
 just write the sphere primitive directly because it is so short, but this example is intentionally short to show how it works; the macros become very handy 
 when they create something much more complicated than just a sphere. 



   There is one important difference between macros in POV-\discretionary{}{}{}Ray and real substitution macros: Any {\small\texttt{\#local}} statement inside the macro definition 
 will be parsed at the visibility level of the macro only, that is, it will have no effect on the environment where the macro was called from. The following 
 example shows what I am talking about: 


{\small\begin{verbatim}
#macro Sphere(Radius)
  #local Color = <1,1,1>;
  sphere { 0, Radius pigment { rgb Color } }
#end

#declare Color = <1,0,0>;
object { Sphere(3) }
   // 'Color' is still <1,0,0> here, 
   // thus the following box will be red:
box { -1,1 pigment { rgb Color } }
\end{verbatim}}


   In the example above, although the macro creates a local identifier called {\small\texttt{Color}} and there is an identifier with the same name at global 
 level, the local definition does not affect the global one. Also even if there was not any global definition of {\small\texttt{Color}}, the one inside the 
 macro is not seen outside it. 



   There is one important exception to this, and this is one of the most powerful features of macros (thanks to this they can be used as if they were 
 functions): If an identifier (be it local or global) appears alone in the body of a macro (usually at the end), its value will be passed outside the macro (as 
 if it was a return value). The following example shows how this works: 


{\small\begin{verbatim}
#macro Factorial(N)
  #local Result = 1;
  #local Ind = 2;
  #while(Ind <= N)
    #local Result = Result*Ind;
    #local Ind = Ind+1;
  #end
  Result
#end

#declare Value = Factorial(5);
\end{verbatim}}


   Although the identifier {\small\texttt{Result}} is local to the macro, its value is passed as if it was a return value because of the last line of the macro 
 (where {\small\texttt{Result}} appears alone) and thus the identifier {\small\texttt{Value}} will be set to the factorial of 5. 


\subsubsection{The ray-\discretionary{}{}{}sphere intersection macro}

% tutorial/000149.html



   Here is again the macro at the beginning of the page so that you do not have to scroll so much in order to see it: 


{\small\begin{verbatim}
#macro calcRaySphereIntersection(P, D, sphereInd)
  #local V = P-Coord[sphereInd][0];
  #local R = Coord[sphereInd][1].x;

  #local DV = vdot(D, V);
  #local D2 = vdot(D, D);
  #local SQ = DV*DV-D2*(vdot(V, V)-R*R);
  #if(SQ < 0) #local Result = -1;
  #else
    #local SQ = sqrt(SQ);
    #local T1 = (-DV+SQ)/D2;
    #local T2 = (-DV-SQ)/D2;
    #local Result = (T1<T2 ? T1 : T2);
  #end
  Result
#end
\end{verbatim}}


   The idea behind this macro is that it takes a starting point (ie. the starting point of the ray) a direction vector (the direction where the ray is shot) and 
 an index to the sphere definition array defined previously. The macro returns a factor value; this value expresses how much we have to multiply the direction 
 vector in order to hit the sphere. 



   This means that if the ray hits the specified sphere, the intersection point will be located at:\newline  {\small\texttt{StartingPoint + Result*Direction}} 



   The return value can be negative, which means that the intersection point was actually behind the starting point. A negative value will be just ignored, as 
 if the ray did not hit anything. We can use this to make a little trick (which may seem obvious when said, but not so obvious when you have to figure it out 
 for yourself): If the ray actually does not hit the sphere, we return just a negative value (does not really matter which). 



   And how does the macro do it? What is the theory behind those complicated-\discretionary{}{}{}looking mathematical expressions? 



   I will use a syntax similar to POV-\discretionary{}{}{}Ray syntax to express mathematical formulas here since that is probably the easiest way of doing it. 



   Let's use the following letters: 



   {\small\texttt{P}} = Starting point of the ray\newline  {\small\texttt{D}} = Direction of the ray\newline  {\small\texttt{C}} = Center of the sphere\newline  {\small\texttt{R}} 
 = Radius of the sphere 



   The theory behind the macro is that we have to see what is the value {\small\texttt{T}} for which holds that: 



   {\small\texttt{vlength(P+T*D-\discretionary{}{}{}C) = R}} 



   This means: The length of the vector between the center of the sphere ({\small\texttt{C}}) and the intersection point ({\small\texttt{P+T*D}}) is equal to 
 the radius ({\small\texttt{R}}). 



   If we use an additional letter so that: 



   {\small\texttt{V = P-\discretionary{}{}{}C}} 



   then the formula is reduced to: 



   {\small\texttt{vlength(T*D+V) = R}} 



   which makes our life easier. This formula can be opened as: 



   {\small\texttt{(T*D$_{x}$+V$_{x}$)$^{2}$ + (T*D$_{y}$+V$_{y}$)$^{2}$ + (T*D$_{z}$+V$_{z}$)$^{2}$ - R$^{2}$ = 0}} 



   Solving {\small\texttt{T}} from that is rather trivial math. We get a 2nd order polynomial which has two solutions (I will use the "$\cdot$" symbol 
 to represent the dot-\discretionary{}{}{}product of two vectors): 



   {\small\texttt{T = (-D$\cdot$V $\pm$ sqrt((D$\cdot$V)$^{2}$ - D$^{2}$(V$^{2}$-R$^{2}$))) / D$^{2}$}} 



   \textbf{Note:} {\small\texttt{D$^{2}$}} means actually {\small\texttt{D$\cdot$D}}) 



   When the discriminant (ie. the expression inside the square root) is negative, the ray does not hit the sphere and thus we can return a negative value (the 
 macro returns -1). We must check this in order to avoid the \textit{square root of a negative number} error; as it has a very logical meaning in this case, 
 the checking is natural. 



   If the value is positive, there are two solutions (or just one if the value is zero, but that does not really matter here), which corresponds to the two 
 intersection points of the ray with the sphere. 



   As we get two values, we have to return the one which is smaller (the closest intersection). This is what this portion of the code does: 


{\small\begin{verbatim}
    #local Result = (T1<T2 ? T1 : T2);
\end{verbatim}}


   \textbf{Note:} this is an incomplete algorithm: If one value is negative and the other positive (this happens when the starting point is inside the sphere), 
 we would have to return the positive one. The way it is now results in that we will not see the inner surface of the sphere if we put the camera inside one. 



   For our simple scene this is enough as we do not put our camera inside a sphere nor we have transparent spheres. We could add a check there which looks if 
 one of the values is positive and the other negative and returns the positive one. However, this has an odd and very annoying result (you can try it if you 
 want). This is most probably caused by the inaccuracy of floating point numbers and happens when calculating reflections (the starting point is exactly on the 
 surface of the sphere). We could correct these problems by using epsilon values to get rid of accuracy problems, but in our simple scene this will not be 
 necessary. 


\subsection{The Trace macro}

% tutorial/000148.html


{\small\begin{verbatim}
#macro Trace(P, D, recLev)
\end{verbatim}}


   If the ray-\discretionary{}{}{}sphere intersection macro was the core of the raytracer, then the Trace-\discretionary{}{}{}macro is practically everything else, the "body" of the 
 raytracer. 



   The Trace-\discretionary{}{}{}macro is a macro which takes the starting point of a ray, the direction of the ray and a recursion count (which should always be 1 when calling the 
 macro from outside; 1 could be its default value if POV-\discretionary{}{}{}Ray supported default values for macro parameters). It calculates and returns a color for that ray. 



   This is the macro we call for each pixel we want to calculate. That is, the starting point of the ray is our camera location and the direction is the 
 direction of the ray starting from there and going through the "pixel" we are calculating. The macro returns the color of that pixel. 



   What the macro does is to see which sphere (if any) does the ray hit and then calculates the lighting for that intersection point (which includes calculating 
 reflection), and returns the color. 



   The Trace-\discretionary{}{}{}macro is \textit{recursive}, meaning that it calls itself. More specifically, it calls itself when it wants to calculate the ray reflected from the 
 surface of a sphere. The {\small\texttt{recLev}} value is used to stop this recursion when the maximum recursion level is reached (ie. it calculates the 
 reflection only if {\small\texttt{recLev $<$ MaxRecLev}}). 



   Let's examine this relatively long macro part by part: 


\subsubsection{Calculating the closest intersection}

% tutorial/000147.html


{\small\begin{verbatim}
  #local minT = MaxDist;
  #local closest = ObjAmnt;

  // Find closest intersection:
  #local Ind = 0;
  #while(Ind < ObjAmnt)
    #local T = calcRaySphereIntersection(P, D, Ind);
    #if(T>0 \& T<minT) 
      #local minT = T;
      #local closest = Ind;
    #end
    #local Ind = Ind+1;
  #end
\end{verbatim}}


   A ray can hit several spheres and we need the closest intersection point (and to know which sphere does it belong to). One could think that calculating the 
 closest intersection is rather complicated, needing things like sorting all the intersection points and such. However, it is quite simple, as seen in the code 
 above. 



   If we remember from the previous part, the ray-\discretionary{}{}{}sphere intersection macro returns a factor value which tells us how much do we have to multiply the direction 
 vector in order to get the intersection point. What we do is just to call the ray-\discretionary{}{}{}sphere intersection macro for each sphere and take the smallest returned 
 value (which is greater than zero). 



   First we initialize the {\small\texttt{minT}} identifier, which will hold this smallest value to something big (this is where we need the {\small\texttt{MaxDist}} 
 value, although modifying this code to work around this limitation is trivial and left to the user). Then we go through all the spheres and call the 
 ray-\discretionary{}{}{}sphere intersection macro for each one. Then we look if the returned value was greater than 0 and smaller than {\small\texttt{minT}}, 
 and if so, we assign the value to {\small\texttt{minT}}. When the loop ends, we have the smallest intersection point in it. 



   \textbf{Note:} we also assign the index to the sphere which the closest intersection belongs to in the {\small\texttt{closest}} identifier. 



   Here we use a small trick, and it is related to its initial value: {\small\texttt{ObjAmnt}}. Why did we initialize it to that? The purpose of it was to 
 initialize it to some value which is not a legal index to a sphere ({\small\texttt{ObjAmnt}} is not a legal index as the indices go from 0 to {\small\texttt{ObjAmnt-1}}); 
 a negative value would have worked as well, it really does not matter. If the ray does not hit any sphere, then this identifier is not changed and so we can 
 see it afterwards. 


\subsubsection{If the ray doesn't hit anything}

% tutorial/000146.html


{\small\begin{verbatim}
  // If not found, return background color:
  #if(closest = ObjAmnt)
    #local Pixel = BGColor;
\end{verbatim}}


   If the ray did not hit any sphere, what we do is just to return the bacground color (defined by the {\small\texttt{BGColor}} identifier). 


\subsubsection{Initializing color calculations}

% tutorial/000144.html



   Now comes one of the most interesting parts of the raytracing process: How do we calculate the color of the intersection point? 



   First we have to pre-\discretionary{}{}{}calculate a couple of things: 


{\small\begin{verbatim}
  #else
    // Else calculate the color of the intersection point:
    #local IP = P+minT*D;
    #local R = Coord[closest][1].x;
    #local Normal = (IP-Coord[closest][0])/R;

    #local V = P-IP;
    #local Refl = 2*Normal*(vdot(Normal, V)) - V;
\end{verbatim}}


   Naturally we need the intersection point itself (needed to calculate the normal vector and as the starting point of the reflected ray). This is calculated 
 into the {\small\texttt{IP}} identifier with the formula which I have been repeating a few times during this tutorial. 



   Then we need the normal vector of the surface at the intersection point. A normal vector is a vector perpendicular (ie. at 90 degrees) to the surface. For a 
 sphere this is very easy to calculate: It is just the vector from the center of the sphere to the intersection point. 



   \textbf{Note:} we normalize it (ie. convert it into a unit vector, ie. a vector of length 1) by dividing it by the radius of the sphere. The normal vector 
 needs to be normalized for lighting calculation. 



   Now a tricky one: We need the direction of the reflected ray. This vector is of course needed to calculate the reflected ray, but it is also needed for 
 specular lighting. 



   This is calculated into the {\small\texttt{Refl}} identifier in the code above. What we do is to take the vector from the intersection point to the starting 
 point ({\small\texttt{P-\discretionary{}{}{}IP}}) and "mirror" it with respect to the normal vector. The formula for "mirroring" a vector {\small\texttt{V}} 
 with respect to a unit vector (let's call it {\small\texttt{Axis}}) is: 



   {\small\texttt{MirroredV = 2*Axis*(Axis$\cdot$V) - V}} 



   (We could look at the theory behind this formula in more detail, but let's not go too deep into math in this tutorial, shall we?) 


\subsubsection{Going through the light sources}

% tutorial/000143.html


{\small\begin{verbatim}
    // Lighting:
    #local Pixel = AmbientLight;
    #local Ind = 0;
    #while(Ind < LightAmnt)
      #local L = LVect[Ind][0];
\end{verbatim}}


   Now we can calculate the lighting of the intersection point. For this we need to go through all the light sources. 



   \textbf{Note:} {\small\texttt{L}}contains the direction vector which points towards the light source, not its location. 



   We also initialize the color to be returned ({\small\texttt{Pixel}}) with the ambient light value (given in the global settings part). The goal is to add 
 colors to this (the colors come from diffuse and specular lighting, and reflection). 


\subsubsection{Shadow test}

% tutorial/000142.html



   The very first thing to do for calculating the lighting for a light source is to see if the light source is illuminating the intersection point in the first 
 place (this is one of the nicest features of raytracing: shadow calculations are laughably easy to do): 


{\small\begin{verbatim}
      // Shadowtest:
      #local Shadowed = false;
      #local Ind2 = 0;
      #while(Ind2 < ObjAmnt)
        #if(Ind2!=closest \& calcRaySphereIntersection(IP,L,nd2)>0)
          #local Shadowed = true;
          #local Ind2 = ObjAmnt;
        #end
        #local Ind2 = Ind2+1;
      #end
\end{verbatim}}


   What we do is to go through all the spheres (we skip the current sphere although it is not necessary, but a little optimization is still a little 
 optimization), take the intersection point as starting point and the light direction as the direction vector and see if the ray-\discretionary{}{}{}sphere intersection test 
 returns a positive value for any of them (and quit the loop immediately when one is found, as we do not need to check the rest anymore). 



   The result of the shadow test is put into the {\small\texttt{Shadowed}} identifier as a boolean value ({\small\texttt{true}} if the point is shadowed). 


\subsubsection{Diffuse lighting}

% tutorial/000141.html



   The diffuse component of lighting is generated when a light ray hits a surface and it is reflected equally to all directions. The brightest part of the 
 surface is where the normal vector points directly in the direction of the light. The lighting diminishes in relation to the cosine of the angle between the 
 normal vector and the light vector. 


{\small\begin{verbatim}
      #if(!Shadowed)
        // Diffuse:
        #local Factor = vdot(Normal, L);
        #if(Factor > 0)
          #local Pixel = 
             Pixel + LVect[Ind][1]*Coord[closest][2]*Factor;
        #end
\end{verbatim}}


   The code for diffuse lighting is surprisingly short. 



   There is an extremely nice trick in mathematics to get the cosine of the angle between two unit vectors: It is their dot-\discretionary{}{}{}product. 



   What we do is to calculate the dot-\discretionary{}{}{}product of the normal vector and the light vector (both have been normalized previously). If the dot-\discretionary{}{}{}product is negative 
 it means that the normal vector points in the opposite direction than the light vector. Thus we are only interested in positive values. 



   Thus, we add to the pixel color the color of the light source multiplied by the color of the surface of the sphere multiplied by the dot-\discretionary{}{}{}product. This gives 
 us the diffuse component of the lighting. 


\subsubsection{Specular lighting}

% tutorial/000140.html



   The specular component of lighting comes from the fact that most surfaces do not reflect light equally to all directions, but they reflect more light to the 
 "reflected ray" direction, that is, the surface has some mirror properties. The brightest part of the surface is where the reflected ray points in the 
 direction of the light. 



   Photorealistic lighting is a very complicated issue and there are lots of different lighting models out there, which try to simulate real-\discretionary{}{}{}world lighting more 
 or less accurately. For our simple raytracer we just use a simple Phong lighting model, which suffices more than enough. 


{\small\begin{verbatim}
        // Specular:
        #local Factor = vdot(vnormalize(Refl), L);
        #if(Factor > 0)
          #local Pixel = Pixel + LVect[Ind][1]*
                         pow(Factor, Coord[closest][3].x)*
                         Coord[closest][3].y;
        #end
\end{verbatim}}


   The calculation is similar to the diffuse lighting with the following differences: 


\begin{itemize}
 
 \item 
   We do not use the normal vector, but the reflected vector. 
 

 \item 
   The color of the surface is not taken into account (a very simple Phong lighting model). 
 

 \item 
   We do not take the dot-\discretionary{}{}{}product as is, but we raise it to a power given in the scene definition ("phong size"). 
 

 \item 
   We use a brightness factor given in the scene definition to multiply the color ("phong amount"). 
 

\end{itemize}


   Thus, the color we add to the pixel color is the color of the light source multiplied by the dot-\discretionary{}{}{}product (which is raised to the given power) and by the 
 given brightness amount. 



   Then we close the code blocks: 


{\small\begin{verbatim}
      #end // if(!Shadowed)
      #local Ind = Ind+1;
    #end // while(Ind < LightAmnt)
\end{verbatim}}

\subsubsection{Reflection Calculation}

% tutorial/000139.html


{\small\begin{verbatim}
    // Reflection:
    #if(recLev < MaxRecLev \& Coord[closest][1].y > 0)
      #local Pixel = 
        Pixel + Trace(IP, Refl, recLev+1)*Coord[closest][1].y;
    #end
\end{verbatim}}


   Another nice aspect of raytracing is that reflection is very easy to calculate. 



   Here we check that the recursion level has not reached the limit and that the sphere has a reflection component defined. If both are so, we add the reflected 
 component (the color of the reflected ray multiplied by the reflection factor) to the pixel color. 



   This is where the recursive call happens (the macro calls itself). The recursion level (recLev) is increased by one for the next call so that somewhere down 
 the line, the series of Trace() calls will know to stop (preventing a ray from bouncing back and forth forever between two mirrors). This is basically how the 
 max\_\-trace\_\-level global setting works in POV-\discretionary{}{}{}Ray. 



   Finally, we close the code blocks and return the pixel color from the macro: 


{\small\begin{verbatim}
  #end // else

  Pixel
#end
\end{verbatim}}

\subsection{Calculating the image}

% tutorial/000137.html


{\small\begin{verbatim}
#debug "Rendering...\n\n"
#declare Image = array[ImageWidth][ImageHeight]

#declare IndY = 0;
#while(IndY < ImageHeight)
  #declare CoordY = IndY/(ImageHeight-1)*2-1;
  #declare IndX = 0;
  #while(IndX < ImageWidth)
    #declare CoordX =
       (IndX/(ImageWidth-1)-.5)*2*ImageWidth/ImageHeight;
    #declare Image[IndX][IndY] =
      Trace(-z*3, <CoordX, CoordY, 3>, 1);
    #declare IndX = IndX+1;
  #end
  #declare IndY = IndY+1;
  #debug concat("\rDone ", str(100*IndY/ImageHeight,0,1),
    "\%  (line ", str(IndY,0,0)," out of ",str(ImageHeight,0,0),")")
#end
#debug "\n"
\end{verbatim}}


   Now we just have to calculate the image into an array of colors. This array is defined at the beginning of the code above; it is a two-\discretionary{}{}{}dimensional array 
 representing the final image we are calculating. 



   Note how we use the {\small\texttt{\#debug}} stream to output useful information about the rendering process while we are calculating. This is nice because 
 the rendering process is quite slow and it is good to give the user some feedback about what is happening and how long it will take. (Also note that the "{\small\texttt{\%}}" 
 character in the string of the second {\small\texttt{\#debug}} command will work ok only in the Windows version of POV-\discretionary{}{}{}Ray; for other versions it may be 
 necessary to convert it to "{\small\texttt{\%\%}}".) 



   What we do here is to go through each "pixel" of the "image" (ie. the array) and for each one calculate the camera location (fixed to {\small\texttt{-z*3}} 
 here) and the direction of the ray that goes through the pixel (in this code the "viewing plane" is fixed and located in the x-\discretionary{}{}{}y-\discretionary{}{}{}plane and its 
 height is fixed to 1). 



   What the following line: 


{\small\begin{verbatim}
  #declare CoordY = IndY/(ImageHeight-1)*2-1;
\end{verbatim}}


   does is to scale the {\small\texttt{IndY}} so that it goes from -1 to 1. It is first divided by the maximum value it gets (which is {\small\texttt{ImageHeight-1}}) 
 and then it is multiplied by 2 and substracted by 1. This results in a value which goes from -1 to 1. 



   The {\small\texttt{CoordX}} is calculated similarly, but it is also multiplied by the aspect ratio of the image we are calculating (so that we do not get a 
 squeezed image). 


\subsection{Creating the colored mesh}

% tutorial/000151.html



   If you think that these things we have been examining are advanced, then you have not seen anything. Now comes real hard-\discretionary{}{}{}core advanced POV-\discretionary{}{}{}Ray code, so be 
 prepared. This could be called \textit{The really advanced section}. 



   We have now calculated the image into the array of colors. However, we still have to show these color "pixels" on screen, that is, we have to make 
 POV-\discretionary{}{}{}Ray to render our pixels so that it creates a real image. 



   There are several ways of doing this, all of them being more or less "kludges" (as there is currently no way of directly creating an image map from 
 a group of colors). One could create colored boxes representing each pixel, or one could output to an ascii-\discretionary{}{}{}formatted image file (mainly PPM) and then read it 
 as an image map. The first one has the disadvantage of requiring huge amounts of memory and missing bilinear interpolation of the image; the second one has 
 the disadvantage of requiring a temporary file. 



   What we are going to do is to calculate a colored mesh2 which represents the "screen". As colors are interpolated between the vertices of a 
 triangle, the bilinear interpolation comes for free (almost). 


\subsubsection{The structure of the mesh}

% tutorial/000156.html



   Although all the triangles are located in the x-\discretionary{}{}{}y plane and they are all the same size, the structure of the mesh is quite complicated (so complicated it 
 deserves its own section here). 



   The following image shows how the triangles are arranged for a 4x3 pixels image: 



   \begin{figure} \centering\includegraphics[scale=0.30]{../final/tex/images/tutorial/triangles} \caption{Triangle arrangement for a 4x3 image} \end{figure} 



   The number pairs in parentheses represent image pixel coordinates (eg. {\small\texttt{(\discretionary{0,}{}{0,}0)}} refers to the pixel at the lower left corner of the image and {\small\texttt{(\discretionary{3,}{}{3,}2)}} 
 to the pixel at the upper right corner). That is, the triangles will be colored as the image pixels at these points. The colors will then be interpolated 
 between them along the surface of the triangles. 



   The filled and non-\discretionary{}{}{}filled circles in the image represent the vertex points of the triangles and the lines connecting them show how the triangles are 
 arranged. The smaller numbers near these circles indicate their index value (the one which will be created inside the {\small\texttt{mesh2}}). 



   We notice two things which may seem odd: Firstly there are extra vertex points outside the mesh, and secondly, there are extra vertex points in the middle of 
 each square. 



   Let's start with the vertices in the middle of the squares: We could have just made each square with two triangles instead of four, as we have done here. 
 However, the color interpolation is not nice this way, as there appears a clear diagonal line where the triangle edges go. If we make each square with four 
 triangles instead, then the diagonal lines are less apparent, and the interpolation resembles a lot better a true bilinear interpolation. And what is the 
 color of the middle points? Of course it is the average of the color of the four points in the corners. 



   Secondly: Yes, the extra vertex points outside the mesh are completely obsolete and take no part in the creation of the mesh. We could perfectly create the 
 exact same mesh without them. However, getting rid of these extra vertex points makes our lives more difficult when creating the triangles, as it would make 
 the indexing of the points more difficult. It may not be too much work to get rid of them, but they do not take any considerable amount of resources and they 
 make our lives easier, so let's just let them be (if you want to remove them, go ahead). 


\subsubsection{Creating the mesh}

% tutorial/000155.html



   What this means is that for each pixel we create two vertex points, one at the pixel location and one shifted by "0.5" in the x and y directions. 
 Then we specify the color for each vertex points: For the even vertex points it is directly the color of the correspondent pixel; for the odd vertex points it 
 is the average of the four surrounding pixels. 



   Let's examine the creation of the mesh step by step: 


\subsubsection{Creating the vertex points}

% tutorial/000154.html


{\small\begin{verbatim}
#default { finish { ambient 1 } }

#debug "Creating colored mesh to show image...\n"
mesh2
{ vertex_vectors
  { ImageWidth*ImageHeight*2,
    #declare IndY = 0;
    #while(IndY < ImageHeight)
      #declare IndX = 0;
      #while(IndX < ImageWidth)
        <(IndX/(ImageWidth-1)-.5)*ImageWidth/ImageHeight*2,
         IndY/(ImageHeight-1)*2-1, 0>,
        <((IndX+.5)/(ImageWidth-1)-.5)*ImageWidth/ImageHeight*2,
         (IndY+.5)/(ImageHeight-1)*2-1, 0>
        #declare IndX = IndX+1;
      #end
      #declare IndY = IndY+1;
    #end
  }
\end{verbatim}}


   First of all we use a nice trick in POV-\discretionary{}{}{}Ray: Since we are not using light sources and there is nothing illuminating our mesh, what we do is to set the 
 ambient value of the mesh to 1. We do this by just making it the default with the {\small\texttt{\#default}} command, so we do not have to bother later. 



   As we saw above, what we are going to do is to create two vertex points for each pixel. Thus we know without further thinking how many vertex vectors there 
 will be: {\small\texttt{ImageWidth*ImageHeight*2}} 



   That was the easy part; now we have to figure out how to create the vertex points themselves. Each vertex location should correspond to the pixel location it 
 is representing, thus we go through each pixel index (practically the number pairs in parentheses in the image above) and create vertex points using these 
 index values. The location of these pixels and vertices are the same as we assumed when we calculated the image itself (in the previous part). Thus the y 
 coordinate of each vertex point should go from -1 to 1 and similarly the x coordinate, but scaled with the aspect ratio. 



   If you look at the creation of the first vector in the code above, you will see that it is almost identical to the direction vector we calculated when 
 creating the image. 



   The second vector should be shifted by 0.5 in both directions, and that is exactly what is done there. The second vector definition is identical to the first 
 one except that the index values are shifted by 0.5. This creates the points in the middle of the squares. 



   The index values of these points will be arranged as shown in the image above. 


\subsubsection{Creating the textures}

% tutorial/000153.html


{\small\begin{verbatim}
  texture_list
  { ImageWidth*ImageHeight*2,
    #declare IndY = 0;
    #while(IndY < ImageHeight)
      #declare IndX = 0;
      #while(IndX < ImageWidth)
        texture { pigment { rgb Image[IndX][IndY] } }
        #if(IndX < ImageWidth-1 \& IndY < ImageHeight-1)
          texture { pigment { rgb
            (Image[IndX][IndY]+Image[IndX+1][IndY]+
             Image[IndX][IndY+1]+Image[IndX+1][IndY+1])/4 } }
        #else
          texture { pigment { rgb 0 } }
        #end
        #declare IndX = IndX+1;
      #end
      #declare IndY = IndY+1;
    #end
  }
\end{verbatim}}


   Creating the textures is very similar to creating the vertex points (we could have done both inside the same loop, but due to the syntax of the {\small\texttt{mesh2}} 
 we have to do it separately). 



   So what we do is to go through all the pixels in the image and create textures for each one. The first texture is just the pixel color itself. The second 
 texture is the average of the four surrounding pixels. 



   \textbf{Note:} we can calculate it only for the vertex points in the middle of the squares; for the extra vertex points outside the image we just define a 
 dummy black texture. 



   The textures have the same index values as the vertex points. 


\subsubsection{Creating the triangles}

% tutorial/000152.html



   This one is a bit trickier. Basically we have to create four triangles for each "square" between pixels. How many triangles will there be? 



   Let's examine the creation loop first: 


{\small\begin{verbatim}
  face_indices
  { (ImageWidth-1)*(ImageHeight-1)*4,
    #declare IndY = 0;
    #while(IndY < ImageHeight-1)
      #declare IndX = 0;
      #while(IndX < ImageWidth-1)

        ...

        #declare IndX = IndX+1;
      #end
      #declare IndY = IndY+1;
    #end
  }
\end{verbatim}}


   The number of "squares" is one less than the number of pixels in each direction. That is, the number of squares in the x direction will be one less 
 than the number of pixels in the x direction. The same for the y direction. As we want four triangles for each square, the total number of triangles will then 
 be {\small\texttt{(ImageWidth-1)*(ImageHeight-1)*4}}. 



   Then to create each square we loop the amount of pixels minus one for each direction. 



   Now in the inside of the loop we have to create the four triangles. Let's examine the first one: 


{\small\begin{verbatim}
        <IndX*2+  IndY    *(ImageWidth*2),
         IndX*2+2+IndY    *(ImageWidth*2),
         IndX*2+1+IndY    *(ImageWidth*2)>,
         IndX*2+  IndY    *(ImageWidth*2),
         IndX*2+2+IndY    *(ImageWidth*2),
         IndX*2+1+IndY    *(ImageWidth*2),
\end{verbatim}}


   This creates a triangle with a texture in each vertex. The first three values (the indices to vertex points) are identical to the next three values (the 
 indices to the textures) because the index values were exactly the same for both. 



   The {\small\texttt{IndX}} is always multiplied by 2 because we had two vertex points for each pixel and {\small\texttt{IndX}} is basically going through the 
 pixels. Likewise {\small\texttt{IndY}} is always multiplied by {\small\texttt{ImageWidth*2}} because that is how long a row of index points is (ie. to get 
 from one row to the next at the same x coordinate we have to advance {\small\texttt{ImageWidth*2}} in the index values). 



   These two things are identical in all the triangles. What decides which vertex point is chosen is the "+1" or "+2" (or "+0" 
 when there is nothing). For {\small\texttt{IndX}} "+0" is the current pixel, "+1" chooses the point in the middle of the square and 
 "+2" chooses the next pixel. For {\small\texttt{IndY}} "+1" chooses the next row of pixels. 



   Thus this triangle definition creates a triangle using the vertex point for the current pixel, the one for the next pixel and the vertex point in the middle 
 of the square. 



   The next triangle definition is likewise: 


{\small\begin{verbatim}
        <IndX*2+  IndY    *(ImageWidth*2),
         IndX*2+  (IndY+1)*(ImageWidth*2),
         IndX*2+1+IndY    *(ImageWidth*2)>,
         IndX*2+  IndY    *(ImageWidth*2),
         IndX*2+  (IndY+1)*(ImageWidth*2),
         IndX*2+1+IndY    *(ImageWidth*2),
\end{verbatim}}


   This one defines the triangle using the current point, the point in the next row and the point in the middle of the square. 



   The next two definitions define the other two triangles: 


{\small\begin{verbatim}
        <IndX*2+  (IndY+1)*(ImageWidth*2),
         IndX*2+2+(IndY+1)*(ImageWidth*2),
         IndX*2+1+IndY    *(ImageWidth*2)>,
         IndX*2+  (IndY+1)*(ImageWidth*2),
         IndX*2+2+(IndY+1)*(ImageWidth*2),
         IndX*2+1+IndY    *(ImageWidth*2),

        <IndX*2+2+IndY    *(ImageWidth*2),
         IndX*2+2+(IndY+1)*(ImageWidth*2),
         IndX*2+1+IndY    *(ImageWidth*2)>,
         IndX*2+2+IndY    *(ImageWidth*2),
         IndX*2+2+(IndY+1)*(ImageWidth*2),
         IndX*2+1+IndY    *(ImageWidth*2)
\end{verbatim}}

\subsection{The Camera-\discretionary{}{}{}setup}

% tutorial/000138.html



   The only thing left is the camera definition, so that POV-\discretionary{}{}{}Ray can calculate the image correctly: 


{\small\begin{verbatim}
  camera { orthographic location -z*2 look_at 0 }
\end{verbatim}}


   Why "2"? As the default {\small\texttt{direction}} vector is {\small\texttt{$<$\discretionary{0,}{}{0,}\discretionary{0,}{}{0,}1$>$}} and the default {\small\texttt{up}} vector is {\small\texttt{$<$\discretionary{0,}{}{0,}\discretionary{1,}{}{1,}0$>$}} 
 and we want the up direction to cover 2 units, we have to move the camera two units away. 


\clearpage \chapter{Questions and Tips}

% tutorial/000004.html

\index{Questions and Tips}\index{VFAQ}\index{FAQ}

   This section contains answers to frequently asked questions about POV-\discretionary{}{}{}Ray as well as many useful tips not covered in other parts of this documentation. 



   While it was current at the time that this POV-\discretionary{}{}{}Ray documentation help file was created, it will almost certainly be out of date by the time you are reading 
 this. So, if you do not find an answer to your question here, please check out the current version\footnote{ http://\discretionary{www.}{}{www.}\discretionary{povray.}{}{povray.}org/search/redirect?VFAQ} 
 on the internet. 



   If you have some question not answered in this FAQ, do not be afraid to contact the TAG\footnote{ http://\discretionary{tag.}{}{tag.}\discretionary{povray.}{}{povray.}org/} 
 or ask in the proper group of the POV-\discretionary{}{}{}Ray news-\discretionary{}{}{}server\footnote{ news://\discretionary{news.}{}{news.}\discretionary{povray.}{}{povray.}org}. 


\section{Language Tips and tricks to achieve useful things}

% tutorial/000204.html


\subsection{How do I make a visible light source?}

% tutorial/000243.html



   \textit{"How do I make a visible light source?"} or: \textit{"Although I put the camera just in front of my light source, I cannot see 
 anything. What am I doing wrong?"} 



   A light source in POV-\discretionary{}{}{}Ray is only a concept. When you add a light source to the scene, you are actually saying to POV-\discretionary{}{}{}Ray "hey, there is light coming 
 from this point". As the name says, it is a light \textbf{source}, not a physical light (like a light bulb or a bright spot like a star). POV-\discretionary{}{}{}Ray does 
 not add anything to that place where the light is coming, ie. there is nothing there, only empty space. It is just a kind of mathematical point POV-\discretionary{}{}{}Ray uses 
 to make shading calculations. 



   To make the light source visible, you have to put something there. There is a {\small\texttt{looks\_\-like}} keyword in the {\small\texttt{light\_\-source}} block 
 which allows to easily attach an object to the light source. This object implicitly does not cast any shadows. You can make something like this: 


{\small\begin{verbatim}
light_source
{ <0,0,0> color 1
  looks_like
  { sphere
    { <0,0,0>,0.1
      color { rgb 1 }
      finish { ambient 1 }
    }
  }
  translate <10,20,30>
}
\end{verbatim}}


   It is a good idea to define both things, the light source and the looks\_\-like object, at the origin, and then translate them to their right place. 



   Note also the '{\small\texttt{finish \{ ambient 1 \}}}' which makes the sphere to apparently glow (see also the next question). 



   You can also get visible light sources using other techniques: Media, lens flare (available as 3rd party include file), glow patch, etc. 


\subsection{How do I make bright objects?}

% tutorial/000242.html



   \textit{"How do I make bright objects, which look like they are emitting light?" } 



   There is a simple trick to achieve this: Set the ambient value of the object to 1 or higher. This makes POV-\discretionary{}{}{}Ray to add a very bright illumination value to 
 the object so the color of the object is in practice taken as is, without darkening it due to shadows and shading. This results in an object which seems to 
 glow light by itself even if it is in full darkness (useful to make visible light sources, or small lights like leds which do not cast any considerable light 
 to their surroundings but can be easily seen even in the darkness). 



   A more sophisticated method would be using an emitting media inside the object (and making the object itself transparent or semi-\discretionary{}{}{}transparent). 


\subsection{How do I move the camera in a circular path?}

% tutorial/000241.html



   \textit{"How do I move the camera in a circular path while looking at the origin?" } 



   There are two ways to make this: The easy (and limited) way, and the more mathematical way. 



   The easy way: 


{\small\begin{verbatim}
camera
{ location <0,0,-10>
  look_at 0
  rotate <0,clock*360,0>
}
\end{verbatim}}


   This puts the camera at 10 units in the negative Z-\discretionary{}{}{}axis and then rotates it around the Y-\discretionary{}{}{}axis while looking at the origin (it makes a circle of radius 10). 



   The mathematical way: 


{\small\begin{verbatim}
camera
{ location <10*sin(2*pi*clock),0,-10*cos(2*pi*clock)>
  look_at 0
}
\end{verbatim}}


   This makes exactly the same thing as the first code, but this way you can control more precisely the path of the camera. For example you can make the path 
 elliptical instead of circular by changing the factors of the sine and the cosine (for example instead of 10 and 10 you can use 10 and 5 which makes an 
 ellipse with the major radius 10 and minor radius 5). 



   An easier way to do the above is to use the vrotate() function, which handles the sin() and cos() stuff for you, as well as allowing you to use more complex 
 rotations. 


{\small\begin{verbatim}
camera
{ location vrotate(x*10, y*360*clock)
  look_at 0
}
\end{verbatim}}


   To get an ellipse with this method, you can just multiply the result from vrotate by a vector, scaling the resulting circle. With the last two methods you 
 can also control the look\_\-at vector (if you do not want it looking just at the origin). 



   You could also do more complex transformations combining translate, scale, rotate, and matrix transforms by replacing the vrotate() call with a call of the 
 vtransform() function found in {\small\texttt{\discretionary{functions.}{}{functions.}inc}} (new in POV-\discretionary{}{}{}Ray 3.5). 


\subsection{How do I use an image to texture my object?}

% tutorial/000240.html



   The answer to this question can be easily found in the POV-\discretionary{}{}{}Ray documentation, so I will just quote the syntax: 


{\small\begin{verbatim}
pigment
{ image_map
  { gif "image.gif"
    map_type 1
  }
}
\end{verbatim}}


   (Note that in order for the image to be aligned properly, either the object has to be located at the origin when applying the pigment or the pigment has to 
 be transformed to align with the object. It is generally easiest to create the object at the origin, apply the texture, then move it to wherever you want it.) 



   Substitute the keyword {\small\texttt{gif}} with the type of image you are using (if it is not a GIF): {\small\texttt{tga, iff, ppm, pgm, png or sys}}. 



   A {\small\texttt{map\_\-type 0}} gives the default planar mapping.\newline  A {\small\texttt{map\_\-type 1}} gives a spherical mapping (maps the image onto a 
 sphere).\newline  With {\small\texttt{map\_\-type 2}} you get a cylindrical mapping (maps the image onto a cylinder).\newline  Finally {\small\texttt{map\_\-type 5}} 
 is a torus or donut shaped mapping (maps the image onto a torus). 



   See the documentation for more details. 


\subsection{How can I generate a spline?}

% tutorial/000239.html



   \textit{"How can I generate a spline, for example for a camera path for an animation?"} 



   POV-\discretionary{}{}{}Ray 3.6 has a splines feature that allows you to create splines. This is covered in the documentation and there are demo files showing examples of use. 
 There exist also third party include files for spline generation that have greater flexibility than the internal splines, for example the spline macros by 
 Chris Colefax\footnote{ http://\discretionary{www.}{}{www.}\discretionary{geocities.}{}{geocities.}com/ccolefax/spline/\discretionary{index.}{}{index.}html}. 


\subsection{How can I simulate motion blur?}

% tutorial/000238.html



   The official POV-\discretionary{}{}{}Ray 3.6 does not support motion blur calculations, but there are some patched versions which do. 



   You can also use other tools to make this. One way to simulate motion blur is calculating a small animation and then averaging the images together. This 
 averaging of several images can be made with third party programs, such as the Targa Averager program\footnote{ http://\discretionary{iki.}{}{iki.}fi/warp/PovUtils/average/}. 
 


\subsection{How can I find the size of a text object?}

% tutorial/000237.html



   \textit{"How can I find the size of a text object / center text / justify text?" } 



   You can use the {\small\texttt{min\_\-extent()}} and {\small\texttt{max\_\-extent()}} functions to get the corners of the bounding box of any object. While this is 
 sometimes not the actual size of the object, for text objects this should be fairly accurate, enough to do alignment of the text object. 


\subsection{How do I make extruded text?}

% tutorial/000236.html



   POV-\discretionary{}{}{}Ray has true type font support built in that allows you to have 3D text in your scenes (see the documentation about the 'text' object for more details). 



   There are also some outside utilities that will import true type fonts and allow user manipulation on the text. One of these programs is called Elefont. 


\subsection{How do I make an object hollow?}

% tutorial/000235.html



   This question usually means "how do I make a hollow object, like a waterglass, a jug, etc". 



   Before answering that question, let me explain some things about how POV-\discretionary{}{}{}Ray handles objects: 



   Although the POV-\discretionary{}{}{}Ray documentation talks about "solid" and "hollow" objects, that is not how it actually works. "Solid" and 
 "hollow" are a bit misleading terms to describe the objects. You can also make an object "hollow" with that same keyword, but it is not that simple. 



   Firstly: POV-\discretionary{}{}{}Ray only handles surfaces, not solid 3D-\discretionary{}{}{}objects. When you specify a sphere, it is actually just a spherical surface. It is only a surface and it 
 is not filled by anything. This can easily be seen by putting the camera inside the sphere or by clipping a hole to one side of the sphere with the clipped\_\-by 
 keyword (so you can look inside). 



   People often think that POV-\discretionary{}{}{}Ray objects are solid, really 3D, with solid material filling the entire object because they make a 'difference' CSG object and 
 it seems like the object is actually solid. What the 'difference' CSG actually does is to cut away a part of the object and \textbf{add a new surface} in the 
 place of the hole, which completely covers the hole, so you cannot see inside the object (this new surface is actually the part of the second object which is 
 "inside" the first object). Again, if you move the camera inside the object, you will see that actually it is hollow and the object is just a surface. 



   So what is all this "solid" and "hollow" stuff the documentation talks of, and what is the "hollow" keyword used for? 



   Although objects are actually surfaces, POV-\discretionary{}{}{}Ray handles them as if they were solid. For example, fog and media do not go inside solid objects. If you put a 
 glass sphere into the fog, you will see that there is no fog inside the sphere. 



   If you add the "hollow" keyword to the object, POV-\discretionary{}{}{}Ray will no longer handle it as solid, so fog and atmosphere will invade the inside of the 
 object. This is the reason why POV-\discretionary{}{}{}Ray issues a warning when you put the camera inside a non-\discretionary{}{}{}hollow object (because, as it says, fog and other atmospheric 
 effects may not work as you expected). 



   If your scene does not use any atmospheric effect (fog or media) there is not any difference between a "solid" or "hollow" object. 



   So all the objects in POV-\discretionary{}{}{}Ray are hollow. But the surface of the objects is always infinitely thin, and there is only one surface. With real world hollow 
 objects you have always two surfaces: an outer surface and an inner surface. 



   Usually people refer to these kind of objects when they ask for hollow objects. This kind of objects are easily achieved with a 'difference' CSG operation, 
 like this: 


{\small\begin{verbatim}
// A simple water glass made with a difference:
difference
{ cone { <0,0,0>,1,<0,5,0>,1.2 }
  cone { <0,.1,0>,.9,<0,5.1,0>,1.1 }
  texture { Glass }
}
\end{verbatim}}


   The first cone limits the outer surface of the glass and the second cone limits the inner surface. 


\subsection{How can I fill a glass with water or other objects?}

% tutorial/000234.html



   As described in the "hollow objects" question above, hollow objects have always two surfaces: an outer surface and an inner surface. If we take the 
 same example, a simple glass would be like: 


{\small\begin{verbatim}
// A simple water glass made with a difference:
#declare MyGlass=
difference
{ cone { <0,0,0>,1,<0,5,0>,1.2 }
  cone { <0,.1,0>,.9,<0,5.1,0>,1.1 }
  texture { Glass }
}
\end{verbatim}}


   The first cone limits the outer surface of the glass and the second cone limits the inner surface. 



   If we want to fill the glass with water, we have to make an object which coincides with the inner surface of the glass. Note that you have to avoid the coincident 
 surfaces problem so you should scale the "water" object just a little bit smaller than the inner surface of the glass. So we make something like 
 this: 


{\small\begin{verbatim}
#declare MyGlassWithWater=
union
{ object { MyGlass }
  cone
  { <0,.1,0>,.9,<0,5.1,0>,1.1
    scale .999
    texture { Water }
  }
}
\end{verbatim}}


   Now the glass is filled with water. But there is one problem: There is too much water. The glass should be filled only up to certain level, which should be 
 definable. Well, this can be easily made with a CSG operation: 


{\small\begin{verbatim}
#declare MyGlassWithWater=
union
{ object { MyGlass }
  intersection
  { cone { <0,.1,0>,.9,<0,5.1,0>,1.1 }
    plane { y,4 }
    scale .999
    texture { Water }
  }
}
\end{verbatim}}


   Now the water level is at a height of 4 units. 


\subsection{How can I bend a object?}

% tutorial/000233.html



   There is no direct support for bending in POV-\discretionary{}{}{}Ray, but you can achieve acceptable bending with the Object Bender by Chris Colefax\footnote{ http://\discretionary{www.}{}{www.}\discretionary{geocities.}{}{geocities.}com/SiliconValley/Lakes/1434/\discretionary{bend.}{}{bend.}html}. 
 



   Some objects can be "bent" by just modelling it with other objects. For example a bent cylinder can be more easily (and accurately) achieved using 
 the intersection of a torus and some limiting objects. 



   It might be a bit strange why most renderers support bending but POV-\discretionary{}{}{}Ray does not. To understand this one has to know how other renderers (the so-\discretionary{}{}{}called 
 "scanline-\discretionary{}{}{}renderers" work): 



   In the so-\discretionary{}{}{}called "scanline renders" all objects are modelled with triangle meshes (or by primitives such as NURBS or bezier patches which can be 
 very easily converted to triangles). The "bending" is, in fact, achieved by moving the vertices of the triangles. 



   In this context the term "bending" is a bit misleading. Strictly speaking, bending a triangle mesh would also bend the triangles themselves, not 
 only move their vertices. No renderer can do this. (It can be, however, simulated by splitting the triangles into smaller triangles, and so the 
 "bending" effect is more accurate, although not yet perfect.) What these renderers do is not a true bending in the strict mathematical sense, but only an 
 approximation achieved by moving the vertices of the triangles. 



   This difference might sound irrelevant, as the result of this kind of "fake" bending usually looks as good as a true bending. However, it is not 
 irrelevant from the point of view of POV-\discretionary{}{}{}Ray. This is because POV-\discretionary{}{}{}Ray does not represent the objects with triangles, but they are true mathematical surfaces. 
 POV-\discretionary{}{}{}Ray cannot "fake" a bending by moving vertices because there are no vertices to move. In practice bending (and other 
 non-\discretionary{}{}{}linear transformations) would require the calculation of the intersection of the object surface and a curve (instead of a straight 
 line), which is pretty hard and many times analytically not possible. 



   Note that isosurface objects can be modified with proper functions in order to achieve all kinds of transformations (linear and non-\discretionary{}{}{}linear) and thus they are 
 not really bound to this limitation. However, achieving the desired transformation needs some knowledge of mathematics. 



   See also the variable ior question. 


\subsection{Can I get non-\discretionary{}{}{}grainy focal blur?}

% tutorial/000232.html



   \textit{"The focal blur is very grainy. Can I get rid of the graininess?"} 



   Yes. Set {\small\texttt{variance}} to 0 (or to a very small value, like for example 1/100000) and choose a high enough {\small\texttt{blur\_\-samples}}. The 
 rendering will probably slow down quite a lot, but the result should be very good. 


\section{Language Things that don't work as one expects}

% tutorial/000231.html


\subsection{Using several transparent objects makes them black?}

% tutorial/000230.html



   \textit{"When I put several transparent objects one in front of another or inside another, POV-\discretionary{}{}{}Ray calculates a few of them, but the rest are completely 
 black, no matter what transparency values I give."} 



   Short answer: Try increasing the {\small\texttt{max\_\-trace\_\-level}} value in the {\small\texttt{global\_\-settings}} block (the default is 5). 



   Long answer: 



   Raytracing has a peculiar feature: It can calculate reflection and refraction. Each time a ray hits the surface of an object, the program looks if this 
 surface is reflective and/or refractive. If so, it shoots another ray from this point to the appropriate direction. 



   Now, imagine we have a glass sphere. Glass reflects and refracts, so when the ray hits the sphere, two additional rays are calculated, one outside the sphere 
 (for the reflection) and one inside (for the refraction). Now the inside ray will hit the sphere again, so two new rays are calculated, and so on and so on... 



   You can easily see that there must be a maximum number of reflections/refractions calculated, because otherwise POV-\discretionary{}{}{}Ray would calculate that one pixel 
 forever. 



   This number can be set with the {\small\texttt{max\_\-trace\_\-level}} option in the {\small\texttt{global\_\-settings}} block. The default value is 5, which is 
 enough for most scenes. Sometimes it is not enough (specially when there are lots of semitransparent objects one over another) so you have to increase it. 



   So try something like: 


{\small\begin{verbatim}
global_settings
{
  max_trace_level 10
}
\end{verbatim}}

\subsection{I'm getting color banding in the image}

% tutorial/000229.html



   \textit{"When I make an image with POV-\discretionary{}{}{}Ray, it seems to use just a few colors since I get color banding or concentric circles of colors or whatever 
 where it should not. How can I make POV-\discretionary{}{}{}Ray to use more colors?"} 



   POV-\discretionary{}{}{}Ray always writes true color images (ie. with 16777216 colors, ie. 256 shades of red, 256 shades of green and 256 shades of blue) (this can be changed 
 when outputting to PNG or to B/W TGA but this is irrelevant when answering to this question). 



   So POV-\discretionary{}{}{}Ray is not guilty. It always uses the maximum color resolution available in the target image file format. 



   This problem usually happens when you are using windows with 16-bit colors (ie. only 65536 colors, the so-\discretionary{}{}{}called hicolor mode) and open the image created by 
 POV-\discretionary{}{}{}Ray with a program which does not dither the image. The image is still true color, but the program is unable to show all the colors, 
 but shows only 65536 of them (dithering is a method that "fakes" more colors by mixing pixels of two adjacent colors to simulate the in-\discretionary{}{}{}between 
 colors). 



   So the problem is not in POV-\discretionary{}{}{}Ray, but in your image viewer program. Even if POV-\discretionary{}{}{}Ray shows a poor image while rendering because you have a resolution with too 
 few colors, the image file created will have full color range. 


\subsection{Rotation behaves very strangely}

% tutorial/000228.html



   \textit{"When I rotate an object, it dissapears from the image or moves very strangely. Why?"} 



   You need to understand how rotation works in POV-\discretionary{}{}{}Ray. 



   Objects are \textbf{always} rotated around the axes. When you rotate, for example, {\small\texttt{$<$\discretionary{20,}{}{20,}\discretionary{0,}{}{0,}0$>$}}, that means that you are rotating around 
 the X-\discretionary{}{}{}axis 20 degrees (counter-\discretionary{}{}{}clockwise). This is independent of the location of the object: It always rotates around the axis (what is the center of the 
 object anyways? how do you locate it?). This means that if the object is not centered in the axis, it will orbit this axis like the Moon orbits the Earth 
 (showing always the same side to the Earth). 



   It is a very good practice to define all objects centered at the origin (ie. its 'center' is located at {\small\texttt{$<$\discretionary{0,}{}{0,}\discretionary{0,}{}{0,}0$>$}}). Then you can rotate 
 it arbitrarily. After this you can translate it to its proper location in the scene. It is a good idea to do this to every object even if you do not rotate it 
 (because you cannot never say if you will rotate it some day nevertheless). 



   What if, after all, you have a very complex object defined, but its center is not at the origin, and you want to rotate it around its center? Then you can 
 just translate it to the origin, rotate it and then translate it back to its place. Suppose that the center of the object is located at {\small\texttt{$<$\discretionary{10,}{}{10,}20,-30$>$}}; 
 you can rotate it this way: 


{\small\begin{verbatim}
translate -<10,20,-30>
rotate <whatever>
translate <10,20,-30>
\end{verbatim}}

\subsection{The image gets distorted when rendering a square image}

% tutorial/000227.html



   \textit{"If I tell POV-\discretionary{}{}{}Ray to render a square image or otherwise change the aspect ratio, the output image is distorted. What am I doing wrong?"} 



   The problem is that the camera is set to an aspect ratio of 4/3, while the picture you are trying to render has an aspect ratio of 1/1 (or whatever). 



   You can set the aspect ratio with the 'right' keyword in the camera block. The general way to set the correct aspect ratio for your image dimensions is: 


{\small\begin{verbatim}
camera
{ right x*ImageWidth/ImageHeight
  (other camera settings...)
}
\end{verbatim}}


   This keyword can also be used to change the handedness of POV-\discretionary{}{}{}Ray (see the question about Moray and POV-\discretionary{}{}{}Ray handedness for more details). 



   Note: One could think "why does not POV-\discretionary{}{}{}Ray always set automatically the aspect ratio of the camera according to the resolution of the image?". 



   There is one thing wrong in this thought: It assumes that pixels are always square (ie. the aspect ratio of the pixels is 1/1). The logic of this behaviour 
 comes clear with an example: 



   Suppose that you design a scene using a regular 4/3 aspect ratio, as usual (like 320x240, 640x480 and so on). This image is designed to look good when 
 viewing in a 4/3 monitor (as they all are in home computers). 



   Now you want to render this image for the Windows startup image. The resolution of the Windows startup image is 320x400. This resolution has not an aspect 
 ratio of 4/3 and the pixels are not square (the pixels have an aspect ratio of 1/0.6 instead of 1/1). Now, when you render your image at a resolution of 
 320x400 with POV-\discretionary{}{}{}Ray and show it with the monitor set to that resolution (as it is set at windows startup when the startup image is shown), the aspect ratio 
 will be the correct one so the image will have the correct proportions (and it will not be squeezed in any direction). 



   If you had changed the aspect ratio of the camera to 320/400 (instead of using the default 4/3) you would not only have got a different image (showing parts 
 of the scene not shown in the original or hiding parts visible in the original), but it would have looked sqeezed when shown in the 320x400 screen resolution. 



   Thus, the camera aspect ratio is the aspect ratio of the final image on screen, when viewed in the final resolution (which might not be a 4/3-resolution). 
 Since the monitor screen has an aspect ratio of 4/3, this is the default for the camera as well. 


\subsection{Why are there strange dark pixels or noise on my CSG object?}

% tutorial/000226.html

\index{black spots}

   This is the typical 'coincident surfaces problem'. This happens when two surfaces are exactly at the same place. For example: 


{\small\begin{verbatim}
union
{ box { <-1,0,-1>,<1,-2,1> texture { Texture1 } }
  box { <-2,0,-2>,<2,-1,2> texture { Texture2 } }
}
\end{verbatim}}


   The top surface of the first box is coincident with the top surface of the second box. When a ray hits this area, POV-\discretionary{}{}{}Ray has to decide which surface is 
 closest. It cannot, since they are exactly in the same place. Which one it actually chooses depends on the float number calculations, rounding error, initial 
 parameters, position of the camera, etc, and varies from pixel to pixel, causing those seemingly "random" pixels. 



   The solution to the problem is to decide which surface you want to be on top and translate that surface just a bit, so it protrudes past the unwanted 
 surface. In the example above, if we want, for example, that the second box is at the top, we will type something like: 


{\small\begin{verbatim}
union
{ box { <-1,0,-1>,<1,-2,1> texture { Texture1 } }
  box { <-2,0.001,-2>,<2,-1,2> texture { Texture2 } }
}
\end{verbatim}}


   Note that a similar problem appears when a light source is exactly on a surface: POV-\discretionary{}{}{}Ray cannot calculate accurately if it is actually inside or outside the 
 surface, so dark (shadowed) pixels appear on every surface that is illuminated by this light. 


\subsection{Why won't the textures in \discretionary{stars.}{}{stars.}inc work with my sky\_\-sphere?}

% tutorial/000225.html



   The only thing that works with a {\small\texttt{sky\_\-sphere}} is pigments. Textures and finishes are not allowed. Do not be discouraged though because you can 
 still use the textures in \discretionary{stars.}{}{stars.}inc with the following method: 



   Extract only the pigment statement from the declared textures. For example: 


{\small\begin{verbatim}
texture
{
  pigment { color_map { [0 rgb ..][.5 rgb ..][1.0 rgb ..] } scale .. }
  finish { .. }
}
\end{verbatim}}


   becomes: 


{\small\begin{verbatim}
pigment { color_map { [0 rgb ..][.5 rgb ..][1.0 rgb ..] } scale .. }
\end{verbatim}}


   The reason for this is that {\small\texttt{sky\_\-sphere}} does not have a surface, it is not an actual object. It is really just a fancy version of the 
 background feature which extracts a color from a pigment instead of being a flat color. Because of this, normal and finish features, which depend on the 
 characteristics of the surface of an object for their calculations, cannot be used. The textures in {\small\texttt{\discretionary{stars.}{}{stars.}inc}} were intended to be mapped onto 
 a real sphere, and can be used something like this: 


{\small\begin{verbatim}
sphere
{ 0, 1
  hollow // So it doesn't interfere with any media in the scene
  texture { YourSkyTexture }
  scale 100000
}
\end{verbatim}}

\subsection{When I use filter or transmit with my .tga image map nothing happens.}

% tutorial/000224.html



   POV-\discretionary{}{}{}Ray can only apply filter or transmit to 8 bit 256 color palleted images. Since most {\small\texttt{.tga}}, {\small\texttt{.png}}, and {\small\texttt{.bmp}} 
 images are 24bit and 16 million colors they do not work with filter or transmit. If you must use filter or transmit with your image maps you must reduce the 
 color depth to a format the supports 256 colors such as the {\small\texttt{.gif}} image format. 



   You might also check the POV-\discretionary{}{}{}Ray docs on using the alpha channel of {\small\texttt{.png}} files if you need specific areas that are transparent. 


\subsection{Isosurface not rendering properly?}

% tutorial/000223.html



   \textit{"My isosurface is not rendering properly: there are holes or random noise or big parts or even the whole isosurface just disappears."} 



   The most common reason for these type of phenomena with isosurfaces is a too low {\small\texttt{max\_\-gradient}} value. Use {\small\texttt{evaluate}} to make 
 POV-\discretionary{}{}{}Ray calculate a proper {\small\texttt{max\_\-gradient}} for the isosurface (remember to specify a sensible {\small\texttt{max\_\-gradient}} 
 even when you use {\small\texttt{evaluate}} or else the result may not be correct). 



   Sometimes a too high {\small\texttt{accuracy}} value can also cause problems even when the {\small\texttt{max\_\-gradient}} is ok. If playing with the latter 
 does not seem to help, try also lowering the {\small\texttt{accuracy}}. 



   Remember that specifying a {\small\texttt{max\_\-gradient}} which is too high for an isosurface, although it gives the correct result, is needlessly slow, so 
 you should always calculate the proper {\small\texttt{max\_\-gradient}} for each isosurface you make. 



   Note that there are certain pathological functions where no {\small\texttt{max\_\-gradient}} or {\small\texttt{accuracy}} will help. These functions usually 
 have discontinuities or similar "ill-\discretionary{}{}{}behaving" properties. With those you just have to find a solution which gives the best quality/speed tradeoff. 
 Isosurfaces work best with functions which give smooth surfaces. 


\section{Language related things}

% tutorial/000222.html


\subsection{How do I turn animation on?}

% tutorial/000221.html



   \textit{"How do I turn animation on? I have used the {\small\texttt{clock}}-variable in my scene, but POV-\discretionary{}{}{}Ray still only calculates one frame."} 



   The easiest way is to just specify the appropriate command line parameter on the command line or in the command line field in the rendering settings menu (in 
 the Windows version). For example, if you want to create 20 frames, type this: {\small\texttt{+kff20}} 



   This will create 20 frames with the {\small\texttt{clock}} variable going from 0 to 1. The other command line parameters are found in the POV-\discretionary{}{}{}Ray 
 documentation. 



   Ken Tyler has also another good solution for this: 



   In the directory that you installed POV-\discretionary{}{}{}Ray into you will find a subdirectory called scenes and another inside that called animate. You will find several 
 example files showing you how to write your scene to use the clock variable. You will still need to activate POV-\discretionary{}{}{}Ray's animation feature by using an {\small\texttt{.ini}} 
 file with the correct info or with command line switches. I personaly like to use the ini file method. If you try this open the master {\small\texttt{\discretionary{povray.}{}{povray.}ini}} 
 file from the tools menu and add the following lines: 


{\small\begin{verbatim}
;clock=1
;Initial_Frame=1
;Final_Frame=20
;Cyclic_Animation = on
;Subset_Start_Frame=6
;Subset_End_Frame=9
\end{verbatim}}


   Save the file and close it. When you need to use the animation feature simply go in and edit the {\small\texttt{\discretionary{povray.}{}{povray.}ini}} file and uncomment out the 
 functions you want to use. At a minimum you will need to use the {\small\texttt{initial\_\-frame}} and {\small\texttt{final\_\-frame}} option to make it work. Once 
 you have stopped rendering your series of frames be sure to comment out the clock variables in the ini file. After you have rendered a series of individual 
 frames you will still need to compile them into the animation format that you wish to use such as AVI or MPEG. See our links collection on our website\footnote{ http://\discretionary{povray.}{}{povray.}org/links/3D\_\-Animation\_\-Utilities/} 
 for programs that can help you do this. POV-\discretionary{}{}{}Ray has no internal ability to do this for you except on the Macintosh platform of the program. 



   The Mac version normally does not use {\small\texttt{.ini}} files and lacks any command line, but uses a completely graphical interface instead. To activate 
 animation, choose the render settings item from the Edit menu (right under "Preferences", it will be titled "FILENAME Settings", where 
 FILENAME is the name of your file), click on the Animation tab, and enter the needed information in the text boxes. 


\subsection{Can POV-\discretionary{}{}{}Ray use multiple processors?}

% tutorial/000220.html



   Short answer: The only way to run POV-\discretionary{}{}{}Ray on multiple processors is to run several copies of POV-\discretionary{}{}{}Ray. 



   Long answer: 



   Making a program use multiple threads is not as trivial as it may sound. Here are some reasons why it is quite difficult to make with POV-\discretionary{}{}{}Ray: 


\begin{itemize}
 
 \item 
   You cannot do it with standard C (nor C++), and POV-\discretionary{}{}{}Ray is intended to be very portable. This is not just an issue of philosophy or purism, POV-\discretionary{}{}{}Ray is 
  really used on a large variety of different platforms. 
 

 \item 
   Multithreading is a very complex issue and it is much more difficult to make a bugless multithreaded program than a single-\discretionary{}{}{}threaded (there are several 
  things in multithreading, like mutual exclusion problems, which make the multithreaded program very non-\discretionary{}{}{}deterministic). It is not impossible, though, since 
  it has been done (there are patched versions of POV-\discretionary{}{}{}Ray with multithreading support). However, it is far from trivial. 
 

 \item 
   Raytracing is usually thought as an easily threaded problem. You just calculate one pixel and draw it on screen, independent of the other pixels. 
  However, with advanced techniques, like antialiasing and specially stochastic global illumination calculation (referred as "radiosity" in POV-\discretionary{}{}{}Ray's 
  documentation and syntax) this is not true anymore. 
  \begin{itemize}
   
   \item 
     To speed up antialiasing, a threshold value is used between pixels. If the difference in color between two pixels is higher than the threshold, then 
    antialiasing is calculated. Of course we need info from the nearby pixels for this. 
   

   \item 
     In global illumination calculations lighting values are stored in a spatial tree structure. The following pixels may use the information stored in 
    this tree for their illumination. This means that the pixel calculation at the upper left corner may affect on the color of the pixel in the lower right 
    corner. This is the reason why calculating a radiosity image in parts does not work very well. 
   

  \end{itemize}
   Both problems can probably be solved in some way, but as said, it is far from trivial. 
 

\end{itemize}


   An excellent article about the issue can be found on the  Ray Tracing News web page\footnote{ http://\discretionary{www.}{}{www.}\discretionary{acm.}{}{acm.}org/tog/resources/RTNews/html/\discretionary{rtnv12n2.}{}{rtnv12n2.}html\#art3}. 
 



   Here is an answer from John M. Dlugosz with useful tips: 



   The POV-\discretionary{}{}{}Ray rendering engine is a single thread of execution, so when run on a dual Pentium Pro (running NT4) the CPU indicator only goes up to about 50\%. 
 POV does not use more than half the available power on the machine. 



   That is the basic issue, though to quibble a bit it is not exactly true: the rendering engine soaks up one whole CPU, but the editor runs on its own thread, 
 and operating system functions (writing to the file, updating the display, network activity, system background tasks) run on different threads. This gives a 
 little bit of a bonus, and the system uses as much as 54\% of available MIPS when watching it. More importantly, the machine is still highly responsive, and 
 editing or other applications continue on without being sluggish. 



   But for a long render, it is annoying to have one CPU be mostly idle. What can be done to cut rendering time in half (from 20 hours down to 10, for example)? 



   The simplest thing is to run two copies of POV on the machine. Have one copy render the top half, and the other render the bottom half. Then paste the halves 
 together in your picture editor. 



   One thing to watch out for: do not just fire up two copies and point them at the same INI file and image file. They will overwrite each other's output and 
 make a big mess. Instead, you must make sure each is writing to a different file. 



   For moderate renders, you might let one copy chug away on the long render, and use a second copy interactivly to continue development in POV. 


\subsection{Can I get a wireframe render of my scene?}

% tutorial/000219.html



   \textit{"Is there a way to generate a wireframe output image from a POV scene file?"} 



   Short answer: No. 



   Long answer: 



   You have to understand the difference between a modeller like 3D-\discretionary{}{}{}Studio and POV-\discretionary{}{}{}Ray in the way they handle objects. Those modellers always use triangle 
 meshes (and some modellers use also NURBS which can be very easily converted into triangles). Triangle meshes are extremely simple to represent in a wireframe 
 format: Just draw a line for each triangle side. 



   However, POV-\discretionary{}{}{}Ray handles most of the objects as mathematical entities, not triangle meshes. When you tell POV-\discretionary{}{}{}Ray to create a sphere, POV-\discretionary{}{}{}Ray only handles it 
 as a point and a radius, nothing else (besides the possible matrix transform applied to it). POV-\discretionary{}{}{}Ray only has a notion of the shape of the object as a 
 mathematical formula (it can calculate the intersection of a line and the sphere). 



   For wireframe output there should be a way to convert that mathematical representation of the object into actual triangles. This is called tesselation. 



   For some mathematical objects, like the sphere, the box, etc, tesselation is quite trivial. For other entities, like CSG difference, intersection, etc, it is 
 more difficult (although not impossible). For other entities it is completely impossible: infinite non-\discretionary{}{}{}flat surfaces like paraboloids and hyperboloids (well, 
 actually it is possible if you limit the size of the surface to a finite shape; still the amount of triangles that needs to be created would be extremely 
 high). 



   There have been lots of discussions about incorporating tesselation into POV-\discretionary{}{}{}Ray. But since POV-\discretionary{}{}{}Ray is just a renderer, not a modeller, it does not seem to 
 be worth the efforts (adding tesselation to all the primitives and CSG would be a \textbf{huge} job). 



   (Of course tesselation could give some other advantages, like the ability to fake non-\discretionary{}{}{}uniform transformations to objects like most triangle mesh modellers 
 do...) 



   If you just want fast previews of the image, you can try to use the quality parameter of POV-\discretionary{}{}{}Ray. For example setting quality to 0 (+q0) can give a very fast 
 render. See also the rendering speed question. 


\subsection{Can I specify variable IOR for an object?}

% tutorial/000218.html

\index{variable ior}

   \textit{"Can I specify variable IOR for an object? Is there any patch that can do this? Is it possible?"} 



   Short answer: No. 



   Long answer: 



   There are basically two ways of defining variable IOR for an object: IOR changing on the surface of the object and IOR changing throughout inside the object. 



   The first one is physically incorrect. For uniform IOR it simulates physical IOR quite correctly since for objects with uniform density the light bends at 
 the surface of the object and nowhere else. However if the density of the object is not uniform but changes throughout its volume, the light will bend inside 
 the object, while travelling through it, not only on the surface of the object. 



   This is why variable IOR on the surface of the object is incorrect and the possibility of making this was removed in POV-\discretionary{}{}{}Ray 3.1. 



   From this we can deduce that a constant IOR is kind of property of the surface of the object while variable IOR is a property of the interior of the object 
 (like media in POV-\discretionary{}{}{}Ray). Of course the physically correct interpretation of this phenomenon is that IOR is always a property of the whole object (ie. its 
 interior), not only its surface (and this is why IOR is now a property of the interior of the object in POV-\discretionary{}{}{}Ray); however, the effect of a constant IOR has 
 effect only at the surface of the object and this is what POV-\discretionary{}{}{}Ray does when bending the rays. 



   The correct simulation for variable IOR, thus, would be to bend the ray inside the object depending on the density of the interior of the object at each 
 point. 



   This is much harder to do than one may think. The reasons are similar to why non-\discretionary{}{}{}uniform transformations are too difficult to calculate reasonably (as far as 
 I know there exists no renderer that calculates true non-\discretionary{}{}{}uniform transformations; mesh modellers just move the vertices, they do not actually transform the 
 object; a true non-\discretionary{}{}{}uniform transformation would bend the triangles). Moreover: Non-\discretionary{}{}{}uniform transformations can be faked if the object is made of many polygons 
 (you can move the vertices as most mesh modellers do), but you cannot fake a variable IOR in this way. 



   Variable IOR is (mostly) impossible to calculate analytically (ie. in a mathematically exact way) at least in a reasonable time. The only way would be to 
 calculate it numerically (usually by super-\discretionary{}{}{}sampling). 



   Media in POV-\discretionary{}{}{}Ray works in this way. It does not even try to analytically solve the color of the media, but supersamples the media along the ray and averages 
 the result. This can be pretty inaccurate as we can see with the media method 1 (the only one which was supported in POV-\discretionary{}{}{}Ray 3.1). However some tricks can be 
 used to make the result more accurate without having to spend too much time, for example antialiasing (which is used by the media method 3). This is a quite 
 easy calculation because the ray is straight, POV-\discretionary{}{}{}Ray knows the start and end points of the ray and it knows that it does not intersect with anything along 
 the ray (so it does not have to make ray-\discretionary{}{}{}object intersection calculations while supersampling). 



   Variable IOR is, however, a completely different story. Here the program would have to shoot a LOT of rays along the path of the bending light ray. For each 
 ray it would have to make all the regular ray-\discretionary{}{}{}object intersection calculations. It is like having hundreds or thousands of transparent objects one inside 
 another (with max\_\-trace\_\-level set so high that the ray will go through all of them). You can easily test how slow this is. It is \textbf{very} slow. 



   One could think that "hey, why not just shoot a few tens of rays and then use some kind of antialiasing to get the fine details, like in media method 
 3". 



   Well, it might work (I have never seen it tested), but I do not think it will help much. The problem is the inaccuracy of the supersampling (even when using 
 antialiasing). In media it is not a big problem; if a very small shadowed area in the media is not detected by the supersampling process, the result will not 
 differ very much from the correct one (since the shadowed area was so small it would have diminished the brightness of that ray just a bit but no more) and it 
 will probably still look good. 



   With IOR this is not anymore true. With IOR even very, very small areas may have very strong effect in the end result, since IOR can drastically change the 
 direction of the ray thus making the result completely different (even very small changes can have great effect if the object behind the current refracting 
 object is far away). 



   This can have disastrous effects. The ior may change drastically from pixel to pixel almost at random, not to talk from frame to frame in an animation.\newline  
 To get a more or less accurate result lots of rays would be needed; just a few rays is not enough. And shooting lots of rays is an extremely slow process. 


\subsection{What is Photon Mapping?}

% tutorial/000217.html



   Photon mapping uses forward raytracing (ie. sending rays from light sources) calculate reflecting and refracting light (aka. caustics). 



   The following is from the homepage of the developer (Nathan Kopp): 



   "My latest fun addition to POV is the photon map. The basic goal of this implementation of the photon map is to render true reflective and refractive 
 caustics. The photon map was first introduced by Henrik Wann Jensen. It is a way to store light information gathered from a backwards ray-\discretionary{}{}{}tracing [sic] step 
 in a data structure independent from the geometry of a scene." 



   It is surprisingly fast and efficient. How is this possible when forward raytracing is so inefficient? For several reasons: 


\begin{enumerate}
 
 \item 
   Photon mapping is only used to calculate illumination, ie. lighting values, not to render the actual scene. Lighting values do not have to be as 
  accurate as the actual rendering (it does not matter if your reflected light "bleeds" a bit out of range; actually this kind of 
  "bleeding" happens in reality as well (due to light diffusing from air), so the result is not unrealistic at all). 
 

 \item 
   Photon mapping is calculated only for those (user-\discretionary{}{}{}specified) objects that need it (ie. objects that have reflection and/or refraction). 
 

 \item 
   The rays are not shot to all directions, towards the entire scene, but only towards those specified objects. Many rays are indeed shot in vain, without 
  them affecting the final image in any way, but since the total amountof rays shot is relatively small, the rendering time does not get inacceptably longer. 
 

 \item 
   The final image itself is rendered with regular backwards raytracing (the photon mapping is a precalculation step done before the actual rendering). 
  The raytracer does not need to use forward raytracing in this process (it just uses the precalculated lighting values which are stored in space). 
 

\end{enumerate}


   As you have seen, for the photon mapping to work in an acceptable way, you have to tell the program which objects you want to reflect/refract light and which 
 you do not. This way you can optimize a lot the photon mapping step. 


\section{File Formats}

% tutorial/000216.html


\subsection{Saving the image to disk.}

% tutorial/000215.html



   \textit{"I have rendered an image with POV-\discretionary{}{}{}Ray, but how do I save it to JPG or GIF or any other image format?"} 



   This is a typical problem of people using the Windows version of the program for first time. 



   POV-\discretionary{}{}{}Ray is a raytracer which has only one purpose: To read a source file describing the scene to raytrace and then calculate it and save it to disk in a 
 supported image format, usually TGA (and optionally PNG, BMP, etc). 



   POV-\discretionary{}{}{}Ray has always had this goal, and still has, and will (desirably) never change. It is mostly command-\discretionary{}{}{}line oriented. It supports non-\discretionary{}{}{}essential things, 
 like showing the image while it is rendering. 



   A GUI does not change anything. POV-\discretionary{}{}{}Ray is still POV-\discretionary{}{}{}Ray, with or without GUI. It takes a source code and calculates the image and saves it to disk. By 
 default it shows the image while it is raytracing it, but that is just a secondary feature, non-\discretionary{}{}{}essential, irrelevant. It can be turned off and POV-\discretionary{}{}{}Ray will 
 still make its job. 



   So the answer to the question is: The image \textbf{is already saved} on disk. 



   Usually it is saved in TGA or BMP format (it depends on the settings) with the same name as the source code (so if the source is named {\small\texttt{\discretionary{CHAIR.}{}{CHAIR.}POV}}, 
 the image will be named {\small\texttt{\discretionary{CHAIR.}{}{CHAIR.}TGA}} or {\small\texttt{\discretionary{CHAIR.}{}{CHAIR.}BMP}} or whatever). The location is either the same directory where the {\small\texttt{.pov}}-file 
 is or else a common directory for images (which you can set up in the main \discretionary{povray.}{}{povray.}ini file). 


\subsection{Can I convert my POV-\discretionary{}{}{}Ray scenes to another format?}

% tutorial/000214.html



   (Answer by Johannes Hubert) 



   For POV-\discretionary{}{}{}Ray 2.2: Try Crossroads\footnote{ http://\discretionary{www.}{}{www.}\discretionary{europa.}{}{europa.}com/\~{}keithr/crossroads} or if you want to 
 convert to Moray MDL files, try POV2MDL\footnote{ http://\discretionary{www.}{}{www.}tb-\discretionary{software.}{}{software.}com/} from Thomas Baier. 



   For POV-\discretionary{}{}{}Ray 3.1 and newer: There is unfortunately not much you can do. There is no real versatile program yet, that can read (and convert) POV-\discretionary{}{}{}Ray 3.1 
 scripts (except for POV-\discretionary{}{}{}Ray itself :-). Your best shots would be: POV2RIB\footnote{ http://\discretionary{www9.}{}{www9.}\discretionary{informatik.}{}{informatik.}uni-\discretionary{erlangen.}{}{erlangen.}de/\~{}cnvogelg/pov2rib/\discretionary{index.}{}{index.}html} 
 if you want to convert to the RIB format. If you know how to program C++, you can get the ParPov C++ library from the same URL. It is a class-\discretionary{}{}{}library for 
 reading POV 3.1 scripts and converting them to C++ objects (it also has been used for POV2RIB). 



   3DWin from Thomas Baier (see the URL above) converts from the POB format to a lot of other formats. POB is a special binary POV-\discretionary{}{}{}Ray format devised by Thomas 
 and is written by a custom-\discretionary{}{}{}compile version of POV-\discretionary{}{}{}Ray 3.0 (get the POB-\discretionary{}{}{}SDK at the same URL): This POV-\discretionary{}{}{}Ray version reads POV-\discretionary{}{}{}scripts and outputs POB files, 
 which can then be converted by 3DWin. The drawback: Although all objects, textures etc. of the scene are in the POB file, they are not all recognized by 
 3DWin. Only triangles and meshes of triangles are recognized. Everything else in the scene is lost.... 


\subsection{How can I convert my scenes from format X to POV-\discretionary{}{}{}Ray format?}

% tutorial/000213.html



   Crossroads\footnote{ http://\discretionary{www.}{}{www.}\discretionary{europa.}{}{europa.}com/\~{}keithr/crossroads} can convert a very limited subset of 
 Povray primitives (spheres and triangles work best). Particularly, it can be used to convert unions of regular (non smooth) triangles to other formats. 



   Another option is 3DWin\footnote{ http://\discretionary{www.}{}{www.}tb-\discretionary{software.}{}{software.}com/}. 


\subsection{How do I import all of my textures I created in 3DS Max into POV-\discretionary{}{}{}Ray?}

% tutorial/000212.html



   As POV-\discretionary{}{}{}Ray supports UV-\discretionary{}{}{}mapping, textured objects used by renderers such as 3D-\discretionary{}{}{}Studio can be used by first converting them with a proper converter. You can 
 find a list of converters and other related software in the  links collection on our website\footnote{ http://\discretionary{www.}{}{www.}\discretionary{povray.}{}{povray.}org/links/3D\_\-Programs/Conversion\_\-Utilities/}. 
 


\subsection{How can I avoid artifacts and still get good JPEG compression?}

% tutorial/000211.html



   (Answer by Peter J. Holzer) 



   First, you have to know a little bit about how a picture is stored in JPEG format. 



   Unlike most image formats it does not store RGB values, but YUV values (1 grayscale value and two "color difference" values) just like they are 
 used in a color TV signal. Since the human eye uses mostly the gray values to detect edges, one can usually get away with storing the color information at a 
 lower resolution - an 800x600 JPEG typically has only grayscale information at 800x600, but color information at 400x300. This is called supersampling. 



   For each color channel separately, the picture is then divided into little squares and the cosine transform of each square is computed. A neat feature of 
 this transformation is that if you throw away only a few of the values, the quality will degrade very little, but the image will compress a lot better. The 
 percentage of values stored is called the quality. 



   Finally, the data is compressed. 



   Most programs only let you change the quality setting. This is fine for photos and photorealistic renderings of "natural" scenes. Generally, 
 quality values around 75\% give be best compromise between quality and image size. 



   However, for images which contain very saturated colors, the lower resolution of the color channels causes visible artifacts which are very similar to those 
 caused by low quality settings. They can be minimized by setting an extremely high quality (close to 100\%), but this will dramatically increase the file size, 
 and often the artifacts are still visible. 



   A better method is to turn off supersampling. The higher resolution will cause only a modest increase in file size, which is more than offset by the ability 
 to use a lower quality setting. 



   The cjpeg command line utility (which should be available for all systems which have a command line, \discretionary{e.}{}{e.}g., Linux, MS-\discretionary{}{}{}DOS, Unix, ...) has an 
 "-sample" to set the sampling factors for all passes. 


{\small\begin{verbatim}
        cjpeg -sample 1x1,1x1,1x1 -quality 75 -optimize
\end{verbatim}}


   should be good default values which have to be changed only rarely. 


\subsection{Why are there no converters from POV to other formats?}

% tutorial/000210.html



   \textit{"Why are there so many converters from other 3D file formats to POV, but practically no converters from POV to other formats?"} 



   It is a mistake to think that a POV-\discretionary{}{}{}Ray file is just the same kind of data file as in most other renderers. 



   The file format of most renderers is just a data file containing numerical values (vertex coordinates, triangle indices, textures, uv-\discretionary{}{}{}coordinates, NURBS 
 data...) describing the scene. They usually are very little more than just numerical data containers. 



   However, POV-\discretionary{}{}{}Ray files are much more than just data files. POV-\discretionary{}{}{}Ray files are actually source code of the POV-\discretionary{}{}{}Ray scripting language. The POV-\discretionary{}{}{}Ray scripting 
 language is by many means a full programming language (it is Turing-\discretionary{}{}{}strong). It contains many features typical to programming languages and non-\discretionary{}{}{}typical to 
 data files (such as variables, loops, mathematical functions, macros, etc). It has many features to describe things in a much more abstract way than just 
 plain numbers. 



   This is why converting a POV-\discretionary{}{}{}file to a data file readable by other renderers is so difficult. The converter program would actually have to 
 "execute", that is, interpret the scripting language (in the exact same way as a BASIC or Perl source code is interpreted). Making a scripting language 
 interpreter is a much more laborious job than just converting numerical data from one format to another. 



   There is also another problem: POV-\discretionary{}{}{}Ray describes most of its objects as mathematical entities while most of other renderers just handle triangles (or NURBS 
 or similar easily tesselable primitives). A converter would have to make some tesselation in order to convert most POV-\discretionary{}{}{}Ray primitives to other formats. This 
 can be a quite laborious job for a converter to make (it would have to practically implement an almost fully-\discretionary{}{}{}qualified POV-\discretionary{}{}{}Ray renderer). 



   This is why making a full-\discretionary{}{}{}featured converter from any POV-\discretionary{}{}{}file to any other format is an almost impossible task. 


\subsection{Why are triangle meshes in ASCII format?}

% tutorial/000209.html



   \textit{"Why are triangle meshes in ASCII format? They are huge! A binary format would be a lot smaller. If POV-\discretionary{}{}{}Ray can read binary images, why can it 
 not read binary mesh data?"} 



   It is not as simple as you may think. 



   You cannot compare binary mesh data with image files. Yes, images are binary data, but there is one big difference: Image files use \textbf{integer} numbers 
 (usually bytes, in some cases 16-bit integers), which can be easily read in any system. 



   However, meshes use \textbf{floating point} numbers. 



   It might come as a bit of surprise that it is far from easy to represent them in binary format so that they can be read in every possible system. 



   It is very important to keep in mind that POV-\discretionary{}{}{}Ray is intended to be a very portable program, which should be compilable in virtually any system with a decent 
 C compiler. This is not just mumbo-\discretionary{}{}{}jumbo; POV-\discretionary{}{}{}Ray IS used in a wide variety of operating systems and computer architectures, including Windows, MacOS, Linux, 
 (Sparc) Solaris, Digital Unix and so on. 



   The internal representation of floating point numbers may differ in number of bits and bits reserved for each part of the number inside the data type in 
 different systems. There is also the infamous big-\discretionary{}{}{}endian/low-\discretionary{}{}{}endian problem (that is, although the floating point numbers were identical in two different 
 systems, they may be written in different byte-\discretionary{}{}{}order when writing to a file). 



   If you try to make carelessly a patch which reads and writes floating point numbers in binary format, you will probably quickly find that your patch only 
 works in a certain architecture only (eg. PC) and not others. 



   In order to store floating point numbers so that they can be read in any system, you have to store them in an universal format. ASCII is as good as any 
 other. 



   However, you are not completely out of luck when dealing with compressing mesh data. This has been done before\footnote{ http://\discretionary{www.}{}{www.}\discretionary{geocities.}{}{geocities.}com/ccolefax/\discretionary{pcm.}{}{pcm.}html}. 
 



   Since version 3.5, POV-\discretionary{}{}{}Ray supports a new type of mesh (called mesh2) which stores the mesh data in a more compact format (similar to the one used in the PCM 
 format described in the abovementioned link, but with a bit more 'syntax' around it). 


\section{Utilities, models, etc.}

% tutorial/000208.html


\subsection{What is the best animation program available?}

% tutorial/000249.html



   Check the POV-\discretionary{}{}{}Ray links collection on our website\footnote{ http://\discretionary{povray.}{}{povray.}org/links/3D\_\-Animation\_\-Utilities/}. 


\subsection{Creating/viewing MPEG-\discretionary{}{}{}files.}

% tutorial/000256.html



   \textit{"How can I create/view mpeg-\discretionary{}{}{}files in Windows/Linux/...?"} 



   See the IRTC Animation FAQ\footnote{ http://\discretionary{irtc.}{}{irtc.}org/anims/\discretionary{faq.}{}{faq.}html}. 


\subsection{Where can I find models/textures?}

% tutorial/000255.html



   Check the POV-\discretionary{}{}{}Ray links collection on our website\footnote{ http://\discretionary{povray.}{}{povray.}org/links/POV-\discretionary{}{}{}Ray\_\-Include\_\-Macro\_\-and\_\-Object\_\-Files/Object\_\-and\_\-Scene\_\-Files/}. 
 


\subsection{What are the best modellers for POV-\discretionary{}{}{}Ray?}

% tutorial/000254.html



   Check the POV-\discretionary{}{}{}Ray links collection on our website\footnote{ http://\discretionary{povray.}{}{povray.}org/links/3D\_\-Programs/POV-\discretionary{}{}{}Ray\_\-Modelling\_\-Programs/}). 
 


\subsection{Any POV-\discretionary{}{}{}Ray modellers for Mac?}

% tutorial/000253.html



   (Answer by Henri Sivonen) 



   Yes there are. However, a text editor is still needed. 



   Most of the available modelers are listed on the Official POV-\discretionary{}{}{}Ray MacOS Info Page\footnote{ http://\discretionary{mac.}{}{mac.}\discretionary{povray.}{}{povray.}org/}. 
 



   DOS, Windows and Linux i386 modelers can be used with an Intel PC emulator. With Mac OS X most Linux-\discretionary{}{}{}compatible applications with freely available source 
 code can be compiled and then run natively. 


\subsection{Is there any user gallery of POV-\discretionary{}{}{}Ray images?}

% tutorial/000252.html



   There are literaly hundreds of POV-\discretionary{}{}{}Ray users galleries. Almost anybody that uses POV-\discretionary{}{}{}Ray and has a web page has some sort of picture gallery set up. Look for 
 web page address's at the bottoms of the messages posted to the newsgroup \discretionary{comp.}{}{comp.}graphics.\discretionary{rendering.}{}{rendering.}raytracing and the povray newsgroups. 



   There are 2 places officially supported by the POV-\discretionary{}{}{}Team. They are: 



   - The POV-\discretionary{}{}{}Ray users gallery located on our web server\footnote{ http://\discretionary{www.}{}{www.}\discretionary{povray.}{}{povray.}org/}. 



   - On our private news server\footnote{ http://\discretionary{www.}{}{www.}\discretionary{povray.}{}{povray.}org/\discretionary{groups.}{}{groups.}html} (not 
 connected with USENET) in the \discretionary{povray.}{}{povray.}\discretionary{binaries.}{}{binaries.}images newsgroup, you will find many images posted from other POV-\discretionary{}{}{}Ray users. There are also discussion groups, 
 and plenty of sample code and scenes. 



   You should also check the Internet Raytracing Competition homepage\footnote{ http://\discretionary{www.}{}{www.}\discretionary{irtc.}{}{irtc.}org/}. 


\subsection{Any good heightfield modellers?}

% tutorial/000251.html



   Check the POV-\discretionary{}{}{}Ray links collection on our website\footnote{ http://\discretionary{povray.}{}{povray.}org/links/3D\_\-Programs/Height\_\-Field\_\-Modelling\_\-Programs\_\-and\_\-Utilities/}. 
 


\subsection{Any easy way of creating trees?}

% tutorial/000250.html



   A program called Tree designer by Johannes Hubert\footnote{ http://\discretionary{free.}{}{free.}\discretionary{prohosting.}{}{prohosting.}com/\~{}jhubert/TreeDesigner/} 
 is an excellent modelling program for trees. 



   There are also a several good include files for this purpose. Check out our link collection to Include Macro and Object Files\footnote{ http://\discretionary{www.}{}{www.}\discretionary{povray.}{}{povray.}org/links/POV-\discretionary{}{}{}Ray\_\-Include\_\-Macro\_\-and\_\-Object\_\-Files/}). 
 


\section{Rendering speed}

% tutorial/000207.html


\subsection{Will POV-\discretionary{}{}{}Ray render faster with a 3D card?}

% tutorial/000257.html



   \textit{"Will POV-\discretionary{}{}{}Ray render faster if I buy the latest and fastest 3D videocard?"} 



   No. 



   3D-\discretionary{}{}{}cards are not designed for raytracing. They read polygon meshes and then scanline-\discretionary{}{}{}render them. Scanline rendering has very little, if anything, to do with 
 raytracing. 3D-\discretionary{}{}{}cards cannot calculate typical features of raytracing as reflections etc. The algorithms used in 3D-\discretionary{}{}{}cards have nothing to do with raytracing. 



   This means that you cannot use a 3D-\discretionary{}{}{}card to speed up raytracing (even if you wanted to do so). Raytracing makes lots of float number calculations, and this 
 is very FPU-\discretionary{}{}{}consuming. You will get much more speed with a very fast FPU than a 3D-\discretionary{}{}{}card. 



   What raytracing does is actually this: Calculate 1 pixel color and (optionally) put it on the screen. You will get little benefit from a fast videocard since 
 only individual pixels are drawn on screen. 


\subsection{How do I increase rendering speed?}

% tutorial/000260.html



   This question can be divided into 2 questions: 



   1) What kind of hardware should I use to increase rendering speed? 



   (Answer by Ken Tyler) 



   The truth is the computations needed for rendering images are both complex and time consuming. This is one of the few program types that will actualy put 
 your processors FPU to maximum use. 



   The things that will most improve speed, roughly in order of appearance, are: 


\begin{enumerate}
 
 \item 
   CPU speed 
 

 \item 
   FPU speed 
 

 \item 
   Buss speed and level one and two memory cache - More is better. The faster the buss speed the faster the processor can swap out computations into its 
  level 2 cache and then read them back in. Buss speed therefore can have a large impact on both FPU and CPU calculation times. The more cache memory you have 
  available the faster the operation becomes because the CPU does not have to rely on the much slower system RAM to store information in. 
 

 \item 
   Memory amount, type, and speed. Faster and more is undoubtably better. Swapping out to the hard drive for increasing memory should be considered the 
  last possible option for increasing system memory. The speed of the read/write to disk operation is like walking compared to driving a car. Here again is 
  were buss speed is a major player in the fast rendering game. 
 

 \item 
   Your OS and number of applications open. Closing open applications, including background items like system monitor, task scheduler, internet 
  connections, windows volume control, and all other applications people have hiding in the background, can greatly increase rendering time by stealing cpu 
  cycles. Open task manager and see what you have open and then close everything but the absolute necessities. Other multi-\discretionary{}{}{}tasking OS's have other methods of 
  determining open application and should be used accordingly. 
 

 \item 
   And lastly your graphics card. This may seem unlikely to you but it is true. If you have a simple 16 bit graphics card your render times, compared to 
  other systems with the same processor and memory but better CG cards, will be equal. No more no less. If you play a lot of games or watch a lot of mpeg 
  movies on your system then by all means own a good CG card. If it is rendering and raytracing you want to do then invest in the best system speed and 
  architecture your money can buy. The graphics cards with hardware acceleration are designed to support fast shading of simple polygons, prevalent in the 
  gaming industry, and offer no support for the intense mathematical number crunching that goes on inside a rendering/raytracing program like Pov-\discretionary{}{}{}Ray, Studio 
  Max, and Lightwave. If your modeling program uses OpenGl shading methods then a CG card with support for OpenGL will help increase the speed of updating the 
  shading window but when it comes time to render or raytrace the image its support dissapears. 
 

\end{enumerate}


   2) How should I make the POV-\discretionary{}{}{}Ray scenes so that they will render as fast as possible? 



   These are some things which may speed up rendering without having to compromise the quality of the scene: 


\begin{itemize}
 
 \item 
   Bounding boxes: Sometimes POV-\discretionary{}{}{}Ray's automatic bounding is not perfect and considerable speed may be achieved by bounding objects by hand. These kind of 
  objects are, for example, CSG differences and intersections, blobs and poly objects. See also: CSG speed. 
 

 \item 
   Number of light sources: Each light source slows down the rendering. If your scene has many light sources, perhaps you should see if you can remove 
  some of them without loosing much quality. Also replace point light sources with spotlights whenever possible. If a light source only lights a little part of 
  the scene, a spotlight is better than a point light, since the point light is tested for each pixel while the spotlight is only tested when the pixel falls 
  into the cone of the light. 
 

 \item 
   Area lights are very slow to calculate. If you have big media effects, they are \textit{extremely} slow to calculate. Use as few area lights as 
  possible. Always use adaptive area lights unless you need very high accuracy. Use spot area lights whenever possible. 
 

 \item 
   When you have many objects with the same texture, union them and apply the texture only once. This will decrease parse time and memory use. (Of course 
  supposing that it does not matter if the texture does not move with the object anymore...) 
 

 \item 
   Things to do when doing fast test renderings: 
  \begin{itemize}
   
   \item 
     Use the quality command line parameter (ie. {\small\texttt{+Q}}). 
   

   \item 
     Comment out (or enclose with {\small\texttt{\#if}}-statements) the majority of the light sources and leave only the necessary ones to see the scene. 
   

   \item 
     Replace (with {\small\texttt{\#if}}-statements) slow objects (such as superellipsoids) with faster ones (such as boxes). 
   

   \item 
     Replace complex textures with simpler ones (like uniform colors). You can also use the {\small\texttt{quick\_\-color}} statement to do this (it will 
    work when you render with quality 5 or lower, ie. command line parameter {\small\texttt{+Q5}}). 
   

   \item 
     Reflection and refraction: When an object reflects and refracts light (such as a glass object) it usually slows down the rendering considerably. For 
    test renderings turning off one of them (reflection or refraction) or both should greatly increase rendering speed. For example, while testing glass 
    objects it is usually enough to test the refraction only and add the reflection only to the final rendering. (The problem with both reflecting and 
    refracting objects is that the rays will bounce inside the object until max\_\-trace\_\-level is reached, and this is very slow.) 
   

   \item 
     If you have reflection/refraction and a very high {\small\texttt{max\_\-trace\_\-level}}, try setting the adc\_\-bailout value to something bigger than the 
    default 1/256. 
   

  \end{itemize}
   
 

\end{itemize}

\subsection{CSG speed}

% tutorial/000259.html



   \textit{"How do the different kinds of CSG objects compare in speed? How can I speed them up?"} 



   There is a lot of misinformation about CSG speed out there. A very common allegation is that "merge is always slower than union". This statement is 
 not true. Merge is sometimes slower than union, but in some cases it is even faster. For example, consider the following code: 


{\small\begin{verbatim}
global_settings { max_trace_level 40 }
camera { location -z*8 look_at 0 angle 35 }
light_source { <100,100,-100> 1 }
merge
{ #declare Ind=0;
  #while(Ind<20)
    sphere { z*Ind,2 pigment { rgbt .9 } }
    #declare Ind=Ind+1;
  #end
}
\end{verbatim}}


   There are 20 semitransparent merged spheres there. A test render took 64 seconds. Substituting 'merge' with 'union' took 352 seconds to render (5.5 times 
 longer). The difference in speed is very notable. 



   So why is 'merge' so much faster than 'union' in this case? Well, the answer is probably that the number of visible surfaces play a very important role in 
 the rendering speed. When the spheres are unioned there are 18 inner surfaces, while when merged, those inner surfaces are gone. POV-\discretionary{}{}{}Ray has to calculate 
 lighting and shading for each one of those surfaces and that makes it so slow. When the spheres are merged, there is no need to perform lighting and shading 
 calculations for those 18 surfaces. 



   So is 'merge' always faster than 'union'? No. If you have completely non-\discretionary{}{}{}transparent objects, then 'merge' is slightly slower than 'union', and in that case 
 you should always use 'union' instead. It makes no sense using 'merge' with non-\discretionary{}{}{}transparent objects. 



   Another common allegation is "difference is very slow; much slower than union". This can also be proven as a false statement. Consider the 
 following example: 


{\small\begin{verbatim}
camera { location -z*12 look_at 0 angle 35 }
light_source { <100,100,-100> 1 }
difference
{ sphere { 0,2 }
  sphere { <-1,0,-1>,2 }
  sphere { <1,0,-1>,2 }
  pigment { rgb <1,0,0> }
}
\end{verbatim}}


   This scene took 42 seconds to render, while substituting the 'difference' with a 'union' took 59 seconds (1.4 times longer). 



   The crucial thing here is the size of the surfaces on screen. The larger the size, the slower to render (because POV-\discretionary{}{}{}Ray has to do more lighting and shading 
 calculations). 



   But the second statement is much closer to the truth than the first one: differences are usually slow to render, specially when the member objects of the 
 difference are very much bigger than the resulting CSG object. This is because POV-\discretionary{}{}{}Ray's automatic bounding is not perfect. A few words about bounding: 



   Suppose you have hundreds of objects (like spheres or whatever) forming a bigger CSG object, but this object is rather small on screen (like a little house 
 for example). It would be really slow to test ray-\discretionary{}{}{}object intersection for each one of those objects for each pixel of the screen. This is speeded up by 
 bounding the CSG object with a bounding shape (such as a box). Ray-\discretionary{}{}{}object intersections are first tested for this bounding box, and it is tested for the 
 objects inside the box only if it hits the box. This speeds rendering considerably since the tests are performed only in the area of the screen where the CSG 
 object is located and nowhere else. 



   Since it is rather easy to automatically calculate a proper bounding box for a given object, POV-\discretionary{}{}{}Ray does this and thus you do not have to do it by yourself. 



   But this automatic bounding is not perfect. There are situations where a perfect automatic bounding is very hard to calculate. One situation is the 
 difference and the intersection CSG operations. POV-\discretionary{}{}{}Ray does what it can, but sometimes it makes a pretty poor job. This can be specially seen when the 
 resulting CSG object is very small compared to the CSG member objects. For example: 


{\small\begin{verbatim}
intersection
{ sphere { <-1000,0,0>,1001 }
  sphere { <1000,0,0>,1001 }
}
\end{verbatim}}


   (This is the same as making a difference with the second sphere inversed) 



   In this example the member objects extend from $<$-2001,-1001,-1001$>$ to $<$\discretionary{2001,}{}{2001,}\discretionary{1001,}{}{1001,}1001$>$ although the resulting CSG object is a pretty small 
 lens-\discretionary{}{}{}shaped object which is only 2 units wide in the x direction and perhaps 10 or 20 or something wide in the y and z directions. As you 
 can see, it is very difficult to calculate the actual dimensions of the object (but not impossible). 



   In this type of cases POV-\discretionary{}{}{}Ray makes a huge bounding box which is useless. You should bound this kind of objects by hand (specially when the it has lots of 
 member objects). This can be done with the bounded\_\-by keyword. 



   Here is an example: 


{\small\begin{verbatim}
camera { location -z*80 look_at 0 angle 35 }
light_source { <100,200,-150> 1 }
#declare test =
difference
{ union
  { cylinder {<-2, -20, 0>, <-2, 20, 0>, 1}
    cylinder {<2, -20, 0>, <2, 20, 0>, 1}
  }
  box {<-10, 1, -10>, <10, 30, 10>}
  box {<-10, -1, -10>, <10, -30, 10>}
  pigment {rgb <1, .5, .5>}
  bounded_by { box {<-3.1, -1.1, -1.1>, <3.1, 1.1, 1.1>} }
}
 
#declare copy = 0;
#while (copy < 40)
  object {test translate -20*x translate copy*x}
  #declare copy = copy + 3;
#end
\end{verbatim}}


   This took 51 seconds to render. Commenting out the 'bounded\_\-by' line increased the rendering time to 231 seconds (4.5 times slower). 


\subsection{Does POV-\discretionary{}{}{}Ray support 3DNow?}

% tutorial/000258.html



   No, and most likely never will. 



   There are several good reasons for this: 


\begin{itemize}
 
 \item 
   3DNow uses single precision numbers while POV-\discretionary{}{}{}Ray needs (yes, it needs) double precision numbers. Single precision is not enough (this has been tested 
  in practice).\newline  (To better understand the difference between single and double precision numbers, imagine that you could represent values between 0 
  and 1000 with single precision numbers. With double precision numbers you do not get a scale from 0 to 2000 (as one might think), but from 0 to 1000000. The 
  difference is enormous and single precision is not precise enough for what POV-\discretionary{}{}{}Ray does.) 
 

 \item 
   Adding support for 3DNow (or any other CPU-\discretionary{}{}{}specific feature) to POV-\discretionary{}{}{}Ray would make it platform-\discretionary{}{}{}dependant and not portable. Of course one could make a 
  separate binary for AMD supporting 3DNow, but there are only two ways of doing this: 
  \begin{enumerate}
   
   \item 
     Compiling POV-\discretionary{}{}{}Ray with a compiler which automatically can make 3DNow code from C. As far as I know, no such compiler exists which converts double 
    precision math used in POV-\discretionary{}{}{}Ray to single precision math needed by 3DNow. I do not event know if there is any compiler that supports 3DNow at all. 
   

   \item 
     Changing the source code by hand in order to use 3DNow instructions. This is a whole lot of work (specially because you will probably have to use 
    inline assembler). The source code of POV-\discretionary{}{}{}Ray is not very small. Would it be worth the efforts? 
   

  \end{enumerate}
   
 

\end{itemize}


   Note: There are a few things in POV-\discretionary{}{}{}Ray that use single precision math (such as color handling). This is one field where some optimization might be possible 
 without degrading the image quality. 


\section{Miscellaneous questions}

% tutorial/000244.html


\subsection{Where do I suggest new features?}

% tutorial/000261.html



   \textit{"I would like to suggest some new features for the program. Who should I talk to?"} 



   This is best discussed on the Pov news groups (\discretionary{news.}{}{news.}\discretionary{povray.}{}{povray.}org) in both the general news group and the windows news group. The Pov team does skim through the 
 message posted there and occasionaly impliment ideas that have been posted by users. 



   You may also contact any of the POV-\discretionary{}{}{}Ray \discretionary{T.}{}{T.}\discretionary{A.}{}{A.}G. members with suggestions, comments, or ideas for improvements to POV-\discretionary{}{}{}Ray. You can learn more about the POV-\discretionary{}{}{}Ray 
 \discretionary{T.}{}{T.}\discretionary{A.}{}{A.}G. and their contact information on the TAG web page\footnote{ http://\discretionary{tag.}{}{tag.}\discretionary{povray.}{}{povray.}org/}. 
 


\subsection{I'm getting a "Illegal grid value in dda\_\-traversal()"}

% tutorial/000265.html



   \textit{"When I render a height field I get lots of warning messages saying "Illegal grid value in dda\_\-traversal()". How can I correct 
 that?"} 



   (Answer by Jerry Anning) 



   Basically, you have a ray going "between the cracks" of the height field due to an arithmetic accuracy problem. Sometimes it does no harm. Sometime 
 you get black dot or line artifacts. I know of no successful patch so far. I also know no completely reliable workaround. The best bet is to slightly joggle 
 the camera position and/or angle. 


\subsection{No beep when finished?}

% tutorial/000264.html



   \textit{"How can I get rid of the beep after POV-\discretionary{}{}{}Ray has calculated the image" } 



   Usually using the {\small\texttt{-P}} command-\discretionary{}{}{}line option should help (POV-\discretionary{}{}{}Ray will not pause after it has calculated the image). If you are using the 
 windows version of POV-\discretionary{}{}{}Ray, you can try Render -$>$ On Completion -$>$ Remove [v] in front of "Beep". 


\subsection{POV-\discretionary{}{}{}Ray viruses?}

% tutorial/000263.html



   \textit{"Are there any POV-\discretionary{}{}{}Ray viruses out there? Can one be done?"} 



   At the time of writing this documentation, no known viruses or trojans made with the POV-\discretionary{}{}{}Ray Scene Description Language (SDL) are known to exist. 



   Due to the properties of the POV-\discretionary{}{}{}Ray SDL, writing a working virus (that is, a piece of code which spreads, without the user knowing, by copying itself to 
 non-\discretionary{}{}{}infected files) is very difficult, if not impossible to do. The main obstacle in making a POV-\discretionary{}{}{}Ray virus is that there is no way for 
 the SDL code to reside in memory, infecting files when it sees them; another problem is that there is no way to get file listings in the POV-\discretionary{}{}{}Ray SDL, so the 
 code cannot infect other .pov files at parse time. 



   However, trojans (\discretionary{i.}{}{i.}e. a malicious piece of code which attempts to harm the system, but will not infect other files) are much more likely. It is possible 
 with the POV-\discretionary{}{}{}Ray SDL to open a file and write practically anything to it. This can be used to cause severe damage to an unprotected file system. 



   Note, however, that in POV-\discretionary{}{}{}Ray 3.5 the concept of I/O restrictions was introduced in order to protect the user from these kinds of malicious scripts. Setting 
 the I/O restrictions properly will prevent the SDL from being able to open files for writing (and optionally even for reading). You should check that your 
 copy of POV-\discretionary{}{}{}Ray 3.5 has these restrictions properly set, especially if you render files not made by you. Note, however, that not all versions of POV-\discretionary{}{}{}Ray 3.5 
 for different platforms may have these restrictions implemented. Consult section 1 of the POV-\discretionary{}{}{}Ray 3.5 documentation for more details about the I/O 
 restrictions. 



   Regardless of this, it is always a good idea to run only scripts which you have received from trusted sources. This is particularly true if you are using a 
 version of POV-\discretionary{}{}{}Ray older than 3.5. 



   The POV-\discretionary{}{}{}Ray community consists mostly of benevolent people and it is generally safe to try POV-\discretionary{}{}{}Ray scripts made by them. However, it is often better to be 
 safe than to be sorry. 


\subsection{GUI for Unix POV-\discretionary{}{}{}Ray?}

% tutorial/000262.html



   \textit{"Does POV-\discretionary{}{}{}Ray for Unix have a GUI like in Windows?"} 



   No. 



   POV-\discretionary{}{}{}Ray has always been a command-\discretionary{}{}{}line utility. Even the core code of POV-\discretionary{}{}{}Ray for Windows is exactly the same as the generic command-\discretionary{}{}{}line POV-\discretionary{}{}{}Ray. The 
 graphical interfaces of the Windows and Mac versions of POV-\discretionary{}{}{}Ray are exclusive to them (and non-\discretionary{}{}{}portable). They are much like separate "add-\discretionary{}{}{}ons". 



   There is no official GUI done for the Unix version of POV-\discretionary{}{}{}Ray. Some third-\discretionary{}{}{}parties have tried to make some GUIs for it (and you might find them in the links 
 collection on our website\footnote{ http://\discretionary{povray.}{}{povray.}org/links/}) but it seems to be a general phenomenon that Unix people like to use 
 just the command-\discretionary{}{}{}line version with a proper and powerful text editor (such as Emacs). 



   I am sorry but there is no advice right now here about how to configure Emacs in order to smoothly handle POV-\discretionary{}{}{}Ray file editing, but I might write a page 
 about that some day, when I have the time. 


\section{The shadow line artifact}

% tutorial/000247.html


\subsection{What is the problem?}

% tutorial/000269.html



   People often find an annoying problem when applying normal modifier patterns to objects. It is said that one image tells more than a thousand words, and this 
 saying also applies here. This image shows two cases where the problem appears: 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/pic1} \caption{Sometimes odd shadow lines appear on certain objects} \end{figure} 
 



   


\begin{itemize}
 
 \item 
   The object in the left of the image is just a regular POV-\discretionary{}{}{}Ray sphere with a normal modifier made with the bump pattern. 
 

 \item 
   The object in right of the image is a mesh of smooth triangles. 
 

\end{itemize}


   As you notice, there are two clear artifacts in the image. The sphere has a straight shadow line which seems unnatural and the mesh has a non-\discretionary{}{}{}straight shadow 
 line when it is supposed to have a straight one. 



   Although the artifacts look quite different in nature, they are, in fact caused by the exact same problem. \newline  



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/pic2} \caption{The image one would expect.} \end{figure} 



   What one could expect would be something like this image (do not mind about the bright part under the triangle mesh; this is explained later). \newline  


\subsection{What causes the problem?}

% tutorial/000268.html



   Let's start with the sphere with the perturbed normal, since it is easier to explain. 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/shadowtest} \caption{Shadow line test with modified normals} \end{figure} 



   This image shows graphically what happens. 



   The problem happens in the "dark side" of the object, that is, the side which does not "see" the light source. 



   Although the surface normal points away from the light source (ie. its angle is $>$90 degrees from the light source), the perturbed normal points towards it 
 (ie. its angle is $<$90 degrees) and thus, according to the normal vector, the light source should illuminate the point in question. 



   However, when doing the shadow-\discretionary{}{}{}ray test, POV-\discretionary{}{}{}Ray sees that the test ray intersects with a surface (in this case the surface of the same sphere, but at the 
 "other side"). Thus it decides that the surface in question is shadowing the current point and thus the light source does not illuminate it. 



   This is what causes the straight shadow exactly where the (non-\discretionary{}{}{}perturbed) surface normal is exactly at 90 degrees from the light source. \newline  



   The problem with the mesh of smooth triangles is a bit more difficult, although very similar (and caused by the exact same problem). 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/shadowtest2} \caption{Shadow test of a triangle mesh} \end{figure} 



   This image shows graphically what happens. 



   Although there is no explicit normal perturbation, the fact that the surface is a mesh of smooth triangles means that there is an implicit normal 
 perturbation. 



   In order to get a smooth appearance, each vertex has a normal vector and the normal vector at any point in the surface of the triangle is calculated by 
 interpolating the normal vectors of the vertices. 



   Here the problem happens when the shadow line should pass across a triangle and the unperturbed normal vector of that triangle points away from the light 
 source. As seen in the figure, a triangle that is closer to the light source will shadow the point in the current triangle (it is not necessarily the adjacent 
 triangle, but if the mesh is closed, some triangle will surely shadow the point in question). 



   This means that this unfortunate triangle will be completely shadowed, thus causing a triangular artifact in the shadow line of the mesh. \newline  



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/pic3} \caption{The shadow line corresponds to the non-\discretionary{}{}{}smooth mesh.} \end{figure} 
 



   The image on the left shows more clearly why the shadow line of the smooth triangle mesh is like it appeared in the first image of this page. 



   The object at the left is the same triangle mesh, but with flat triangles, and the object at the right is the same object as in the image at the beginning of 
 this page. 



   Notice how the shadowed triangles of the flat mesh correspond exactly to the artifacts in the shadow line of the smooth mesh. The reason for this was 
 explained in the figure above. \newline  


\subsection{Can this problem be solved?}

% tutorial/000267.html



   And how did I correct the problem in the second image at the beginning of this page? 



   Firstly, do not think that it is a bug in POV-\discretionary{}{}{}Ray. It is not a bug, but a real problem caused be the lighting model used in the renderer engine that is quite 
 difficult to surpass. It is not a problem in POV-\discretionary{}{}{}Ray in particular, but a problem in raytracing in general. Every raytracer will have this same problem when 
 using perturbed surface normals (unless there is some fix coded into it). 



   Perturbed surface normals are used, in fact, to simulate the perturbation of the surface itself. When calculating the lighting of the object, the surface 
 normal perturbation will give the impression that the surface itself is perturbed (eg. in the images at the beginning of this page the sphere looks like it 
 has a bumpy surface). 



   In triangle meshes the normal interpolation is used to simulate curvature of the surface (a curvature which actually is not there). 



   However, since the normal vector perturbation does not affect the surface itself in any way, this kind of artifact will be the price to pay (another one is 
 that although the surface looks bumpy or smooth, its silhouette will still look straight or polygonized, but this usually is not such a big problem). 



   This is a real problem that happens even to the best. For example, check this IRTC winner image\footnote{ http://\discretionary{oz.}{}{oz.}\discretionary{irtc.}{}{irtc.}org/ftp/pub/stills/1998-10-31/\discretionary{running.}{}{running.}jpg}. 
 Notice the straight shadow lines on the rocks (specially in the closest rock)? 



   However, there are certain things that can be done to alleviate the problem. 


\subsection{Possible solutions?}

% tutorial/000266.html



   1) So what did I do to get the second image at the beginning of this page? 



   I just made the objects shadowless. This gets rid of the problem of the surface shadowing the wrong point. 



   This, of course, has severe problems. Since the object does not cast shadows anymore, it probably cannot be used in any real scene (although making the rocks 
 shadowless in the IRTC winning image mentioned above would have perhaps helped the image a lot without making it too unrealistic). 



   With smooth triangle meshes it also introduces another artifact, which can be seen in the second image at the beginning of the page. I do not know the exact 
 mechanism of this artifact but it is a direct consequence of the mesh being shadowless (it may have something to do with the fact that smooth triangles are 
 double-\discretionary{}{}{}illuminated in POV-\discretionary{}{}{}Ray). 



   2) Perhaps a future version of POV-\discretionary{}{}{}Ray or one of its patches may introduce a way to stop self-\discretionary{}{}{}shadowing (while still casting shadows on other objects). 



   This would alleviate the problem of the completely shadowless object since this object could be used in real scenes and they will cast shadows on other 
 objects and they will not have the shadow line artifact. 



   However, this solution applies only to a few range of objects (mainly convex objects). Objects where self-\discretionary{}{}{}shadowing is essential (imagine a coffee cup, for 
 example) will still have problems. 



   3) I have proposed this sophisticated algorithm to get rid of the problem: 



   When doing shadow ray tests, do the following: 


\begin{enumerate}
 
 \item 
   Make the regular shadow ray test, which gets all the intersections of the ray with all the surfaces that are between the current point and the light 
  source. 
 

 \item 
   Look if in the current point the unperturbed normal vector points away from the light source and the perturbed normal vector points towards the light 
  source. 
 

 \item 
   If so, check if the closest intersection point of the shadow ray belongs to the current object. 
 

 \item 
   If so, remove that intersection point from the list. 
 

\end{enumerate}


   If we want to be more sure, we could also check if we are hitting the "inside" of the surface at this closest intersection point and only then 
 remove it. This might be necessary for non-\discretionary{}{}{}closed surfaces. 



   This algorithm will eliminate the shadowline artifact without eliminating shadowing and self-\discretionary{}{}{}shadowing of the object. 



   It has its defects, though: 


\begin{enumerate}
 
 \item 
   For example, if the camera is inside the object in question (and all the light sources are outside), we would expect to get a completely shadowed view 
  of the surface. However, if the surface has perturbed normal, we will see some illuminated parts of the surface. However, I think that this problem is quite 
  irrelevant in the vast majority of scenes (and it should be possible to turn the fix off anyways). 
 

 \item 
   It has several problems which can happen with non-\discretionary{}{}{}convex objects (thanks to Ron Parker to pointing this out). The object can shadow itself with more 
  than one surface. If it shadows itself from the outside (eg. a coffee cup), there is no problem, but if it "shadows itself" from the inside (eg. a 
  coffee cup upside down) this shadow will be seen in an unrealistic way in the outermost surface of the object. There might not be any easy way to detect, 
  which one is the case. 
 

 \item 
   Another problem similar to the above is that if there is another object inside this object we are calculating, that another object will itself also 
  "cast a shadow" on the surface (this might be possible to fix by ignoring all the objects inside the current object; this is possible to do in a rather 
  simple way; however, it is does not work in all cases). 
 

 \item 
   We still get the same artifact in triangle meshes as is shown in the second image at the beginning of the page. However, I am sure that this problem 
  could be fixed as well (although I may be wrong, of course). 
 

\end{enumerate}

\section{Smooth triangle artifact}

% tutorial/000248.html


\subsection{What is the problem?}

% tutorial/000272.html



   There is a peculiar problem with smooth triangles which shows as a lighting artifact in certain cases. This can happen in individual smooth triangles, meshes 
 with smooth triangles and smooth heightfields. The problem also manifests itself when using the slope pattern in the same situation. This image shows the two 
 cases: 



   \begin{figure} \centering \includegraphics[scale=0.60]{../final/tex/images/tutorial/startifacts} \caption{Lighting and slope pattern artifacts in a smooth triangle} \end{figure} 
 



   The source code of this image is the following: 


{\small\begin{verbatim}
camera { right x*4 location <0,1,-5> look_at 0 angle 35 }
light_source { y*100, 1 }
light_source { -y*100, x }

smooth_triangle
{ <-.5,0,-1>,<-1,1,-1>, <.5,0,-1>,<1,1,-1>, <0,0,1>,<0,1,1>
  pigment { rgb 1 }
  translate -x*.6
}
smooth_triangle
{ <-.5,0,-1>,<-1,1,-1>, <.5,0,-1>,<1,1,-1>, <0,0,1>,<0,1,1>
  pigment { slope y color_map { [0 rgb z][1 rgb x+y] } }
  finish { ambient 1 }
  translate x*.6
}
\end{verbatim}}


   The triangle at the left is a regular smooth triangle which is illuminated by a white light source from above. There is also a red light source illuminating 
 the triangle from below. As you can see, the farther part of the triangle is wrongly illuminated as red. No part of the triangle should be illuminated by the 
 red light source because the upper side of the triangle is nowhere facing down. 



   The triangle at the right is the same smooth triangle with a slope pattern applied to it, which goes from blue (in the negative y direction) to yellow (in 
 the positive y direction). Lighting has been eliminated by specifying a high ambient. As all the parts of the upper side of the triangle are pointing upwards, 
 the whole triangle should be colored with shades of yellow, but as you can see, the same farther part is wrongly colored blue. 



   (If you guessed that the problem happens when the normal vector of the triangle is pointing away from the camera, then you guessed right.) 


\subsection{What causes the problem?}

% tutorial/000271.html



   The problem is caused by the rendering algorithm used in POV-\discretionary{}{}{}Ray. The following text is quite technical, so if you just want to read about possible solutions 
 to this problem, you can skip to the next subsection. 



   The problem is that the rendering engine assumes that objects return the \textit{true} normal vector for the given point in their surface. For an object to 
 render correctly, it \textit{must} give the exact normal vector (ie. a vector which is exactly perpendicular to the surface at that point). 



   Smooth meshes and heightfields do not do this. They return normal vectors which are not perpendicular to the actual surface. This causes errors in the 
 rendering. 



   What happens is that when the rendering engine shoots a ray and it hits the surface of an object, the engine asks the object "what is the normal vector 
 at this point in your surface?". Now, if the angle between the returned normal vector and the ray vector is less than 90 degrees (that is, the normal 
 vector points away from the point of view of the starting point of the ray), then the engine reverses the returned normal vector. This is essential for the 
 lighting to work properly (if the normal is not reversed in this case, you would get all kind of errors in lighting, ie. surfaces which are illuminated from 
 behind when they should not, or surface which are not illuminated even though they are facing a light source). 



   This assumes that the normal vector returned by the object is a \textit{true} normal vector, and it works perfectly when this is so. 



   However, if the object returns an erroneous normal vector, ie. a vector which is not perpendicular to the surface, rendering errors can occur. 



   Smooth triangles and heightfields do this, and the price to pay are the artifacts in the lighting in certain situations. 



   The artifact is produced when the true normal vector would have an angle larger than 90 degrees with the ray, but the the actual vector returned by the 
 object has an angle smaller than 90 degrees with the ray. In this case the rendering engine reverses the normal vector even though it should not. This is 
 because it assumes that it is the true normal vector when in fact it is not. 



   This problem could be solved by making the decision of inverting the returned normal vector according to the true normal vector of the surface instead of the 
 returned vector. However, due to the internal implementation of the rendering engine in the current POV-\discretionary{}{}{}Ray 3.5, doing this is not trivial. It may be fixed in 
 POV-\discretionary{}{}{}Ray 4.0, where the rendering engine will be written again and this kind of things can be taken into account from the very beginning. 


\subsection{Can this problem be solved?}

% tutorial/000270.html



   You can get rid of the lighting artifact by applying {\small\texttt{double\_\-illuminate}} to the object in question. When a surface is double illuminated, it 
 does not matter which way its normal points - it will always be illuminated regardless of which side the light source is. Of course it should not matter that 
 the object is now illuminated from both sides. If this is a problem, then the problem is not easily solvable. 



   Note that in the example given at the beginning of this section this solution does not work: It would illuminate the whole triangle with both light sources! 
 However, this solution works well with closed triangle meshes, where the inner side of the mesh is shadowed by the mesh itself. However, if you are using {\small\texttt{no\_\-shadow}} 
 in the object (for example to get rid of shadow line artifacts), new problems can arise in the lighting (such as bright parts in places where there should not 
 be any; these are all cause by this same problem). 



   The slope pattern is more problematic and there is no generic solution which will work in all cases. Fortunately the most common use of the slope pattern is 
 in heightfields, and there a solution is possible: 



   If you are having this problem in a smooth heightfield, the solution is to mirror the color\_\-map (or whatever map you are using) around 0.5. This way it does 
 not matter if the normal is reversed. That is, if you had something like this in a heightfield: 


{\small\begin{verbatim}
  slope y color_map
  { [0.50 rgb <.5,.5,.5>] // rock
    [0.75 rgb <.8,.4,.1>] // ground
    [1.00 rgb <.4,1,.4>] // grass
  }
\end{verbatim}}


   you simply have to mirror the map around 0.5, ie. add the values from 0 to 0.5 in reverse order: 


{\small\begin{verbatim}
  slope y color_map
  { [0.00 rgb <.4,1,.4>] // grass
    [0.25 rgb <.8,.4,.1>] // ground
    [0.50 rgb <.5,.5,.5>] // rock
    [0.75 rgb <.8,.4,.1>] // ground
    [1.00 rgb <.4,1,.4>] // grass
  }
\end{verbatim}}


   Besides this you should, of course, apply {\small\texttt{double\_\-illuminate}} to the heightfield in order to get the proper lighting. 


\clearpage \chapter{Appendices}

% tutorial/000005.html


\section{POV-\discretionary{}{}{}Ray User License}

% tutorial/000166.html

\index{\discretionary{POVLEGAL.}{}{POVLEGAL.}DOC}\index{POVLEGAL}\index{License}\index{pov-\discretionary{}{}{}ray license}\index{user license}\index{POV-\discretionary{}{}{}Ray Legal Document}

   % ERROR: povdocgen found tag <div class="LicenseHeader"> in output!
  POV-\discretionary{}{}{}Ray License Agreement\newline  GENERAL LICENSE AGREEMENT\newline  FOR PERSONAL USE\newline  
 Persistence of Vision Ray Tracer\texttrademark  (POV-\discretionary{}{}{}Ray\texttrademark )\newline  Version 3.6 License\newline  and Terms \& Conditions of Use\newline  version of 7 June 
 2004\newline  (also known as \discretionary{POVLEGAL.}{}{POVLEGAL.}DOC)\newline   % ERROR: povdocgen found tag </div> in output!
 



   Please read through the terms and conditions of this license carefully. This license is a binding legal agreement between you, the 'User' (an individual or 
 single entity) and Persistence of Vision Raytracer Pty. Ltd. ACN 105 891 870 (herein also referred to as the "Company"), a company incorporated in 
 the state of Victoria, Australia, for the product known as the "Persistence of Vision Ray Tracer\texttrademark ", also referred to herein as 
 "POV-\discretionary{}{}{}Ray\texttrademark ". 



   YOUR ATTENTION IS PARTICULARLY DRAWN TO THE DISCLAIMER OF WARRANTY AND NO LIABILITY AND INDEMNITY PROVISIONS. TO USE THE PERSISTENCE OF VISION RAY TRACER 
 ("POV-\discretionary{}{}{}RAY") YOU MUST AGREE TO BE BOUND BY THE TERMS AND CONDITIONS SET OUT IN THIS DOCUMENT. IF YOU DO NOT AGREE TO ALL THE TERMS AND 
 CONDITIONS OF USE OF POV-\discretionary{}{}{}RAY SET OUT IN THIS LICENSE AGREEMENT, OR IF SUCH TERMS AND CONDITIONS ARE NOT BINDING ON YOU IN YOUR JURISDICTION, THEN YOU MAY NOT 
 USE POV-\discretionary{}{}{}RAY IN ANY MANNER. THIS GENERAL LICENSE AGREEMENT MUST ACCOMPANY ALL POV-\discretionary{}{}{}RAY FILES WHETHER IN THEIR OFFICIAL OR CUSTOM VERSION FORM. IT MAY NOT BE 
 REMOVED OR MODIFIED. THIS GENERAL LICENSE AGREEMENT GOVERNS THE USE OF POV-\discretionary{}{}{}RAY WORLDWIDE. THIS DOCUMENT SUPERSEDES AND REPLACES ALL PREVIOUS GENERAL LICENSES. 



   \textbf{INTRODUCTION} 



   This document pertains to the use of the Persistence of Vision Ray Tracer\texttrademark  (also known as POV-\discretionary{}{}{}Ray\texttrademark ). It applies to all POV-\discretionary{}{}{}Ray program source 
 files, executable (binary) files, scene files, documentation files, help files, bitmaps and other POV-\discretionary{}{}{}Ray files contained in official Company archives, 
 whether in full or any part thereof, and are herein referred to as the "Software". The Company reserves the right to revise these rules in future 
 versions and to make additional rules to address new circumstances at any time. Such rules, when made, will be posted in a revised license file, the latest 
 version of which is available from the Company website at http://\discretionary{www.}{}{www.}\discretionary{povray.}{}{povray.}org/\discretionary{povlegal.}{}{povlegal.}html . 



   \textbf{USAGE PROVISIONS} 



   Subject to the terms and conditions of this agreement, permission is granted to the User to use the Software and its associated files to create and render 
 images. The creator of a scene file retains all rights to any scene files they create, and any images generated by the Software from them. Subject to the 
 other terms of this license, the User is permitted to use the Software in a profit-\discretionary{}{}{}making enterprise, provided such profit arises primarily from use of the 
 Software and not from distribution of the Software or a work including the Software in whole or part. 



   Please refer to http://\discretionary{www.}{}{www.}\discretionary{povray.}{}{povray.}org/\discretionary{povlegal.}{}{povlegal.}html for licenses covering distribution of the Software and works including the Software. 



   The User is also granted the right to use the scene files, fonts, bitmaps, and include files distributed in the INCLUDE and SCENES$\backslash$\discretionary{}{}{}INCDEMO sub- directories 
 of the Software in their own scenes. Such permission does not extend to any other files in the SCENES directory or its sub-\discretionary{}{}{}directories. The SCENES files are 
 for the User's enjoyment and education but may not be the basis of any derivative works unless the file in question explicitly grants permission to do such. 



   This licence does not grant any right of re-\discretionary{}{}{}distribution or use in any manner other than the above. The Company has separate license documents that apply to 
 other uses (such as re-\discretionary{}{}{}distribution via the internet or on CD); please visit http://\discretionary{www.}{}{www.}\discretionary{povray.}{}{povray.}org/\discretionary{povlegal.}{}{povlegal.}html for links to these. In particular you are 
 advised that the sale, lease, or rental of the Software in any form without written authority from the Company is explicitly prohibited. 



   \textbf{COPYRIGHT} 



   Copyright \copyright  1991-2003, Persistence of Vision Team.\newline  Copyright \copyright  2003-2004, Persistence of Vision Raytracer Pty. Ltd.\newline  Windows 
 version Copyright \copyright  1996-2003, Christopher Cason.\newline  



   Copyright subsists in this Software which is protected by Australian and international copyright laws. The Software is NOT PUBLIC DOMAIN. 



   Nothing in this agreement shall give you any rights in respect of the intellectual property of the Company and you acknowledge that you do not acquire any 
 rights in respect of such intellectual property rights. You acknowledge that the Software is the valuable intellectual property of the Company and that if you 
 use, modify or distribute the Software for unauthorized purposes or in an unauthorized manner (or cause or allow the forgoing to occur), you will be liable to 
 the Company for any damages it may suffer (and which you acknowledge it may suffer) as well as statutory damages to the maximum extent permitted by law and 
 also that you may be liable to criminal prosecution. You indemnify the Company and the authors of the Software for every single consequence flowing from the 
 aforementioned events. 



   \textbf{DISCLAIMER OF WARRANTY} 



   This Software is provided on an "AS IS" basis, without warranty of any kind, express or implied, including without limitation, any implied 
 warranties of merchantability, fitness for a particular purpose and non-\discretionary{}{}{}infringement of intellectual property of any third party. This Software has inherent 
 limitations including design faults and programming bugs. The entire risk as to the quality and performance of the Software is borne by you, and it is your 
 responsibility to ensure that it does what you require it to do prior to using it for any purpose (other than testing it), and prior to distributing it in any 
 fashion. Should the Software prove defective, you agree that you alone assume the entire cost resulting in any way from such defect. 



   This disclaimer of warranty constitutes an essential and material term of this agreement. If you do not or cannot accept this, or if it is unenforceable in 
 your jurisdiction, then you may not use the Software in any manner. 



   \textbf{NO LIABILITY} 



   When you use the Software you acknowledge and accept that you do so at your sole risk. You agree that under no circumstances shall you have any claim against 
 the Company or anyone associated directly or indirectly with the Company whether as employee, subcontractor, agent, representative, consultant, licensee or 
 otherwise ("Company Associates") for any loss, damages, harm, injury, expense, work stoppage, loss of business information, business interruption, 
 computer failure or malfunction which may be suffered by you or by any third party from any cause whatsoever, howsoever arising, in connection with your use 
 or distribution of the Software even where the Company were aware, or ought to have been aware, of the potential of such loss. Damages referred to above shall 
 include direct, indirect, general, special, incidental, punitive and/or consequential. 



   This disclaimer of liability constitutes an essential and material term of this agreement. If you do not or cannot accept this, or if it is unenforceable in 
 your jurisdiction, then you may not use the Software. 



   \textbf{INDEMNITY} 



   You indemnify the Company and Company Associates and hold them harmless against any claims which may arise from any loss, damages, harm, injury, expense, 
 work stoppage, loss of business information, business interruption, computer failure or malfunction, which may be suffered by you or any other party 
 whatsoever as a consequence of any act or omission of the Company and/or Company Associates, whether negligent or not, arising out of your use and/or 
 distribution of the Software, or from any other cause whatsoever, howsoever arising, in connection with the Software. These provisions are binding on your 
 estate, heirs, executors, legal successors, administrators, parents and/or guardians. 



   This indemnification constitutes an essential and material term of this agreement. If you do not or cannot accept this, or if it is unenforceable in your 
 jurisdiction, then you may not use the Software. 



   \textbf{HIGH RISK ACTIVITIES} 



   This Software and the output produced by this Software is not fault-\discretionary{}{}{}tolerant and is not designed, manufactured or intended for use as on-\discretionary{}{}{}line control 
 equipment in hazardous environments requiring fail-\discretionary{}{}{}safe performance, in which the failure of the Software could lead or directly or indirectly to death, 
 personal injury, or severe physical or environmental damage ("High Risk Activities"). The Company specifically disclaims any express or implied 
 warranty of fitness for High Risk Activities and explicitly prohibits the use of the Software for such purposes. 



   \textbf{MISCELLANEOUS} 



   This Agreement constitutes the complete agreement concerning this license. Any changes to this agreement must be in writing and may take the form of 
 notifications by the Company to you, or through posting notifications on the Company website. THE USE OF THIS SOFTWARE BY ANY PERSON OR ENTITY IS EXPRESSLY 
 MADE CONDITIONAL ON THEIR ACCEPTANCE OF THE TERMS SET FORTH HEREIN. 



   Except where explicitly stated otherwise herein, if any provision of this Agreement is found to be invalid or unenforceable, the invalidity or 
 unenforceability of such provision shall not affect the other provisions of this agreement, and all provisions not affected by such invalidity or 
 unenforceability shall remain in full force and effect. In such cases you agree to attempt to substitute for each invalid or unenforceable provision a valid 
 or enforceable provision which achieves to the greatest extent possible, the objectives and intention of the invalid or unenforceable provision. The validity 
 and interpretation of this agreement will be governed by the laws of Australia in the state of Victoria (except for conflict of law provisions). 



   \textbf{CONTACT INFORMATION} 



   License inquiries can be made via email; please use the following address (but see below prior to emailing) : 



       {\small\texttt{team-\discretionary{}{}{}coord-[three-\discretionary{}{}{}letter month]-[four-\discretionary{}{}{}digit year]@\discretionary{povray.}{}{povray.}org}} 



   for example, {\small\texttt{team-\discretionary{}{}{}coord-\discretionary{}{}{}jun-2004@\discretionary{povray.}{}{povray.}org}} should be used if at the time you send the email it is the month of June 2004. The changing 
 email addresses are necessary to combat spam and email viruses. Old email addresses may be deleted at our discretion. 



   Note that the above address may change for reasons other than that given above; please check the version of this document on the WWW at 
 http://\discretionary{www.}{}{www.}\discretionary{povray.}{}{povray.}org/\discretionary{povlegal.}{}{povlegal.}html for the current address. Note that your 
 inability or failure to contact us for any reason is not an excuse for violating this licence. 



   Do NOT send any attachments of any sort other than by prior arrangement. EMAIL MESSAGES INCLUDING ATTACHMENTS WILL BE DELETED UNREAD. 



   The following postal address is only for official license business. Please note that it is preferred that initial queries about licensing be made via email; 
 postal mail should only be used when email is not possible, or when written documents are being exchanged by prior arrangement. 



       Persistence of Vision Raytracer Pty. Ltd.\newline      PO Box 407\newline      Williamstown,\newline  
     Victoria 3016\newline      Australia\newline  


\section{Citing POV-\discretionary{}{}{}Ray in Academic Publications}

% tutorial/000319.html

\index{reference}\index{citations}

   To reference POV-\discretionary{}{}{}Ray (\discretionary{e.}{}{e.}g. in academic papers), you may use one of the below: 


{\small\begin{verbatim}
  Persistence of Vision Pty. Ltd. (2004)
    Persistence of Vision Raytracer (Version 3.6)
    [Computer software].
      Retrieved from http://www.povray.org/download/
\end{verbatim}}


   or 


{\small\begin{verbatim} 
  Persistence of Vision Pty. Ltd. (2004).
  Persistence of Vision (TM) Raytracer.
  Persistence of Vision Pty. Ltd., Williamstown, Victoria, Australia.
   http://www.povray.org/
\end{verbatim}}

\section{The POV-\discretionary{}{}{}Team}

% tutorial/000167.html



   Following is a list in alphabetic order of all people who have ever worked on the POV-\discretionary{}{}{}Ray Team or who have made a note-\discretionary{}{}{}worthy contribution. 



   \textbf{Current POV-\discretionary{}{}{}Team Members} 


\begin{description}
 
 \item 
   Chris Cason 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Member 1993-, Team leader 1999-, windows version author, other contributions 
 \end{list}

 \item 
   Nicolas Calimet 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   3.6 UNIX development 
 \end{list}

 \item 
   Dale C. Brodin 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Alpha \& Beta tester, forum support 
 \end{list}

 \item 
   Alexander Enzmann 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   POV-\discretionary{}{}{}Ray 1.0/2.0/3.0 developer 
 \end{list}

 \item 
   Thorsten Fr\"{o}hlich 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Mac developer 
 \end{list}

 \item 
   Christoph Hormann 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   3.6 UNIX development 
 \end{list}

 \item 
   Alan Kong 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Alpha \& Beta tester, forum support 
 \end{list}

 \item 
   Nathan Kopp 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Photons, u/v mapping, other contributions. 
 \end{list}

 \item 
   Lutz Kretzschmar 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Moray author, MS-\discretionary{}{}{}DOS 24-bit VGA, part of the anti-\discretionary{}{}{}aliasing code 
 \end{list}

 \item 
   Ron Parker 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Core code, jack-\discretionary{}{}{}of-\discretionary{}{}{}all-\discretionary{}{}{}trades 
 \end{list}

 \item 
   Anton Raves 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Alpha \& Beta tester, Mac contributor 
 \end{list}

 \item 
   Erkki Sondergaard 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Alpha \& Beta tester, 3.0 Scene files 
 \end{list}

\end{description}


   \textbf{Past POV-\discretionary{}{}{}Team Members and other Contributors} 


\begin{description}
 
 \item 
   Claire Amundsen 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Tutorials for the POV-\discretionary{}{}{}Ray User Guide 
 \end{list}

 \item 
   Steve Anger 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   POV-\discretionary{}{}{}Ray 2.0/3.0 developer 
 \end{list}

 \item 
   Randy Antler 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   MS-\discretionary{}{}{}Dos display code enhancements 
 \end{list}

 \item 
   John Baily 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   RLE targa code 
 \end{list}

 \item 
   Eric Barish 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Ground fog code 
 \end{list}

 \item 
   Thomas Baier 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   3.1 team member, tester 
 \end{list}

 \item 
   Dieter Bayer 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Wrote sor, lathe, prism, media and many other features 
 \end{list}

 \item 
   Anthony Bennett 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Scene files, documentation 
 \end{list}

 \item 
   Kendall Bennett 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   PMODE library support, paletted display code in Windows version 
 \end{list}

 \item 
   Steve Bennett 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   GIF support 
 \end{list}

 \item 
   Thomas Bily 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Implicit and parametric surfaces 
 \end{list}

 \item 
   Eric Brown 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   no\_\-image, no\_\-reflection, orient and circular area\_\-light 
 \end{list}

 \item 
   Matthew Corey Brown 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   pigment function, warps 
 \end{list}

 \item 
   David Buck 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Original author of DKBTrace, POV-\discretionary{}{}{}Ray 1.0 developer 
 \end{list}

 \item 
   Edward Coffey 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Fade\_\-color 
 \end{list}

 \item 
   Aaron Collins 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Co-\discretionary{}{}{}author of DKBTrace 2.12, POV-\discretionary{}{}{}Ray 1.0 developer 
 \end{list}

 \item 
   Chris Dailey 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   POV-\discretionary{}{}{}Ray 3.0 developer 
 \end{list}

 \item 
   Steve Demlow 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   POV-\discretionary{}{}{}Ray 3.0 developer 
 \end{list}

 \item 
   Andreas Dilger 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Former Unix coordinator, Linux developer, PNG support 
 \end{list}

 \item 
   Joris van Drunen Littel 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Mac beta tester 
 \end{list}

 \item 
   Dan Farmer 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   POV-\discretionary{}{}{}Ray 1.0/2.0/3.0 developer, author of many features, sample scenes, and textures 
 \end{list}

 \item 
   Daniel Fenner 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Splines 
 \end{list}

 \item 
   Hans-\discretionary{}{}{}Detlev Fink 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Slope pattern 
 \end{list}

 \item 
   Charles Fusner 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Blob, lathe and prism tutorial tutorials for the POV-\discretionary{}{}{}Ray User Guide 
 \end{list}

 \item 
   Mark Gordon 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Unix developer 
 \end{list}

 \item 
   J\'{e}r\^{o}me Grimbert 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Mapping warps 
 \end{list}

 \item 
   David Harr 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Mac balloon help and palette code 
 \end{list}

 \item 
   Michael Hazelgrove 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Scene files 
 \end{list}

 \item 
   Jimmy Hoeks 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Original Help file for v3.0 Windows user interface 
 \end{list}

 \item 
   Christoph Hormann 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Scene \& include files, documentation, insert menu 
 \end{list}

 \item 
   Chris Huff 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Object pattern, Interior texture, inverse transform 
 \end{list}

 \item 
   Bob Hughes 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Scene and include files, insert menu 
 \end{list}

 \item 
   Ingo Janssen 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Scene \& include files, documentation 
 \end{list}

 \item 
   Mike Hough 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Spherical camera, Media method 2, uv\_\-mapping for bicubic\_\-patch 
 \end{list}

 \item 
   Rune S. Johansen 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Scene \& include files, documentation 
 \end{list}

 \item 
   Greg M. Johnson 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Scene files 
 \end{list}

 \item 
   Terry Kanakis 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Camera fix 
 \end{list}

 \item 
   Kari Kivisalo 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Ground fog code 
 \end{list}

 \item 
   Tor Olav Kristensen 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Scene files 
 \end{list}

 \item 
   Jochen Lippert 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Sphere\_\-sweep 
 \end{list}

 \item 
   Charles Marslett 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   MS-\discretionary{}{}{}Dos display code 
 \end{list}

 \item 
   Pascal Massimino 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Fractal objects 
 \end{list}

 \item 
   Jim McElhiney 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   POV-\discretionary{}{}{}Ray 3.0 developer 
 \end{list}

 \item 
   Robert A. Mickelsen 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Artist, 3.0 docs contributor 
 \end{list}

 \item 
   Mike Miller 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Artist, scene files, \discretionary{stones.}{}{stones.}inc 
 \end{list}

 \item 
   Fabien Mosen 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Scene \& include files 
 \end{list}

 \item 
   Douglas Muir 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Bump maps, height fields 
 \end{list}

 \item 
   Joel Newkirk 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Former Amiga developer 
 \end{list}

 \item 
   Juha Nieminen 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Fractal patterns 
 \end{list}

 \item 
   Jim Nitchals\footnote{ http://\discretionary{www.}{}{www.}\discretionary{igorlabs.}{}{igorlabs.}com/jim/\discretionary{jim.}{}{jim.}html} 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Mac version, scene files (Jim - famous also for his anti-\discretionary{}{}{}spam crusades - passed 
  away on 5 June 1998\footnote{ http://\discretionary{www.}{}{www.}\discretionary{wired.}{}{wired.}com/news/culture/\discretionary{0,}{}{0,}1284,\discretionary{12832,}{}{12832,}\discretionary{00.}{}{00.}html} 
  but his contributions to POV-\discretionary{}{}{}Ray and responsible use of the internet will not be forgotten) 
 \end{list}

 \item 
   Paul Novak 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Texture contributions 
 \end{list}

 \item 
   Wolfgang Ortmann 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Splines 
 \end{list}

 \item 
   Dave Park 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Amiga support, AGA video code 
 \end{list}

 \item 
   Redaelli Paolo 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Former Amiga developer 
 \end{list}

 \item 
   David Payne 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   RLE targa code 
 \end{list}

 \item 
   Ansgar Philippsen 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Smooth color triangle 
 \end{list}

 \item 
   Bill Pulver 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Time code 
 \end{list}

 \item 
   Dan Richardson 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   3.0 Docs 
 \end{list}

 \item 
   Tim Rowley 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   PPM and Windows-\discretionary{}{}{}specific BMP image format support 
 \end{list}

 \item 
   Eduard Schwan 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Former Mac version coordinator, mosaic preview, docs 
 \end{list}

 \item 
   Daniel Skarda 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Implicit and parametric surfaces 
 \end{list}

 \item 
   Robert Skinner 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Noise functions 
 \end{list}

 \item 
   Yvo \& Ren\'{e} Smellenbergh 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Clock \& Image\_\-size keywords 
 \end{list}

 \item 
   Ryoichi Suzuki 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Isosurfaces 
 \end{list}

 \item 
   Zsolt Szalavari 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Halo code which was later turned into media 
 \end{list}

 \item 
   Scott Taylor 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Leopard and onion textures 
 \end{list}

 \item 
   Gilles Tran 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Scene files 
 \end{list}

 \item 
   John VanSickle 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Cells pattern 
 \end{list}

 \item 
   Mark Wagner 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Splines 
 \end{list}

 \item 
   Timothy Wegner 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Fractal objects, PNG support 
 \end{list}

 \item 
   Drew Wells 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   POV-\discretionary{}{}{}Ray 1.0 developer, POV-\discretionary{}{}{}Ray 1.0 team coordinator 
 \end{list}

 \item 
   Daren Scot Wilson 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Dispersion 
 \end{list}

 \item 
   Chris Young 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Team leader 1992-1999, parser code, other contributions too numerous to list here 
 \end{list}

\end{description}

\subsection{Contacting the Authors}

% tutorial/000168.html



   The POV-\discretionary{}{}{}Team is a collection of volunteer programmers, designers, animators and artists meeting via the internet at http://\discretionary{www.}{}{www.}\discretionary{povray.}{}{povray.}org/. The POV-\discretionary{}{}{}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-\discretionary{}{}{}Ray, please visit our web site for the latest contact information, or see the online version of POVLEGAL\footnote{ http://\discretionary{www.}{}{www.}\discretionary{povray.}{}{povray.}org/\discretionary{povlegal.}{}{povlegal.}html} 
 for the current team coordinators address (this changes from time to time whenever too many email spammers harvest the address). 



   If you have a question regarding commercial use or distribution of POV-\discretionary{}{}{}Ray, please contact Chris Cason, the development team coordinator, via the above 
 method. Please do not email us directly for technical support; we no longer give support via email as too many people abused the privilege. 



   See our web site\footnote{ http://\discretionary{www.}{}{www.}\discretionary{povray.}{}{povray.}org/} and particularly our news server\footnote{ http://\discretionary{www.}{}{www.}\discretionary{povray.}{}{povray.}org/\discretionary{groups.}{}{groups.}html} 
 for online peer support. The news server has a moderated bug reporting newsgroup; please however discuss the issue in the \discretionary{povray.}{}{povray.}general\footnote{ news://\discretionary{news.}{}{news.}\discretionary{povray.}{}{povray.}org/\discretionary{povray.}{}{povray.}general} 
 newsgroup prior to lodging a bug report as we may already know of the issue (or it might not even be a bug). Also, there are several FAQ's on the POV web 
 site, and in general the folks in the newsgroups think rather poorly of users who post complaints without reading the FAQ's first. 



   Finally, there is also a dedicated Technical Assistance Group consisting of a number of trusted, experienced POV-\discretionary{}{}{}Ray users. 


\subsection{The TAG}

% tutorial/000169.html



   Established by the POV-\discretionary{}{}{}Team in late 1999, the TAG (Technical Assistance Group) is made up of selected members of the POV-\discretionary{}{}{}Ray user community. The purpose of 
 the TAG is to aid the POV-\discretionary{}{}{}Team in supporting users of POV-\discretionary{}{}{}Ray around the world, using the collective knowledge of the group to answer users' POV-\discretionary{}{}{}Ray questions 
 and to bring POV-\discretionary{}{}{}Ray related matters to the attention of the POV-\discretionary{}{}{}Team as required. 



   With their range of experiences in particular areas of computing and graphics, TAG members will always try to provide an answer to users' POV-\discretionary{}{}{}Ray questions 
 as best they can. If members of the TAG feel a question or suggestion merits the attention of the POV-\discretionary{}{}{}Team, they will redirect queries to the appropriate 
 members of the Team for consideration. 



   TAG members are not members of the POV-\discretionary{}{}{}Team. But they are, however, an official conduit between us and the outside world. They have direct access to all 
 members of the POV-\discretionary{}{}{}Team. They have the right to speak on our behalf on the POV-\discretionary{}{}{}Ray news server and on any official mailing lists that we set up for this 
 purpose. Not everything they say will be official; only when they sign it as such. They can still act as 'themselves' and have their own opinions at all other 
 times. 



   The TAG has its own website\footnote{ http://\discretionary{tag.}{}{tag.}\discretionary{povray.}{}{povray.}org/}. 



   \textbf{Technical Assistance Group Members} 


\begin{description}
 
 \item 
   Chris Colefax 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Email: {\small\texttt{\discretionary{chris.}{}{chris.}colefax [at] \discretionary{tag.}{}{tag.}\discretionary{povray.}{}{povray.}org }} 
 \end{list}

 \item 
   Chris Huff 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Email: {\small\texttt{\discretionary{chris.}{}{chris.}huff [at] \discretionary{tag.}{}{tag.}\discretionary{povray.}{}{povray.}org }} 
 \end{list}

 \item 
   Ingo Janssen 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Email: {\small\texttt{ingo [at] \discretionary{tag.}{}{tag.}\discretionary{povray.}{}{povray.}org }} 
 \end{list}

 \item 
   Juha Nieminen 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Email: {\small\texttt{warp [at] \discretionary{tag.}{}{tag.}\discretionary{povray.}{}{povray.}org }} 
 \end{list}

 \item 
   Peter Popov 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Email: {\small\texttt{\discretionary{peter.}{}{peter.}popov [at] \discretionary{tag.}{}{tag.}\discretionary{povray.}{}{povray.}org }} 
 \end{list}

 \item 
   Margus Ramst 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Email: {\small\texttt{\discretionary{margus.}{}{margus.}ramst [at] \discretionary{tag.}{}{tag.}\discretionary{povray.}{}{povray.}org }} 
 \end{list}

 \item 
   Gilles Tran 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Email: {\small\texttt{\discretionary{gilles.}{}{gilles.}tran [at] \discretionary{tag.}{}{tag.}\discretionary{povray.}{}{povray.}org }} 
 \end{list}

 \item 
   Ken Tyler 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Email: {\small\texttt{\discretionary{ken.}{}{ken.}tyler [at] \discretionary{tag.}{}{tag.}\discretionary{povray.}{}{povray.}org }} 
 \end{list}

\end{description}

\subsection{POV-\discretionary{}{}{}Ray 3.6 Development}

% tutorial/000170.html



   \textbf{Main 3.6 developers:} 


\begin{description}
 
 \item 
   Chris Cason 
 

 \item 
   Thorsten Fr\"{o}hlich 
 

 \item 
   Nathan Kopp 
 

\end{description}


   \textbf{Contributors of patches in POV-\discretionary{}{}{}Ray 3.6} 


\begin{description}
 
 \item 
   Nicolas Calimet 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   UNIX development 
 \end{list}

 \item 
   Christoph Hormann 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   UNIX development 
 \end{list}

 \item 
   Wlodzimierz 'ABX' Skiba 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Various fixes, uv-\discretionary{}{}{}mapping for parametric and torus 
 \end{list}

 \item 
   Massimo Valentini 
 

 \begin{list}{}{\setlength{\parskip}{-8pt}\setlength{\itemsep}{-2pt}}\item 
   Various fixes 
 \end{list}

\end{description}

\section{What to do if you don't have POV-\discretionary{}{}{}Ray}

% tutorial/000171.html



   This documentation assumes you already have POV-\discretionary{}{}{}Ray installed and running however the POV-\discretionary{}{}{}Team does distribute this file by itself in various formats 
 including online on the internet. If you do not have POV-\discretionary{}{}{}Ray or are not 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. 


\subsection{Which Version of POV-\discretionary{}{}{}Ray should you use?}

% tutorial/000172.html



   POV-\discretionary{}{}{}Ray can be used under Windows 9x/NT/2000, Apple Power PC, x86 Linux, UNIX and other platforms. The latest versions of the necessary files are available 
 on our web site\footnote{ http://\discretionary{www.}{}{www.}\discretionary{povray.}{}{povray.}org/} and through various CD distributions. See section "Where 
 to Find POV-\discretionary{}{}{}Ray Files" for more info. Dos, Windows 3.1, Windows for Workgroups, SunOS and Amiga are no longer supported. If your platform is not 
 supported and you are proficient in compiling source code programs written in C/C++, then you may like to retrieve the source for POV-\discretionary{}{}{}Ray from our website and 
 attempt to built it yourself. Note that the POV-\discretionary{}{}{}Team provides absolutely no support for building POV-\discretionary{}{}{}Ray from the source code, especially on platforms that we 
 do not officially support. 


\subsubsection{Microsoft Windows 9x/NT/2000/XP}

% tutorial/000176.html



   The 32-bit Windows version runs under Windows 95, Windows 98, NT, 2000 and XP or newer. Required hardware and software: Minimum - 486/100 with 32mb RAM and 
 Windows 95. Disk space - 20 megabytes. Recommended - Pentium 4 or equivalent with at least 256mb of RAM running Windows 2000 or XP, equipped with an XGA 
 display (or better) running in true color mode. 



   The forthcoming 64-bit Windows version will initially run under Windows XP 64-bit edition on AMD64-based machines, or those compatibile with them. The 
 recommended configuration has not yet been determined but as a rule of thumb we would suggest at least 256mb RAM (512mb preferred). 



   \textbf{Note:} accelerated graphics hardware will not improve performance. Nor will MMX or 3D Now. These technologies are not aimed at raytracing. 
 SSE2-equipped CPU's (such as the Pentium 4) will enhance performance if and only if an SSE2-enabled version of POV-\discretionary{}{}{}Ray for Windows is installed. If we make 
 such a version available it will be provided on our website and FTP server using a different name than that mentioned below. 



   Required POV-\discretionary{}{}{}Ray files: User archive \discretionary{POVWIN36.}{}{POVWIN36.}EXE - a self-\discretionary{}{}{}extracting archive containing the program, sample scenes, standard include files and 
 documentation. 



   Optional: The source code is not needed to use POV-\discretionary{}{}{}Ray. It is provided for the curious and adventurous. POVWIN\_\discretionary{S.}{}{S.}ZIP --- The C/C++ source code for POV-\discretionary{}{}{}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-\discretionary{}{}{}Ray can only be compiled using C/C++ compilers that create 32-bit Windows applications. 



   We currently support VC++ v7 (v6 will \textbf{not} work due to compiler issues with certain C++ features), Borland C++, Open Watcom, MinGW, and DJGPP (BJGPP 
 2.04 or later), and the Intel C++ Compiler version 8. Support for both Intel and Microsoft's C++ compiler for AMD64 is also in the works and will be 
 forthcoming in a later source code release (once we release an official 64-bit version of POV-\discretionary{}{}{}Ray for Windows). 



   Note that no matter which compiler you use, you will need to obtain the HTML Help API toolkit from Microsoft's web site (unless you already have it 
 installed). This toolkit contains header files and libraries required to compile POV-\discretionary{}{}{}Ray for Windows. 



   \textbf{Note:} while we know for certain that the code will work with VC++ v7 and the Intel compiler v8, the others mentioned above may need some tweaking 
 since we do not regularly test with them and it is possible some later code changes may have broken the build. 


\subsubsection{Linux for Intel x86}

% tutorial/000175.html



   The PC-\discretionary{}{}{}Linux version should run on any GNU/Linux distribution based on the kernel 2.2 series or above using the ELF 32-bit format for executables. The binary 
 is fully static, meaning that it has no external dependencies to system or third-\discretionary{}{}{}party libraries. It includes support for two kinds of display: the standard 
 text-\discretionary{}{}{}based display and the graphics display using either the X Window System or the SVGA library. 



   Required hardware and software: An Intel Pentium-\discretionary{}{}{}compatible CPU (i586 or better) and at least 32 MB of RAM. About 20 MB of disk space to install the program, 
 its documentation, scenes and standard include files. A text editor capable of editing plain ASCII text files. Graphic file viewer capable of viewing image 
 formats such as PNG, TIFF, PPM or TGA. 



   Required POV-\discretionary{}{}{}Ray files: povlinux-3.\discretionary{6.}{}{6.}tgz or povlinux-3.\discretionary{6.}{}{6.}\discretionary{tar.}{}{tar.}gz - archive containing an official binary combining text, SVGALib and X Window displays. Also 
 contains sample scenes, standard include files and documentation in HTML and plain ASCII text. 



   Recommended: Intel Pentium 4 or AMD Athlon XP (faster the better) with 128 MB (text console) / 256 MB (X Window running a window manager) or more RAM. A 
 recent GNU/Linux distribution with kernel 2.\discretionary{4.}{}{4.}x or above running KDE \discretionary{3.}{}{3.}x for full POV-\discretionary{}{}{}Ray integration in the window manager. Alternatively, SVGA display 
 preferably with VESA interface and high color or true color ability. 



   \textbf{Note:} accelerated graphics hardware will not improve performance. 



   Optional: povray-3.\discretionary{6.}{}{6.}tgz or povray-3.\discretionary{6.}{}{6.}\discretionary{tar.}{}{tar.}gz - archive containing the generic UNIX/Linux C++ source code of POV-\discretionary{}{}{}Ray for UNIX. The source code is not needed 
 to use POV-\discretionary{}{}{}Ray. It is provided for the curious and adventurous. The archive contains generic Unix parts and Linux specific parts (namely: support for 
 SVGAlib). This package does also include sample scenes, standard include files and documentation. For displaying purposes, the SVGAlib and X11 (X Window) 
 includes and libraries can be used by the source code of POV-\discretionary{}{}{}Ray for UNIX. See the section related to the generic Unix source code package for further 
 details. 


\subsubsection{Apple Macintosh}

% tutorial/000174.html



   The Macintosh version runs under Apple's Mac OS operating system version 8.6 (it may run on 8.1 and 8.5 as well, but we do not support POV-\discretionary{}{}{}Ray 3.6 running on 
 Mac OS 8.1 and 8.5) or newer with CarbonLib 1.0.4 or newer installed. Note that we no longer support 68K based Macintosh computers. POV-\discretionary{}{}{}Ray 3.6 requires a 
 Power Macintosh! 



   A Power Macintosh is any iMac, iBook, Mac G3, Mac G4, Mac G5, Cube, any older Mac with a four digit model number (\discretionary{i.}{}{i.}e. 5200, 6300, 7200, 8100, 9600) and any 
 third party computer running Mac OS 8.1 or later. Mac OS X 10.2 or later are supported but for maximum render speed it is not recommended to use Mac OS X. 



   Required hardware and software: Power Macintosh computer with at least 16 MB of free RAM. Mac OS 8.6 or newer with CarbonLib 1.0.4 or newer installed 
 CarbonLib 1.0.4. About 20 MB free disk space to install and an additional 5-10 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 applications is good.) 



   Required POV-\discretionary{}{}{}Ray files: \discretionary{POVPMAC.}{}{POVPMAC.}SIT or \discretionary{POVPMAC.}{}{POVPMAC.}HQX - a StuffIt archive containing the native Power Macintosh application, sample scenes, standard include 
 files and documentation. 



   Recommended: Power Macintosh G3 with 64 MB or more of free RAM. Mac OS 9.0.4 or newer with CarbonLib 1.6 (works with Mac OS 8.6 or newer) to access all 
 features of the Mac frontend. CarbonLib 1.6 is available for free download from Apple in the software update section of the Apple website. Color monitor with 
 millions of colors. 



   Optional: The source code is not needed to use POV-\discretionary{}{}{}Ray. It is provided for the curious and adventurous. POV-\discretionary{}{}{}Ray can be compiled using Metrowerks CodeWarrior 
 Pro 7.2 (for other compilers no project or make files are provided). Read the file "How to compile!" before compiling. There is no other support or 
 help for compiling the source code! \discretionary{POVMACS.}{}{POVMACS.}SIT or \discretionary{POVMACS.}{}{POVMACS.}HQX - The full C source code for POV-\discretionary{}{}{}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. 


\subsubsection{Generic Unix}

% tutorial/000180.html



   Because Unix runs on a wide variety of hardware and CPUs, the POV-\discretionary{}{}{}Team cannot provide executable versions for every kind of Unix systems. We distribute a 
 generic, portable C++ source code suitable for running on Unix or Unix-\discretionary{}{}{}like platforms. You will need a recent C++ compiler which follows the ISO C++ standard 
 as close as possible, and (optionally) the X11 and/or SVGA include files and libraries (SVGAlib is for GNU/Linux based systems). Although we provide source 
 code for generic Unix systems, we do not provide technical support on how to compile the program. Support may be obtained from the POV-\discretionary{}{}{}Ray user community on 
 the dedicated POV-\discretionary{}{}{}Ray newsgroups (\discretionary{povray.}{}{povray.}unix at \discretionary{news.}{}{news.}\discretionary{povray.}{}{povray.}org). 



   Required hardware and software: A UNIX operating system with 32 MB of RAM. A recent C++ compiler, a working make utility and Bourne-\discretionary{}{}{}compatible shell; see the 
 INSTALL file in the package for details. Graphic file viewer capable of viewing \discretionary{e.}{}{e.}g. PNG, TIFF, PPM or TGA formats. A text editor capable of editing plain 
 ASCII text files. 



   Required POV-\discretionary{}{}{}Ray files: povray-3.\discretionary{6.}{}{6.}tgz or povray-3.\discretionary{6.}{}{6.}\discretionary{tar.}{}{tar.}gz - the C++ source code of POV-\discretionary{}{}{}Ray for UNIX. Contains generic parts and UNIX/Linux specific parts. 
 The package includes sample scenes, standard include files and documentation in HTML and plain text ASCII format. 



   Recommended: Math co-\discretionary{}{}{}processor. 128 MB (text console) / 256 MB (X Window running a window manager) or more RAM. 



   Optional: The X Window System (\discretionary{e.}{}{e.}g. XFree86) to be able to display the image while rendering. The X Window System is available on most UNIX platforms 
 nowadays. On GNU/Linux platforms, the SVGAlib library can be an alternative to the X Window System, as it allows to display the rendered image directly on the 
 console screen. 


\subsubsection{All Versions}

% tutorial/000179.html



   Each executable archive includes full documentation for POV-\discretionary{}{}{}Ray itself as well as specific instructions for using POV-\discretionary{}{}{}Ray with your type of platform. All 
 versions of the program share the same ray-\discretionary{}{}{}tracing features like shapes, lighting and textures. In other words, an MS-\discretionary{}{}{}Dos-\discretionary{}{}{}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-\discretionary{}{}{}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-\discretionary{}{}{}Dos or Unix users because their documentation is plain ASCII text only. \discretionary{POVUSER.}{}{POVUSER.}PDF - 
 Tutorial and Reference documentation in Adobe Acrobat PDF format. Requires Adobe Acrobat Reader available for Windows \discretionary{3.}{}{3.}x, Windows 95/98/NT, Mac and some Unix 
 systems. \discretionary{POVHTML.}{}{POVHTML.}ZIP - Archive containing Tutorial and Reference documentation in HTML for viewing with any internet browser. 



   See the section "Where to Find POV-\discretionary{}{}{}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. 


\subsection{Where to Find POV-\discretionary{}{}{}Ray Files}

% tutorial/000178.html



   The latest versions of the POV-\discretionary{}{}{}Ray software are available from the following sources. 


\subsubsection{World Wide Website \discretionary{www.}{}{www.}\discretionary{povray.}{}{povray.}org}

% tutorial/000177.html



   The internet home of POV-\discretionary{}{}{}Ray is reachable on the World Wide Web via the address http://\discretionary{www.}{}{www.}\discretionary{povray.}{}{povray.}org/\footnote{ http://\discretionary{www.}{}{www.}\discretionary{povray.}{}{povray.}org/} 
 and via ftp as ftp://\discretionary{ftp.}{}{ftp.}\discretionary{povray.}{}{povray.}org/\footnote{ ftp://\discretionary{ftp.}{}{ftp.}\discretionary{povray.}{}{povray.}org/}. Please stop by often for the latest 
 files, utilities, news and images from the official POV-\discretionary{}{}{}Ray internet site. The POV-\discretionary{}{}{}Team operates its own news server\footnote{ http://\discretionary{www.}{}{www.}\discretionary{povray.}{}{povray.}org/\discretionary{groups.}{}{groups.}html} 
 on the internet with several news groups related to POV-\discretionary{}{}{}Ray and other interesting programs. 


\subsubsection{Books, Magazines and CD-\discretionary{}{}{}ROMs}

% tutorial/000173.html



   If you would like to print our documentation, it is available in a number of formats that are designed for printing. In particular, PDF, postscript, and TeX. 
 See the POV-\discretionary{}{}{}Ray website for more details. 



   Unfortunately all English language books on POV-\discretionary{}{}{}Ray are out of print and there are no plans to reprint them. However there are now several POV-\discretionary{}{}{}Ray books 
 available in Japanese. Many popular computer magazines have been authorized to distribute POV-\discretionary{}{}{}Ray on cover CD's. From time to time we, the makers of POV-\discretionary{}{}{}Ray, 
 will ourselves make CDROM's available, either direct from our website or from authorized distributors. See the our website\footnote{ http://\discretionary{www.}{}{www.}\discretionary{povray.}{}{povray.}org/} 
 for more information, as that location will always contain the most up-\discretionary{}{}{}to-\discretionary{}{}{}date details. 


\section{Suggested Reading}

% tutorial/000096.html



   Beside the POV-\discretionary{}{}{}Ray material mentioned in "Books, Magazines and CD-\discretionary{}{}{}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. 


\begin{enumerate}
 
 \item 
   "An Introduction to Ray tracing" Andrew S. Glassner (editor) \newline ISBN 0-12-286160-4; Academic Press; 1989 
 

 \item 
   "Realistic Image Synthesis Using Photon Mapping" Henrik Wann Jensen \newline ISBN: 1568811470; AK Peters; July 2001 
 

 \item 
   "3D Artist" Newsletter, "The Only Newsletter about Affordable PC 3D Tools and Techniques") \newline Publisher: Bill Allen; \discretionary{P.}{}{P.}O. Box 
  4787; Santa Fe, NM 87502-4787; (505) 982-3532 
 

 \item 
   "Image Synthesis: Theory and Practice" Nadia Magnenat-\discretionary{}{}{}Thalman and Daniel Thalmann; \newline Springer-\discretionary{}{}{}Verlag; 1987 
 

 \item 
   "The RenderMan Companion" Steve Upstill; \newline Addison Wesley; 1989 
 

 \item 
   "Graphics Gems" Andrew S. Glassner (editor); \newline Academic Press; 1990 
 

 \item 
   "Fundamentals of Interactive Computer Graphics" J. D. Foley and A. Van Dam; \newline ISBN 0-201-14468-9; Addison-\discretionary{}{}{}Wesley 1983 
 

 \item 
   "Computer Graphics: Principles and Practice (2nd Ed.)" J. D. Foley, A. van Dam, J. F. Hughes; \newline ISBN 0-201-12110-7; Addison-\discretionary{}{}{}Wesley; 
  1990 
 

 \item 
   "Computers, Pattern, Chaos, and Beauty" Clifford Pickover; \newline \discretionary{St.}{}{St.}Martin's Press; 
 

 \item 
   "SIGGRAPH Conference Proceedings"; \newline Association for Computing Machinery Special Interest Group on Computer Graphics 
 

 \item 
   "IEEE Computer Graphics and Applications"; The Computer Society; \newline 10662, Los Vaqueros Circle; Los Alamitos, CA 90720 
 

\end{enumerate}


   The POV-\discretionary{}{}{}Team \textbf{no longer recommends} books from CRC Press. Go read Eric's commentary\footnote{ http://\discretionary{mathworld.}{}{mathworld.}\discretionary{wolfram.}{}{wolfram.}com/erics\_\discretionary{commentary.}{}{commentary.}html} 
 to find out why. 


\cleardoublepage

\printindex

\end{document}
