OS/2 Professional/OS2PRO194.ISO/os2/graphic/dkb/docs/dkb212.doc

Text File | 1991-05-04 | 153.8 KB | 3,693 lines

                        DKBTrace Ray-Tracer,
                          Version 2.12
              "It's free, and it's well worth the price!"


This program was written by:

    David Buck
    22C Sonnet Cres.
    Nepean, Ontario
    Canada, K2H 8W7

It has been made freely distributable.  The author retains the
copyright to the program but authorizes free distribution by BBS'es,
networks or by magnetic media.  The distributor may choose to charge
for the cost of the disk but must not sell the software for profit.
Non-profit organizations such as clubs may charge for the software so
long as the price is reasonable (less than $5.00 more than the cost of
the disk) and so long as the buyers are informed that the program is
freely distributable.

The images and data files generated by the raytracer are the property
of the user of the software and may be used for any purpose without
restriction.

The author makes no guarantees or warranties with this program and
claims no responsibility for any damage or loss of time caused by this
program. Bug reports may be sent to the author but the author is under
no obligation to provide bug fixes, features, or any support for this
software.

I would also like to place the following conditions on the use of this program:

 1) that it should not be used as part of any commercial package without my
    explicit written consent.
 2) if you make any neat and interesting pictures, please send them to me.
 3) If you make any changes to the source code, please let me know. I'd like
    to see what you've done.
 4) This text file should accompany the program.


I can be reached on the following BBS'es:

    OMX       [phone]
    Mystic    [phone] or [phone]
    FidoNet   1:163/109.9
    Internet  [e-mail]
    CIS       70521,1371
    "You can call me Ray"   [phone]

Aaron Collins (IBM port) can be reached on the following BBS'es

    "You can call me Ray"   [phone]

AAC:  As of July of 1990, there is a Ray-Trace specific BBS in the (708) Area
Code (Chicago suburbia) for all you Traceaholics out there.  The phone number
of this new BBS is [phone].  I am Co-Sysop of that board, and David is
a frequent caller.  There is now also a Ray-Trace and Computer-Generated Art
specific SIG on Compuserve, GO COMART.  And now, back to the DOCS...

The GIF file reader was written by Steven A. Bennett.  Here's his copyright
notice:

    * DECODER.C - An LZW decoder for GIF
    * Copyright (C) 1987, by Steven A. Bennett
    *
    * Permission is given by the author to freely redistribute and include
    * this code in any program as long as this credit is given where due.
    *
    * In accordance with the above, I want to credit Steve Wilhite, who
    * wrote the code which this is heavily inspired by...
    *
    * GIF and 'Graphics Interchange Format' are trademarks (tm) of
    * Compuserve, Incorporated, an H&R Block Company.

The Noise and DNoise functions (used for texturing) were written by
Robert Skinner and used here with his permission.



This manual is divided into the following sections:
   1) Program Description
   2) Program History and Information
   3) Getting Started
   4) Command Line Parameters
   5) A Tutorial Walkthrough
   6) The Scene Description Language
   7) Displaying the Images
   8) DKBTrace Utilities
   9) How it All Works (or How to Get What You Want)
  10) Common Questions and Answers
  11) Converting Data Files from Versions Prior to 2.10
  12) Handy Hints
  13) Compiling the Code
  14) Porting to Different Platforms
  15) References
  16) Concluding Remarks

Some sample worlds and their corresponding images are provided with this
distribution.  To be honest, the images I usually create are dull boring
test files.  Other people, however, have created some really spectacular
images.  Looking at the data files for these will give you some ideas and
help you design your own data files.




1)  Program Description


This program is a ray tracer written completely in C.  It supports
arbitrary quadric surfaces (spheres, ellipsoids, cones, cylinders,
planes, etc.), constructive solid geometry, and various shading models
(reflection, refraction, marble, wood, and many others).  It also has
special-case code to handle spheres, planes, triangles, and smooth
triangles.  By using these special primitives, the rendering can be
done much more quickly than by using the more general quadrics.  In
order to create pictures with this program, you must describe the
objects in the world.  This description is a text file called
"<filename>.data", and <filename> defaults to "object" if not
specified.  Normally, such files are difficult to write and to read.
In order to make this task easier, the program contains a parser to
read the data file.  It allows the user to easily create complex
worlds from simple components.  Since the parser allows include files,
the user may put the object descriptions into different files and
combine them all into one final image.



2)  Program History and Information


Version 1.2:
    Initial Amiga release.

Version 2.0:
    First release Version 2.0 Conversion to the IBM done by Aaron A. Collins
    New textures, Specular and Phong highlighting added by Aaron A. Collins.
    Triangle, Smooth Triangle, Sphere, Plane support added by David Buck
    RAW, IFF and GIF image mapping added by David Buck and Aaron Collins
    Transparency and Fog added by David Buck
    GIF format file reader by Steve Bennett (used with permission)
    New Noise and DNoise functions by Robert Skinner (used with permission)
    TARGA format output file capability added by Aaron A. Collins
    ANSI-C function prototyping for ALL functions,
    Reversal of the order of writing screen data from the original DKB/QRT
       "RAW" file format.
    For IBM's, it has a crude VGA 320x200 by 256 color display rendering
       ability.

    Version 2.0 compiles under Turbo-C 2.0 on the IBM P.C. and Lattice C
    5.05 on the Amiga.  The only file which contains the ANSI extensions
    is dkbproto.h, so for non-ANSI compilers, you only need to remove the
    declaration of the parameters in the config.h file and the whole thing
    should compile.  There are several example config.h files for Amiga,
    IBM, and Unix.  The appropriate one should be copied over CONFIG.H,
    and the MAKEFILE should be edited for your particular system and
    compiler configuration before compilation.

    Version 2.0 has a significant difference from prior releases:  Speed!
    The new primitives of SPHERE, PLANE, TRIANGLE, etc. greatly speed up
    tracing.  Another significant speed-up is that world X-Y-Z values
    beyond 10 Million or so are ignored, and ray tracing beyond that
    distance will cease.  This produces 2 minor peculiarities:

     1)   A black stripe at the horizon point of Pre-2.0 scene description
          .data files that have "ground" and "sky" planes defined.  The
          planes were traced out to a much greater "infinity" so this effect
          was unnoticeable, prior to version 2.0.

     2)   Tiny black pixels in the texture, or "Surface Acne".


    This is usually caused by rays being refracted or reflected such that
    the ray does not happen to hit any object, and eventually becomes
    black in color as it gets too far away and gets clipped.  This effect
    can be minimized by enclosing the scene with distant "walls",
    "floors", or placing "ocean floors" beneath water, etc.  So far, no
    scenes have required placing such planes behind the camera, unless an
    "environment map" of sorts is desired.  See SKYTEST.DAT for several
    examples of spurious distant planes.  If your "acne" still doesn't go
    away, it may be due to a large pixel sample area and it's accidentally
    picking a point which is just inside the primitive being hit.  This is
    a more tricky problem to solve, and anti-aliasing the image will
    definitely help if this sort of thing occurs.

Version 2.10:
    A few unofficial releases were made between 2.01 and 2.10.  The following
    points capture the major changes:

    - Less memory is required for image mapped GIF and IFF files.
    - The output format command-line option was changed to +fx where 'x'
      denotes the output format.
    - The display option +d now takes an optional extra character +dx
      where 'x' is system-dependent.  This allows you to specify the graphics
      mode by a command-line switch.
    - The tokenizing pass has been removed.  It's now called directly by the
      parser.
    - The environment variable DKBOPT is used in addition to the trace.def file
      and the command-line options.
    - The numbers in the data file can now use full scientific notation
      eg. 10.23e-4
    - The +c option was added to continue an aborted trace.
    - You can now colour or texture each component of the CSG's separately.
    - Layered textures implemented (see the section on textures).
    - When using GIF and IFF images for image mapping, you can now indicate that
      specified registers are partially or completely transparent.
    - Textures are now transformed whenever the object or shape they are attached
      to are transformed.
    - The texture CHECKER_TEXTURE has been added.
    - All keywords relating to the appearance of the surface have been made
      illegal in an object definition unless they are inside a TEXTURE block.
    - The "basicshapes.data" file has been split up into shapes.dat, colors.dat,
      and textures.dat.  These files have also been expanded with more useful
      declarations.
    - The -l command-line parameter has been added to support library
      directories.

Version 2.11:
    - Quartic surfaces (4th order) added by Alexander Enzmann.
    - Parser now accepts ^Z as a whitespace
    - Keyword END_SMOOTH_TRIANGLE added (previously, END_TRIANGLE was used.)

Version 2.12:
    - Bug in smooth triangles fixed to allow them to be scaled and translated.
    - METALLIC texture added.

3)  Getting Started

If you've been reading this document diligently until now, you'll probably
want to go in and display some images to see what the raytracer does.
Here's what you need to do:

   1) Put the file "sunset.dat" into your current directory.
   2) Make sure the files "colors.dat", "shapes.dat", and "textures.dat"
      are present.
   3) Set up the default parameters.  This can be done by creating a file
      called "trace.def" or by setting the DKBOPT environment variable.
      In either case, use the following line (you may change these defaults
      to suit your system):

         -w320 -h400 -v +f +d +p +x -a

      Meaning:
         -v    - Don't be verbose, i.e. don't show line numbers during trace.
         +f    - Write an output file in "dump" or "Targa" format (machine
                 specific; IBM default is "Targa", Amiga default is "dump".
         +d    - Display the image while rendering (on some systems, an
                 additional character may follow this option to specify the
                 graphics mode to use for the display).
         -w320 - Make the image 320 pixels wide.
         -h400 - Make the image 400 pixels high.
         +p    - Prompt before exitting to let you look at the picture.
         +x    - Allow exitting with a key hit before the trace is finished.
         -a    - Don't Antialias (Antialiasing smooths out jagged edges).

   4) To render a scene, type:

         dkbxxx -isunset.dat -osunset.dis
           ^
           |_____ See note below:


      Meaning:
         dkbxxx - On different systems, the name of the executable may vary.
                 Check to see what it is on your system.  For the Amiga,
                 for example, two versions are supplied: dkb881 and dkbieee
                 for systems with and without a floating-point accelerator.
                 For the IBM, DKB.EXE is the 20286 optimized/uses 80287 math
                 coprocessor version, and DKBNO87.EXE is the plain 8086/no
         8087 math coprocessor version.

         -isunset.dat
               - Read the input file "sunset.dat"

         -osunset.dis
               - Call the output file "sunset.dis" - this is the usual file
             name extension for "dump" format.  "Targa" format files
         (default for IBM's) generally use the extension ".tga".


   5) Once the image has been rendered, you must use a post-processor to
      create the final viewable image file (i.e. an IFF or GIF file), unless
      you possess 24-bit display hardware and can view the generated output
      files directly.  The post-processor used depends on your system.  See
      the section "Displaying the Images" for more details on post-processing
      the image.

The following section gives a detailed description of the command-line
options.



4)  Command Line Parameters

This program is designed to be run from a command line.  The command-line
parameters may be specified in any order.  Repeated parameters overwrite
the previous values.  Parameters may also be specified in a file called
"trace.def" or by the environment variable "DKBOPT".

     -wxxx     width of the picture in pixels
               (On the Amiga, use 320 for full-sized pictures)
     -hxxx     height of the picture in pixels
               (On the Amiga, use 400 for full-sized pictures)

     +v        verbose option - print out the scan line number.
     -v        disable verbose option

     +f[x]     produce an output file
     -f        don't produce an output file

               If the +f option is used, the ray tracer will produce an
               output file of the picture.  This output file describes each
               pixel with 24 bits.  Currently, three formats of output files
               are supported:

                  +fd    (default) - Dump format (QRT-style)
                  +fr              - Raw format - three files for R, G and B.
                  +ft              - Uncompressed Targa-24 format


               Normally, a post-processor is required to create the final
               finished image from the data file.  See the section on
               "Displaying the Images" for details.


     +d[x]     display the picture while tracing
     -d        don't display the picture while tracing

               If the +d option is used, then the picture will be displayed
               while the program performs the ray tracing.  On most systems,
               this picture is not as good as the one created by the post-
               processor because it does not try to make optimum choices for
               the colour registers.


               Depending on the system, a letter may follow the +d option to
               specify the graphics mode to use.

                  All systems:
                    +d      Default Format (same as +d0)

                  Amiga:
                    +d0     Ham format
                    +dE     Ham-E format

                  IBM:
                    +d0     Autodetect (S)VGA type
                    +d1     Standard VGA 320x200
                    +d2     Simulated SVGA 360x480
                    +d3     Tseng Labs 3000 SVGA 640x480
                    +d4     Tseng Labs 4000 SVGA 640x480
                    +d5     AT&T VDC600 SVGA 640x400
                    +d6     Oak Technologies SVGA 640x480
                    +d7     Video 7 SVGA 640x480
                    +d8     Video 7 Vega (Cirrus) VGA 360x480
                    +d9     Paradise SVGA 640x480
                    +dA     Ahead Systems Ver. A SVGA 640x480
                    +dB     Ahead Systems Ver. B SVGA 640x480
                    +dC     Chips & Technologies SVGA 640x480
                    +dD     ATI SGVA 640x480
                    +dE     Everex SVGA 640x480
                    +dF     Trident SVGA 640x480
                    +dG     VESA Standard SVGA Adapter 640x480


     +p        wait for prompt (IBM: beep and pause) before quitting
     -p        finish without waiting

               The +p option makes the program wait for a carriage return
               before exitting (and closing the graphics screen).  This gives
               you time to admire the final picture before destroying it.


  -ifilename   set the input filename
  -ofilename   set output filename

               If your input file is not "Object.dat", then you can use -i
               to set the filename.  The default output filename will be
               "data.dis" for dump mode, "data.red", "data.grn" or "data.blu"
               for raw mode, and "data.tga" for Targa mode.  If you want a
               different output file name, use the -o option.

               (on IBM's, the default extensions for raw mode are ".r8",
               ".g8", and ".b8" to conform to PICLAB's "raw" format).

     +a[xxx]   anti-alias - xxx is an optional tolerance level (default 0.3)
     -a        don't anti-alias

               The +a option enables adaptive anti-aliasing.  The number
               after the +a option determines the threshold for the anti-
               aliasing.  If the colour of a pixel differs from its neighbor
               (to the left or above) by more than the threshold, then the
               pixel is subdivided and super-sampled.

               If the anti-aliasing threshold is 0.0, then every pixel is
               supersampled.  If the threshold is 1.0, then no anti-aliasing
               is done.  Good values seem to be around 0.2 to 0.4.

               The super-samples are jittered to introduce noise and make the
               pictures look better.  Note that the jittering "noise" is non-
               random and repeatable in nature, based on an object's 3-D
               orientation in space.  Thus, it's okay to use anti-aliasing for
               animation sequences, as the anti-aliased pixels won't vary and
               flicker annoyingly from frame to frame.

     +x        allow early exit by hitting any key (IBM only)
     -x        lock in trace until finished        (IBM only)

               On the IBM, the -x option disables the ability to abort the
               trace by hitting a key.  If you are unusually clumsy or have
               CATS that stomp on your keyboard (like I do - AAC :-)), you
               may want to use it.  If you are writing a file, the system
               will recognize ^C at the end of line if the system "BREAK"
               is "ON".  If you aren't writing a file, you won't be able to
               abort the trace until it's done.

               This option was meant for big, long late-nite traces that take
               ALL night (or longer!), and you don't want them interrupted by
               anything less important than a natural disaster such as hur-
               ricane, fire, flood, famine, etc.

     -bxxx     use an output file buffer of xxx kilobytes.
               (if 0, flush the file on every line - this is the default)

               The -b option allows you to assign large buffers to the output
               file.  This reduces the amount of time spent writing to the
               disk and prevents unnecessary wear (especially for floppies).
               If this parameter is zero, then as each scanline is finished,
               the line is written to the file and the file is flushed.  On
               most systems, this operation insures that the file is written
               to the disk so that in the event of a system crash or other
               catastrophic event, at least part of the picture has been
               stored properly on disk.

     +c        Continue Rendering

               If, for some reason, you abort a raytrace while it's in progress
               or if you used the -exxx option (below) to end the raytrace
               prematurely, you can use the +c option to continue the raytrace
               when you get back to it.  This option reads in the previously
               generated output file, displays the image to date on the screen,
               then proceeds with the raytracing.  In many cases, this feature
               can save you a lot of rendering time when things go wrong.

               (If you want to impress your friends with the speed of your
               computer, take an image you've already rendered and use +c
               in the command-line.  It renders REAL fast that way!  :-)

     -sxxx     start tracing at line number xxx.
     -exxx     end tracing at line number xxx.

               The -s option allows you to start rendering an image starting
               from a specific scan line.  This is useful for rendering part
               of a scene to see what it looks like without having to render
               the entire scene from the top.  Alternatively, you can render
               groups of scanlines on different systems and concatenate them
               later.  WARNING: If you are merging output files from different
               systems, make sure that the random number generators are the
               same.  If not, the textures from one will not blend in with the
               textures from the other.  There is an example of a standard
               ANSI "C" random number generator in the file IBM.C.  Cut it
               out and paste it into your machine-specific .C file if you
               plan to try "distributed processing" and are not sure if you
               need this standardization.

               The -s option has no effect when continuing a raytrace using
               the +c option.  The renderer will figure out where to restart.

     -qx       rendering quality

               The -q option allows you to specify the image rendering quality,
               for quickly rendering images for testing.  The parameter can
               range from 0 to 9.  The values correspond to the following
               quality levels:

               0,1  Just show colours.  Ambient lighting only.
               2,3  Show Diffuse and Ambient light
               4,5  Render shadows
               6,7  Create surface textures
               8,9  Compute reflected, refracted, and transmitted rays.

               The default is -q9 (maximum quality) if not specified.

               You may specify the default parameters by modifying the file
               "trace.def" which contains the parameters in the above format.
               This filename contains a complete command line as though you
               had typed it in, and is processed before any options supplied
               on the command line are recognized.


     -lpath    The -l option may be used to specify a "library" pathname to
               look into for data files to include or for images.  Up to 10
               -l options may be used to specify a search path.  The home
               (current) directory will be searched first followed by the
               indicated library directories in order.

     +z        The +z option is an undocumented feature.  You will not see any
               references to it in this or any other documentation file for
               DKBTrace.  In fact, no other section of the document will even
               admit that it was mentioned here. If you really want to know
               what it does, then you will have to look into the source code
               (trace.c) and read the comment just above the +z option that
               says "Turn on debugging print statements."  The full purpose
               of this option will, therefore, be left as an exercise for
               the reader, but believe me - it's nothing terribly exciting.

               (For those people who run the raytracer on super-fast systems
               and want to slow it down, you may try this option. :-)



5)  A Tutorial Walkthrough


This section, is designed to get you up and running designing your own
pictures without all the nit-picky details.  Once you've made a few
of your own data files, you'll probably want to advance to the next
section to fill in the gaps.

5.1)    The First Image

Let's get right to the meat of the matter and create the data file for a
simple picture.  Since raytracers thrive on spheres, that's what we'll render
first.

First we have to create a viewpoint to tell the computer where our camera is
and where it's looking.  To do this, we use 3D coordinates.  The usual
coordinate system for DKBTrace has Y pointing up, X pointing to the right, and
Z pointing into the screen as follows:


                ^Y
                |
                |   /Z
                |  /
                | /
                |/       X
                |-------->



Using your personal favorite text editor (i.e., user interface), create a file
called "picture1.dat".  Now, type in the following (note:  The input is case
sensitive, so be sure to get capital and lowercase letters correct):

      INCLUDE "colors.dat"
      INCLUDE "shapes.dat"
      INCLUDE "textures.dat"

      VIEW_POINT
         LOCATION  <0 0 0>
         DIRECTION <0 0 1>
         UP        <0 1 0>
         RIGHT     <1.33333 0 0>
      END_VIEW_POINT


The first INCLUDE statement reads in definitions for various useful colours.
(Being a proud Canadian, I spell colour the proper way with a "u".  To avoid
confusing the rest of the world, however, I've set up the raytracer to allow
either spelling of the word.)

The second and third include statements read in some useful shapes and textures
respectively.  When you get a chance, have a look through them to see
but a few of the many possible shapes and textures available.

Include files may be nested, if you like.  The total pre-defined number of
INCLUDE'd files (nested or not) per scene is 10.

Filenames specified in the INCLUDE statements will be searched for in the home
(current) directory first, and if not found, will then be searched for in
directories specified by any "-l" (library path) options active.  This would
facilitate keeping all your "include" (.inc) files, shapes.dat, colors.dat,
and textures.dat in an "include" subdirectory, and giving an "-l" option on
the command line to where your library of include files are.


This viewpoint declaration puts our camera at the center of the universe
(LOCATION <0 0 0>) pointing into the Z direction (DIRECTION <0 0 1>) and with
the camera being held upright (UP <0 1 0>).  The final term compensates for
the aspect ratio of the screen (RIGHT <1.33333 0 0>).  If your computer has
square pixels, you may want to change this to "RIGHT <1.0 0 0>".  For details
on exactly how the camera works, see the section "How it All Works".


Now, let's place a red sphere into the world:

      OBJECT
         SPHERE <0 0 3> 1 END_SPHERE
         TEXTURE
            COLOUR Red
         END_TEXTURE
      END_OBJECT

This sphere is 3 units away from the camera and has a radius of 1.  Note that
any parameter that changes the appearance of the surface (as opposed to the
shape of the surface) is called a texture parameter and MUST be placed into a
TEXTURE-END_TEXTURE block.  In this case, we are just setting the colour.

One more detail - we need a light source:

      OBJECT
         SPHERE <0 0 0> 1 END_SPHERE
         TEXTURE
            COLOUR White
         END_TEXTURE
         TRANSLATE <2 4 -3>     {This is 2 units to our right, 4 units above,}
                                {and 3 units behind our camera.}
         LIGHT_SOURCE
         COLOUR White
      END_OBJECT


(Note:  For light sources, ALWAYS declare them to be centered at the origin
<0 0 0>, then use TRANSLATE to put them where you want.  If you don't do this,
the light source won't work right. We must also specify the colour of the
light source OUTSIDE the TEXTURE block because the renderer doesn't want to
work out the whole surface colour just to get the colour of the light it
emits.)

That's it!  Close the file and render a small picture of it:

      trace -w80 -h100 -f -ipicture1.dat

On the IBM, the command line would be:

      dkb -w80 -h50 -f -ipicture1.dat

(Or "dkbno87 (etc.)" if you have an 8086/8088 system or no math co-processor).

5.2)    Phong Highlights

You've now rendered your first picture.  I know you want to run out and show
all your friends how amazing your computer is to be able to generate such an
incredible picture, but just wait a few minutes - you ain't seen nothin' yet.
(For those people who complained that the picture took too long to draw, just
wait - you ain't seen nothin' yet, either...)

Let's add a nice little specular highlight (shiny spot) to the sphere.  It
gives it that neat "computer graphics" look.  Change the definition of the
sphere to this:

      OBJECT
         SPHERE <0 0 3> 1 END_SPHERE
         TEXTURE
            COLOUR Red
            PHONG 1.0
         END_TEXTURE
      END_OBJECT

Now render this.  In all seriousness, the PHONG highlight does add a lot of
credibility to the picture.  You'll probably want to use it in many of your
pictures.

5.3)    Textures

One of the really nice features of this raytracer is its sophisticated
textures.  Change the definition of our sphere to the following and then
re-render it:

      OBJECT
         SPHERE <0 0 3> 1 END_SPHERE
         TEXTURE
            Dark_Wood
            SCALE <0.2 0.2 0.2>
            PHONG 1.0
         END_TEXTURE
      END_OBJECT


The textures are set up by default to give you one "feature" across a sphere
of radius 1.0.  A "feature" is roughly defined as a colour transition.  For
example, a wood texture would have one band on a sphere of radius 1.0.  By
scaling the wood by <0.2 0.2 0.2>, we shrink the texture to give us about five
bands. Please note that this is not a hard and fast rule.  It's only meant to
give you a rough idea for the scale to use for a texture.  Don't start
reporting problems if you get three bands instead of five.  This rule of thumb
just puts you in the ballpark.

One note about the SCALE operation.  You can magnify or shrink along each
direction separately.  The first term tells how much to magnify or shrink in
the left-right direction.  The second term controls the up-down direction and
the third term controls the front-back direction.

I encourage you to look through the "textures.dat" file to see what textures
are defined there and try them out.  Some of them are quite spectacular.

5.4)    Other Shapes

So far, we've just defined spheres.  There are several other kinds of shapes
that can be rendered by DKBTrace.  Let's try one out with a computer graphics
standard - a checkered floor.  Add the following object to your .dat file:

      OBJECT
         PLANE <0.0 1.0 0.0> -1.0 END_PLANE
         TEXTURE
            CHECKER
               COLOUR RED 1.0
               COLOUR BLUE 1.0
         END_TEXTURE
      END_OBJECT


The object defined here is an infinite plane.  The vector <0.0 1.0 0.0> is the
surface normal of the plane (i.e., if you where standing on the surface, the
normal points straight up.)  The number afterward is the distance that the
plane is displaced along the normal - in this case, we move the floor down one
unit so that the sphere (radius 1) is resting on it.  The checker texture
specifies the two colours to use in the checker pattern.

Looking at the floor, you'll notice that the wooden ball casts a shadow on the
floor.  Shadows are calculated accurately (well, almost - more later) by the
raytracer.


Another kind of shape you can use is called a quadric surface.  To be totally
honest, the shapes you've been using so far have been quadrics.  Spheres and
planes are types of quadric surfaces.  There are many other quadric surfaces
however.  These are all described by a certain kind of mathematical formula
(see the section on Quadrics in the next chapter).  They include cylinders,
cones, paraboloids (like a satellite dish), hyperboloids (saddle-shaped) and
ellipsoids as well as the spheres and planes we've used so far.

All quadrics except for ellipsoids and spheres are infinite in at least one
direction.  For example, a cylinder has no top or bottom - it goes to infinity
at each end.  Quadrics all have one common feature - if you draw any straight
line through a quadric, it will hit the surface at most twice.  A torus
(donut), for example, is not a quadric since a line can hit the surface up to
four times going through.

Enough talk - let's render one of these "quadrics"...  While we're at it,
we'll add a few features to the surface.  Add the following definition to your
.dat file:

      OBJECT
         QUADRIC Cylinder_Y END_QUADRIC
         TEXTURE
            COLOUR GREEN 0.5
            REFLECTION 0.5
         END_TEXTURE
         SCALE <0.4  0.4  0.4>
         TRANSLATE <2 0 5>
      END_OBJECT


This object is a cylinder along the Y (up-down) axis.  It's green in colour
and has a mirrored surface (hence the reflection of 0.5) this means that half
the light coming from the sphere is reflected from other objects in the room.
A reflection of 1.0 is a perfect mirror.

The object has been shrunk by scaling it by <0.4 0.4 0.4>.  Note that since
the cylinder is infinite along the Y axis, the middle term is kind of
pointless.  One four tenths of infinity is still infinity.  (Don't use 0,
though.  That will definitely cause a fatal crash!)  Finally, the cylinder has
been moved back and to the right so you can see it more clearly.

5.5)    Constructive Solid Geometry

The shapes we've talked about so far are nice, but not terribly useful on
their own for making realistic scenes.  It's hard to make interesting objects
when you're limited to spheres, infinite cylinders, infinite planes, and so
forth.

Constructive Solid Geometry (CSG) is a technique for taking these simple
building blocks and combining them together.  You can use a cylinder to bore a
hole through a sphere.  You can use planes to cap cylinders and turn them into
flat circular disks (that are no longer infinite).

Before getting into CSG, however, let me talk about inside and outside.  Every
primitive (except triangles - I'll talk about this later) divides the world
into two regions.  One region is inside the surface and one is outside.  So,
given any point in space, you can say it's either inside or outside any
particular primitive object (well, it could be exactly on the surface, but
usually numerical inaccuracies will put it to one side or the other).  Even
planes have an inside and an outside.  By definition, the surface normal of
the plane points towards the outside of the plane.  (For a simple floor, for
example, the space above the floor is "outside" and the space below the floor
is "inside".  For simple floors this in unimportant, but for planes as parts
of CSG's it becomes much more important).

CSG uses the concepts of inside and outside to combine shapes together.  Take
the following situation:

Note: The diagrams shown here demonstrate the concepts in 2D and are indended
      only as an analogy to the 3D case.  Note that the triangles supported by
      DKBTrace cannot be used in CSG (except for unions) since they have no
      inside and outside.

  * = Shape A
  % = Shape B

                     *  0
                    * *    %
                   *   *  % %
                  *     *%   %
                 *  1   %*    %
                *      %  * 2  %
               *      % 3  *    %
              *******%*******    %
                    %             %
                   %%%%%%%%%%%%%%%%%


There are three CSG operations you can use:

   1) UNION A B END_UNION
        A point is inside the union if it is inside A OR it's inside B
        (or both).  This gives an "additive" effect to the component
        objects:

                     *
                    * *    %
                   *   *  % %
                  *     *%   %
                 *  1       2 %
                *       3      %
               *                %
              *******%           %
                    %             %
                   %%%%%%%%%%%%%%%%%


   2) INTERSECTION A B END_INTERSECTION
        A point is inside the intersection if it's inside both A AND B.  This
        "logical AND's" the shapes and gets the common part, most useful for
        "clipping" infinite shapes off, etc:


                        %*
                       %  *
                      % 3  *
                     %*******

   3) DIFFERENCE A B END_DIFFERENCE
        A point is inside the difference if it's inside A but not inside B.
        The results is a "subtraction" of the 2nd shape from the first shape:


                     *
                    * *
                   *   *
                  *     *
                 *  1   %
                *      %
               *      %
              *******%

Let's give a concrete example by drilling a yellow hole through our sphere.
Go to the definition of the sphere and change it to read the following:


      OBJECT
         DIFFERENCE
            SPHERE <0 0 3> 1 END_SPHERE
            QUADRIC
               Cylinder_Z
               SCALE <0.2 0.2 0.2>
               COLOUR Yellow
            END_QUADRIC
         END_DIFFERENCE
         TEXTURE
            Dark_Wood
            SCALE <0.2 0.2 0.2>
            PHONG 1.0
         END_TEXTURE
      END_OBJECT

One more point about CSG operations.  You can flip a shape inside-out by
putting the keyword INVERSE into the shape's definition.  This keyword will
not change the appearance of the shape unless you're using CSG.  In the case
of CSG, it gives you more flexibility.  For example:

   INTERSECTION B A-INVERSE END_INTERSECTION


                           %
                          % %
                         %   %
                         *    %
                          * 2  %
                           *    %
                     %*******    %
                    %             %
                   %%%%%%%%%%%%%%%%%

(Note that a DIFFERENCE is really just an INTERSECTION of one shape with the
INVERSE of another.  This happens to be how DIFFERENCE is actually implemented
in the code.)

5.6)    Advanced Textures

The textures available in DKBTrace are 3D solid textures.  This means that the
texture defines a colour for any 3D point in space.  Just like a real block of
marble or wood, there is colour all through the block - you just can't see it
until you carve away the wood or marble that's in the way.  Similarly, with a
3D solid texture, you don't see all the colours in the texture - you only see
the colours that happen to be visible at the surface of the object.

As you've already seen, you can scale, translate, and rotate textures.  In
fact, you could make an animation in which the objects stay still and the
textures translate and rotate through the object.  The effect would be like
watching a time-lapse film of a cloudy sky - the clouds would not only move,
but they would also change shape smoothly.

Often, textures are perturbed by noise.  This "turbulence" distorts the
texture so it doesn't look quite so perfect.  Try changing the sphere in the
above example to have the following texture:

         TEXTURE
            Dark_Wood
            TURBULENCE 0.0
            SCALE <0.2 0.2 0.2>
            PHONG 1.0
         END_TEXTURE

When you compare this with the original image, you'll see that the pattern is
much more boring.

Finally, many textures use colour maps.  A colour map translates a number
between 0.0 and 1.0 into a colour.  The number typically represents the
distance into a vein of colour - the further into the vein you get, the more
the colour changes.  Here's a typical colour map.  Try this out on the sphere
defined above by changing the definition to this:


      OBJECT
         SPHERE <0 0 3> 1 END_SPHERE
         TEXTURE
            WOOD
            SCALE <0.2 0.2 0.2>
            COLOUR_MAP
                [0.0 0.3  COLOUR Red   COLOUR Green]
                [0.3 0.6  COLOUR Green COLOUR Blue]
                [0.6 1.01 COLOUR Blue  COLOUR Red]
            END_COLOUR_MAP
            PHONG 1.0
         END_TEXTURE
      END_OBJECT


This means that as the texture enters into a vein of wood, it changes colour
smoothly from red to green, from green to blue, and from blue to red again.
As it leaves the vein, the transition occurs in reverse.  (Since there is no
turbulence on the wood by default, the veins of colour should show up quite
well.)

You can get more "bang for your buck" from textures by using ALPHA properties
of colour.  Every colour you define in DKBTrace is a combination of red,
green, blue and alpha.  The red, green and blue are simple enough.  The alpha
determines how transparent that colour is.  A colour with an alpha of 1.0 is
totally transparent.  A colour with an alpha of 0.0 is totally opaque.  Here's
a neat texture to try:


   TEXTURE
      TURBULENCE 0.5
      BOZO
      COLOUR_MAP
          { transparent to transparent }
          [0.0 0.6   COLOUR RED 1.0 GREEN 1.0 BLUE 1.0 ALPHA 1.0
                     COLOUR RED 1.0 GREEN 1.0 BLUE 1.0 ALPHA 1.0]

          { transparent to white }
          [0.6 0.8   COLOUR RED 1.0 GREEN 1.0 BLUE 1.0 ALPHA 1.0
                     COLOUR RED 1.0 GREEN 1.0 BLUE 1.0]

          { white to grey }
          [0.8 1.001 COLOUR RED 1.0 GREEN 1.0 BLUE 1.0
                     COLOUR RED 0.8 GREEN 0.8 BLUE 0.8]
      END_COLOUR_MAP
      SCALE <0.4  0.08  0.4>
   END_TEXTURE

This is my (famous) cloud texture.  It creates white clouds with grey linings.
The texture is transparent in the places where the clouds disappear so you can
see through it to the objects that are behind.

Now for one more feature which is new for 2.10 (hold onto your hats!)  You can
now layer textures one on top of another to create more sophisticated textures.
For example, suppose I want a wood-coloured cloudy texture.  What I do is put
the wood texture down first followed by my cloud texture.  Wherever the cloud
texture is transparent, the wood texture shows through.  Change your sphere to
the following and you'll see.


      OBJECT
         SPHERE <0 0 3> 1 END_SPHERE
         TEXTURE        { This is the wood texture we used earlier. }
            Dark_Wood
            TURBULENCE 0.0
            SCALE <0.2 0.2 0.2>
            PHONG 1.0
         END_TEXTURE
         TEXTURE        { This is the cloud texture we just defined. }
            TURBULENCE 0.5
            BOZO
            COLOUR_MAP
                { transparent to transparent }
                [0.0 0.6   COLOUR RED 1.0 GREEN 1.0 BLUE 1.0 ALPHA 1.0
                           COLOUR RED 1.0 GREEN 1.0 BLUE 1.0 ALPHA 1.0]

                { transparent to white }
                [0.6 0.8   COLOUR RED 1.0 GREEN 1.0 BLUE 1.0 ALPHA 1.0
                           COLOUR RED 1.0 GREEN 1.0 BLUE 1.0]

                { white to grey }
                [0.8 1.001 COLOUR RED 1.0 GREEN 1.0 BLUE 1.0
                           COLOUR RED 0.8 GREEN 0.8 BLUE 0.8]
            END_COLOUR_MAP
            SCALE <0.4  0.08  0.4>
         END_TEXTURE
      END_OBJECT

Each successive texture is layered on top of the previous textures.  In the
places where you can see through the upper texture, you see through to the
lower textures.


5.7)    Walk-through Wrap-up

In this walk-through, I've only tried to show the highlights of the raytracer
without getting into all possible options and features.  To get all of those,
you'll have to read through the following section on the Object Description
Language.  Hopefully it will be fairly straight forward now that you have a
feel for the language and how it works.  Hopefully you'll find that the
textual interface provided by DKBTrace isn't quite as scary as people think at
first.



6)  The Scene Description Language

The Scene Description Language allows the user to describe the world in a
readable and convenient way.

The language delimits comments by the left and right braces ({ and }). Nested
comments are allowed, but no sane person uses them anyway, right?

The language allows include files to be specified by placing the line:

    INCLUDE "filename"

at any point in the input file (Include files may be nested).  The filename
must be enclosed in double quotes and may be up to 40 characters long,
including the two double-quote (") characters.  You may have at most 10
INCLUDE'd files per scene trace, whether nested or not.



6.1)    The Basic Data Types

     There are several basic types of data:

6.1.1)  Float
Floats are represented by an optional sign (-), some digits, an optional
decimal point, and more digits.  Version 2.10 now supports the "e" notation
for exponents.  The following are valid floats:

     1.0  -2.0  -4  34  3.4e6 2e-5

6.1.2)  Vector
Vectors are arrays of three floats.  They are bracketed by angle brackets
( < and > ), and the three terms usually represent x, y, and z.  For example:

     < 1.0  3.2  -5.4578 >

Vectors typically refer to relative points.  For example, the vector:

     <1 2 3>

means the point that's 1 unit to the right, 2 units up, and 3 units in front.
"Of what?" you ask?  Well, usually it's relative to the center of the
"universe" at <0 0 0>.

In a few places here and there, vectors are used as a convenient notation but
don't represent a point in space. This is the case for the transformations
TRANSLATE, ROTATE, and SCALE.

   TRANSLATE <x y z>       - move the object x units to the right,
                             y units up, and z units away from us.

   SCALE     <xs ys zs>    - scale the object by xs units in the left/right
                             direction, ys units in the up/down direction
                             and zs units in the front/back direction.

   ROTATE    <xr yr zr>    - rotate the object xr degrees about the X axis,
                             then yr degrees about the Y axis, then zr degrees
                             about the Z axis.  (note that the order matters)

To work out the rotation directions, you must perform the famous "Computer
Graphics Aerobics" exercise.  Hold up your left hand.  point your thumb in the
positive direction of the axis you want to rotate about.  Your fingers will
curl in the positive direction of rotation.  This is the famous "left-hand
coordinate system".  If you want to use a right-hand system, as some CAD
systems do, the RIGHT vector in the VIEW_POINT needs to be changed.  See the
detailed description of the VIEW_POINT, and use your right hand for the
"Aerobics".
                       _
                     _| |_  _
                   _| | | |/ \
                  | | | | |  |
                  | | | | |  V
                  | | | | |
                  | | | | |
                  |       \____
                  |         ___|
                  \        /
                   |      /
                   |     |
                   |     |
                   |     |


6.1.3)  Colour

A colour consists of a red component, a green component, a blue component, and
possibly an alpha component.  All four components are floats in the range 0.0
to 1.0.  The syntax for Colours is the word "COLOUR" followed by any or all of
the RED, GREEN, BLUE or ALPHA components in any order.

For example:

     COLOUR  RED 1.0  GREEN 1.0  BLUE 1.0
     COLOUR  BLUE 0.56
     COLOUR  GREEN 0.45 RED 0.3 BLUE 0.1 ALPHA 0.3

Alpha is a transparency indicator.  If an object's colour contains some
transparency, then you can see through it.  If Alpha is 0.0, the object is
totally opaque.  If it is 1.0, it is totally transparent.

For those people who spell "Colour" the American way as "Color", the program
will also accept "COLOR" as equivalent to "COLOUR" in all instances.


6.1.4)  Colour Maps

For wood, marble, spotted, agate, granite, and gradient texturing, the user
may specify arbitrary colours to use for the texture.  This is done by a
colour map or "colour spline".  When the object is being textured, a number
between 0.0 and 1.0 is generated which is then used to form the colour of the
point.  A Colour map specifies the mapping used to change these numbers into
colours.  The syntax is as follows:

     COLOUR_MAP
          [start_value end_value colour1 colour2]
          [start_value end_value colour1 colour2]
          ...
     END_COLOUR_MAP

The numeric value between 0.0 and 1.0 is located in the colour map and the
final colour is calculated by a linear interpolation (a smooth blending)
between the two colours in the located range.


6.2)    The More Complex Data Types

6.2.1)  Declare

The data types used to describe the objects in the world are a bit more
difficult to describe.  To make this task easier, the program allows users to
describe these types in two ways.  The first way is to define it from first
principles specifying all of the required parameters.  The second way allows
the user to define an object as a modification of another object (the other
object is usually defined from first principles but is much simpler).  Here's
how it works:

You can use the term DECLARE to declare a type of object with a certain
description.  The object is not included in the world but is made known to the
program that it can be used as a "prototype" for defining other objects by the
name given, as this basic example shows:

     DECLARE Sphere = QUADRIC   { First Principles definition of a sphere }
          <1.0 1.0 1.0>
          <0.0 0.0 0.0>
          <0.0 0.0 0.0>
          -1.0
     END_QUADRIC

To then reference the declaration elsewhere in your source file or in another
included one, and to actually include the object in the world, you would
define the object using the DECLARE'd object's name, like this:

     OBJECT
          QUADRIC Sphere
               SCALE <20.0 20.0 20.0>
          END_QUADRIC
          TEXTURE
             COLOUR White
             AMBIENT 0.2
             DIFFUSE 0.8
          END_TEXTURE
     END_OBJECT

The real power of declaration becomes apparent when you declare several
primitive types of objects and then define an object with several component
shapes, using either COMPOSITE methods or the CSG methods INTERSECTION, UNION,
or DIFFERENCE.  Also, using the DECLARE keyword to pre- define textures can
make several objects share a texture without the need for each object to store
a duplicate copy of the same texture, for more efficient memory usage.
Example:

     DECLARE Dull TEXTURE  { A Basic, Boring Texture }
          AMBIENT 0.3
          DIFFUSE 0.7
     END_TEXTURE

     OBJECT         { A Hot dog in a Hamburger Bun (?) }
          UNION
               QUADRIC Sphere
                    SCALE <20.0, 10.0, 20.0>
            TEXTURE Dull END_TEXTURE
               END_QUADRIC
               QUADRIC Cylinder_X
                    SCALE <40.0, 20.0, 20.0>
            TEXTURE Dull END_TEXTURE
               END_QUADRIC
          END_UNION
     END_OBJECT


Layered textures, new to version 2.10, may also be DECLARE'd.  The DECLARE
mechanism keeps looking for successive TEXTURE definitions and will layer them
onto the same texture until another DECLARE (or any other statement except
another TEXTURE) is encountered in the input data file.  For example:

 DECLARE Cloud_Wood TEXTURE  { This is the cloudy wood texture used earlier. }
   Dark_Wood
   TURBULENCE 0.0
   SCALE <0.2 0.2 0.2>
   PHONG 1.0
 END_TEXTURE
 TEXTURE        { This is layered onto the wood texture just defined. }
   TURBULENCE 0.5
   BOZO
   COLOUR_MAP
     { transparent to transparent }
     [0.0 0.6   COLOUR RED 1.0 GREEN 1.0 BLUE 1.0 ALPHA 1.0
     COLOUR RED 1.0 GREEN 1.0 BLUE 1.0 ALPHA 1.0]

     { transparent to white }
     [0.6 0.8   COLOUR RED 1.0 GREEN 1.0 BLUE 1.0 ALPHA 1.0
     COLOUR RED 1.0 GREEN 1.0 BLUE 1.0]

     { white to grey }
     [0.8 1.001 COLOUR RED 1.0 GREEN 1.0 BLUE 1.0
     COLOUR RED 0.8 GREEN 0.8 BLUE 0.8]
   END_COLOUR_MAP
   SCALE <0.4  0.08  0.4>
 END_TEXTURE

DECLARE (etc.) { Ends the definition of the layered "Cloud_Wood" texture. }

6.2.2)  Viewpoint

The viewpoint tells the ray tracer the location and orientation of the camera.
The viewpoint is described by four vectors - Location, Direction, Up, and
Right.  Location determines where the camera is located.  Direction determines
the direction that the camera is pointed.  Up determines the "up" direction of
the camera.  Right determines the direction to the right of the camera.

A first principle's declaration of a viewpoint would look like this:

     VIEWPOINT
          LOCATION < 0.0  0.0  0.0>
          DIRECTION < 0.0  0.0  1.0>
          UP < 0.0  1.0  0.0 >
          RIGHT < 1.0  0.0  0.0>
     END_VIEWPOINT

This format becomes cumbersome, however, because the vectors must be hand
calculated.  This is especially difficult when the vectors are not lined up
with the X, Y, and Z axes as they are in the above example. To make it easier
to define the viewpoint, you can define one viewpoint, then modify the
description.  For example,

     VIEWPOINT
          LOCATION < 0.0  0.0  0.0>
          DIRECTION < 0.0  0.0  1.0>
          UP < 0.0  1.0  0.0 >
          RIGHT < 1.0  0.0  0.0 >
          TRANSLATE < 5.0  3.0  4.0 >
          ROTATE < 30.0  60.0  30.0 >
     END_VIEWPOINT

In this example, the viewpoint is created, then translated to another point in
space and rotated by 30 degrees about the X axis, 60 degrees about the Y axis,
and 30 degrees about the Z axis.

Unfortunately, even this is somewhat cumbersome.  So, in version 2.0 and
above, you can now specify two more parameters:

          SKY <vector>
          LOOK_AT <vector>

The SKY keyword tells the viewpoint where the sky is.  It tries to keep the
camera's UP direction aligned as closely as possible to the sky. The LOOK_AT
keyword tells the camera to look at a specific point.  The camera is rotated
as required to point directly at that point.  By changing the SKY vector, you
can twist the camera while still looking at the same point.

One subtle point:  the SKY direction is not necessarily the same as the UP
direction.  For example, consider the following situation:

          S^
           | /U
           |/
           C
            \
             \
              \
               O

If you said that the camera C has a SKY direction S and is looking at O, the
up direction will not point to the sky.  UP's like putting an antenna on your
camera.  If you point the camera downwards, the antenna will no longer point
straight up.

The RIGHT vector, as was mentioned previously, controls the aspect ratio of
the screen display.  It also determines the "handedness" of the coordinate
system in use.  A normal (left-handed) RIGHT statement would be:

    RIGHT < 1.3333 0.0 0.0 >

To use a right-handed coordinate system, as is popular in some CAD programs
and some other ray-tracers, such as Sculpt for the Amiga, use a RIGHT like:

    RIGHT < -1.3333 0.0 0.0 >

Some CAD systems also have the peculiar conception that the Z axis is the
"elevation" and is the "UP" direction instead of the Y axis.  If this is the
case you will want to change your "UP" statement to:

    UP < 0.0 0.0 1.0 >


Note that a pinhole camera model is used, so no focus or depth-of-field
effects are supported at this time.  For more detailed information on the
camera model, see the section "How it All Works."

6.2.3)  Fog

Version 2.0 of the raytracer includes the ability to render fog.  To add fog
to a scene, place the following declaration outside of any object definitions:

     FOG
          COLOUR  {... the fog colour}
          200.0   {... the fog distance}
     END_FOG

The fog to colour ratio is calculated as 1-exp(-depth/distance), so at
depth 0, the colour is pure (1.0) with no fog (0.0).  At the fog distance,
you'll get 63% of the colour from the object's colour and 37% from the
fog colour.

6.2.4)  Shapes

Shapes describe the shape of an object without mentioning any surface
characteristics like colour, surface lighting and reflectivity.

6.2.4.1)    Quadric Shapes

The most general shape used by this system is called a Quadric Surface.
Quadric Surfaces can produce shapes like spheres, cones, cylinders,
paraboloids (dish shapes), and hyperboloids (saddle or hourglass shapes).

The easiest way to define these shapes is to include the standard file
"shapes.dat" into your program and to transform these shapes (using TRANSLATE,
ROTATE, and SCALE) into the ones you want.  To be complete, however, I will
describe the mathematical principles behind quadric surfaces.  Those who are
not interested in the mathematical details can skip to the next section.

The quadric:

      QUADRIC
          <A B C>
          <D E F>
          <G H I>
          J
      END_QUADRIC

defines a surface in three dimensions which satisfies the following equation:


       A y**2  + B y**2  + C z**2
     + D xy    + E xz    + F yz
     + G x     + H y     + I z    + J = 0


(Did you really want to know that?  I didn't think so. :-)  DKB)

Different values of A,B,C,...J will give different shapes.  So, if you take
any three dimensional point and use its x, y, and z coordinates in the above
equation, the answer will be 0 if the point is on the surface of the object.
The answer will be negative if the point is inside the object and positive if
the point is outside the object.  Here are some examples:

     X**2 + Y**2 + Z**2 - 1 = 0     Sphere
     X**2 + Y**2 - 1 = 0            Cylinder along the Z axis
     X**2 + Y**2 - Z**2 = 0         Cone along the Z axis


6.2.4.2)    Quadric surfaces the easy way

Now that doesn't sound so hard, does it?  Well, actually, it does.  Only the
hard-core graphics fanatic would define his objects using the QUADRIC
definition directly.  Even I don't do it that way and I know how it works
(Well, at least I worked it out once or twice :-) - DKB).

Fortunately, there is an easier way. The file "shapes.dat" already includes
the definitions of many quadric surfaces.  They are centered about the origin
< 0 0 0 > and have a radius of 1.  To use them, you can define shapes simply
as follows:

      INCLUDE "colors.dat"
      INCLUDE "shapes.dat"      { This is the important one for this example }
      INCLUDE "textures.dat"

     QUADRIC
          Cylinder_X
          SCALE < 50.0  50.0  50.0 >
          ROTATE < 30.0  10.0  45.0 >
          TRANSLATE < 2.0  5.0  6.0 >
     END_QUADRIC


You may have as many transformation lines (scale, rotate, and translate) as
you like in any order.  Usually, however, it's easiest to do a scale first,
one or more rotations, then finally a translation.  Otherwise, the results may
not be what you expect. (The transformations always transform the object about
the origin.  If you have a sphere at the origin and you translate it then
rotate it, the rotation will spin the sphere around the origin like planets
about the sun).



6.2.4.3)    Spheres

Since spheres are so common in ray traced graphics, A SPHERE primitive has
been added to the system.  This primitive will render much more quickly than
the corresponding quadric shape.  The syntax is:

     SPHERE  <center> radius END_SPHERE

You can also add translations, rotations, and scaling to the sphere. For
example, the following two objects are identical:

     OBJECT
          SPHERE  < 0.0 25.0 0.0 > 10.0 END_SPHERE
          TEXTURE
             COLOR Blue
             AMBIENT 0.3
             DIFFUSE 0.7
          END_TEXTURE
     END_OBJECT

     OBJECT
          SPHERE  < 0.0 0.0 0.0 > 1.0
               TRANSLATE <0.0  25.0  0.0>
               SCALE <10.0  10.0  10.0>
          END_SPHERE
          TEXTURE
             COLOR Blue
             AMBIENT 0.3
             DIFFUSE 0.7
          END_TEXTURE
     END_OBJECT

Note that Spheres may only be scaled uniformly. You cannot use:

     SCALE <10.0 5.0 2.0>

on a sphere.  If you need oblate (flattened) spheroids, use a scaled quadric
"Sphere" shape instead, as it can be arbitrarily scaled in any dimension.

6.2.4.4)    Planes

Another primitive provided to speed up the raytracing is the PLANE. This is a
flat infinite plane.  To declare a PLANE, you specify the direction of the
surface normal to the plane (the UP direction) and the distance from the
origin of the plane to the world's origin. As with spheres, you can translate,
rotate, and scale planes.  Examples:

     PLANE <0.0  1.0  0.0> -10.0 END_PLANE   { A plane in the X-Z axes 10
                                             units below the world origin. }

     PLANE <0.0  1.0  0.0>  10.0 END_PLANE   { A plane in the X-Z axes 10
                                             units above the world origin. }

     PLANE <0.0  0.0  1.0>  -10.0 END_PLANE  { A plane in the X-Y axes 10
                                             units behind the world origin.}



6.2.4.5)    Triangles

In order to make more complex objects than the class of quadrics will
permit, a new primitive shape for triangles has been added.  There are
two different types of triangles:  flat shaded triangles and smooth
shaded (Phong) triangles.

Flat shaded triangles are defined by listing the three vertices of the
triangle.  For example:

     TRIANGLE  < 0.0   20.0  0.0>
               < 20.0  0.0   0.0>
               <-20.0  0.0   0.0>
     END_TRIANGLE

The smooth shaded triangles use Phong Normal Interpolation to calculate the
surface normal for the triangle.  This makes the triangle appear to be a
smooth curved surface.  In order to define a smooth triangle, however, you
must supply not only the vertices, but also the surface normals at those
vertices.  For example:

     SMOOTH_TRIANGLE
          {      points             surface normals     }
          <  0.0  30.0  0.0 >    <0.0   0.7071   -0.7071>
          < 40.0 -20.0  0.0 >    <0.0   -0.8664  -0.5   >
          <-50.0 -30.0  0.0 >    <0.0   -0.5     -0.8664>
     END_SMOOTH_TRIANGLE

As with the other shapes, triangles can be translated, rotated, and scaled.

NOTE 1:  Triangles cannot be used in CSG INTERSECTION or DIFFERENCE types
(described next) since triangles have no clear "inside".  The CSG UNION type
works acceptably, but with no real difference from a COMPOSITE made up of
TRIANGLE primitives.

NOTE 2:  To be honest, I don't expect mere mortals to work out the surface
normals of triangles.  Ideally, you'd have another program generate them for
you.  See the section on "Common Questions and Answers" for details on how
this might be done.


6.2.4.6)    Quartic Surfaces

Quartic surfaces are 4th order surfaces, and can be used to describe a large
class of shapes including the torus, the lemniscate, etc.  The general
equation for a quartic equation in three variables is (hold onto your hat):

   a00 x^4     + a01 x^3 y   + a02 x^3 z   + a03 x^3     + a04 x^2 y^2 +
   a05 x^2 y z + a06 x^2 y   + a07 x^2 z^2 + a08 x^2 z   + a09 x^2 +
   a10 x y^3   + a11 x y^2 z + a12 x y^2   + a13 x y z^2 + a14 x y z +
   a15 x y     + a16 x z^3   + a17 x z^2   + a18 x z     + a19 x +
   a20 y^4     + a21 y^3 z   + a22 y^3     + a23 y^2 z^2 + a24 y^2 z +
   a25 y^2     + a26 y z^3   + a27 y z^2   + a28 y z     + a29 y +
   a30 z^4     + a31 z^3     + a32 z^2     + a33 z       + a34

To declare a quartic surface requires that each of the coefficients
(a0 -> a34) be placed in order into a single long vector of 35 terms.

As an example, the following object declaration is for a torus having major
radius 6.3 minor radius 3.5 (Making the maximum width just under 10).

     { Torus having major radius sqrt(40), minor radius sqrt(12) }
     OBJECT
      QUARTIC
      < 1.0   0.0   0.0    0.0     2.0   0.0   0.0   2.0   0.0 -104.0
        0.0   0.0   0.0    0.0     0.0   0.0   0.0   0.0   0.0    0.0
        1.0   0.0   0.0    2.0     0.0  56.0   0.0   0.0   0.0    0.0
        1.0   0.0 -104.0   0.0   784.0 >
      END_QUARTIC
      BOUNDED_BY
       SPHERE <0 0 0> 10 END_SPHERE
      END_BOUND
     END_OBJECT

The code to calculate Ray-Surface intersections for quartics is somewhat
slower than that for intersections with quadric surfaces.  Benchmarks on
a stock 8Mhz AT (with FPU) give results of around 1400 solutions per second
for 2nd order equations (quadrics) vs 444 per second for 3rd order equations
and 123 per second for 4th order equations (quartics).  So clever use of
bounding shapes can make a big difference in processing time.

While a great deal of time has gone into debugging the code for handling
quartic surfaces, I know for a fact that there are bad combinations of
surface equations and lighting orientations that cause math errors (crash).
If this happens to you, as the joke goes, "then don't DO that."

Here are some surfaces to get you started.

A Torus can be represented by the equation:

   x^4 + y^4 + z^4 + 2 x^2 y^2 + 2 x^2 z^2 + 2 y^2 z^2
   -2 (r0^2 + r1^2) x^2 + 2 (r0^2 - r1^2) y^2 - 2 (r0^2 - r1^2) z^2
   + (r0^2 - r1^2)^2 = 0

Where r0 is the "major" radius of the torus - the distance from the hole
of the donut to the middle of the ring of the donut, and r1 is the "minor"
radius of the torus - the distance from the middle of the ring of the donut
to the outer surface.  Described another way, a torus is a circle that is
revolved around an axis.  The major radius is the distance from the axis to
the center of the circle, the minor radius is the radius of the circle. (If
this were a Mac I could put a drawing in here to show you...)

Note that scaling surfaces like a torus scales everything. In order to change
the relationship between the size of the hole and the size of the ring, it is
necessary to enter new coefficients for the torus.

The only coefficients of the 35 that need to be filled in are:

    a0  = a20 = a30 = 1,
    a4  = a7  = a23 = 2,
    a9  = a32       = -2 (r0^2 + r1^2)
    a25             = 2 (r0^2 - r1^2)
    a34             = 2 (r0^2 - r1^2)^2

the torus can then be rotated and translated into position once its shape
has been defined. (See 'TORUS.DAT')

A generalization of the lemniscate of Gerono can be represented by the
equation:

   c^2 x^4 - a^2 c^2 x^2 + y^2 + z^2 = 0

where good start values are a = 1.0 and c = 1.0, giving the coefficients:

   a0 = a25 = a32 = 1,
   a9 = -1

(See the example file "LEMNISCA.DAT" for a more complete example)

A generalization of a piriform can be represented by the equation:

   -b c^2 x^4 - a c^2 x^3 + y^2 + z^2 = 0

where good start values are a = 4, b = -4, c = 1, giving the coefficients

   a0 = 4,
   a3 = -4,
   a25 = a32 = 1

(See the file "PIRIFORM.DAT" for more on this...)

There are really so many different QUARTIC shapes, we can't even begin to
list or describe them all.  If you are interested and mathematically inclied,
an excellent reference book for curves and surfaces where you'll find more
QUARTIC shape formulas is:

   "The CRC Handbook of Mathematical Curves and Surfaces"
   David von Seggern
   CRC Press
   1990


6.2.4.7)    Constructive Solid Geometry (CSG)

This ray tracer supports Constructive Solid Geometry in order to make the
object definition abilities more powerful.  Constructive Solid Geometry allows
you to define shapes which are the union, intersection, or difference of other
shapes.  Unions superimpose the two shapes.  This has the same effect as
defining two separate objects, but is simpler to create and/or manipulate.
Intersections define the space where the two surfaces meet.  Differences allow
you to cut one object out of another.

CSG Intersections, Unions, and Differences can consist of two or more shapes.
They are defined as follows:

     OBJECT
          INTERSECTION
               QUADRIC
                    ...
               END_QUADRIC

               QUADRIC
                    ...
               END_QUADRIC

               QUADRIC
                    ...
               END_QUADRIC
          END_INTERSECTION
          ...
     END_OBJECT

UNION or DIFFERENCE may be used instead of INTERSECTION.  The order of the
shapes doesn't matter except for the DIFFERENCE shapes.  For CSG differences,
the first shape is visible and the remaining shapes are cut out of the first
(in reverse order from version 1.2 DIFFERENCE's).

Constructive solid geometry shapes may be translated, rotated, or scaled in
the same way as a Quadric surface.  The quadric surfaces making up the CSG
object may be individually translated, rotated, and scaled as well.

When using CSG, it is often useful to invert an shape so that it's inside-out.
The INVERSE keyword can be used to do this for any SPHERE, PLANE, or QUADRIC.
When INVERSE is used, the "inside" of the object is flipped to become the
"outside".  For Planes, "inside" is defined to be "in the opposite direction
to the "normal" or "up" direction.

Note that performing an INTERSECTION between an shape and some other INVERSE
shapes is the same as performing a DIFFERENCE.  In fact, the DIFFERENCE is
actually implemented in this way in the code.

6.2.5)  Objects

There is more to defining an object than just its shape.  You must tell the
ray tracer about the properties of the object like surface colour, alpha,
reflectivity, refractivity, the index of refraction, and so on.  This may be
done by specifying it in the shape or the object.  Generally, an OBJECT
definition will contain two pieces of information about an object: First, what
shape it is, and second, what it's looks like (on the surface and throughout).
A typical object definition looks something like this:

     OBJECT
          QUADRIC Sphere
               TRANSLATE < 40.0 40.0 60.0 >
          END_QUADRIC

          TEXTURE
             AMBIENT  0.3
             DIFFUSE   0.7
             REFLECTION  0.3
             REFRACTION  0.3
             IOR 1.05
             COLOUR RED 1.0 GREEN 1.0 BLUE 1.0 ALPHA 0.5
          END_TEXTURE
     END_OBJECT

The following keywords may be used when defining objects:

6.2.5.1)    COLOUR value

When used on an OBJECT (i.e., not inside a TEXTURE block), the COLOUR keyword
determines what colour to use for a low quality rendering when TEXTURE's are
ignored.  See the +q option for details on setting the low-quality option.

Example:

     COLOUR RED 1.0  BLUE 0.4

          - or -

     DECLARE Yellow = COLOUR RED 1.0 GREEN 1.0
          ...
     COLOUR Yellow


6.2.5.2)    TRANSLATE vector
6.2.5.3)    ROTATE vector
6.2.5.4)    SCALE vector

Objects can be translated, rotated, and scaled just like surfaces.  If an
object is transformed, all textures attached to the object at that time are
transformed as well.  This means that if you have a TRANSLATE, ROTATE, or
SCALE before a TEXTURE, the texture will NOT be transformed.  If the SCALE
TRANSLATE, or ROTATE is after the TEXTURE, the texture will be transformed.

6.2.5.5)    LIGHT_SOURCE

If the LIGHT_SOURCE keyword is used in the definition of an object, then the
object is included in the list of light sources.  It can light objects and
produce shadows.  (You should also specify the COLOUR of the light source, it
will usually be "White").  Light sources have a peculiar restriction:  The
light source MUST be TRANSLATED to its final position in the scene, so the
normal way to define a light source is a sphere or quadric centered about the
origin, then TRANSLATED to where desired in the final scene.  For example:

     OBJECT
          SPHERE <0.0  0.0  0.0> 2.0 END_SPHERE   {could be a quadric, too.}
          TRANSLATE <100.0  120.0  40.0>

          LIGHT_SOURCE
          COLOUR White      { This is the colour of the light emitted }
          TEXTURE
             COLOUR White   { This is the surface colour of the sphere }
             AMBIENT 1.0
             DIFFUSE 0.0
          END_TEXTURE
     END_OBJECT


NOTE: You MUST specify the colour of the light outside the TEXTURE block. This
      allows the renderer to quickly determine the colour of the light source
      without having to plow through the textures.  Any colour information
      inside the TEXTURE block is used to render the light source object itself
      if it is visible in the scene.  The subtle difference between the
      actual sphere object and the light ray emanation point (the center of
      the sphere) is why LIGHT_SOURCE's must be defined at (0,0,0) then
      TRANSLATE'd to where you want them.  It ties together and TRANSLATE's
      both the object itself and the light ray source point to the specified
      point in the scene.  Usually, light sources have an AMBIENT value of 1.0
      and a DIFFUSE of 0.0, but this is not a hard and fast rule.

6.2.6)  TEXTURE

The texture feature is an experiment into functionally based modelling.  This
feature allows you to assign colouring schemes to objects.  Many procedural
surface textures are provided, and by using different colour maps with them,
nearly infinite permutations are possible.  For example, you can make some
object look like wood or marble, etc.  In DKBTrace, any parameter that changes
the appearance of the surface MUST be put into a TEXTURE block.

The basic TEXTURE syntax is as follows:

     TEXTURE
          0.05
          WOOD
          TURBULENCE 0.2
          TRANSLATE < 1.0 2.0 3.0 >
          ROTATE < 0.0 10.0 40.0 >
          SCALE < 10.0 10.0 10.0 >
     END_TEXTURE

Transformations are optional.  They allow you to transform the texture
independent of the object itself.  If you are doing animation, then the
transformations should be the same as the object transformations so that the
texture follows the object through 3-D space.

The floating-point value given immediately following the texture keyword is an
optional "texture randomness" value, which causes a minor random scattering of
calculated colour values and produces a sort of "dithered" appearance.  Note
this is BAD, BAD, BAD for animations!!  This is the ONLY "truly random" thing
in all of DKB, and will produce a most annoying flicker of flying pixels on
any textures animated with a "randomness" value used.

Instead of using WOOD, you may use MARBLE, BOZO, CHECKER, or a handful of
other interesting textures.  The WOOD and MARBLE textures are perturbed by a
turbulence function.  This makes them look more random and irregular than they
would normally appear.  The amount of turbulence can be changed by the
TURBULENCE keyword followed by a number.  Values from 0.1 to 0.3 seem to give
the best results.  The default is 0.0, or no turbulence.

Note some of the textures given are coloration textures, such as MARBLE, WOOD
CHECKER, GRANITE, and AGATE.  These work with colour maps, and have default
"colour maps" they resort to if none are given.  The rest of the textures
available are "surface perturbation" textures, and do not directly affect the
colour of the object, but rather the surface's apparent orientation in space.
Examples of this are WAVES, RIPPLES, DENTS, BUMPS, and WRINKLES.  Note that
any given texture may include up to two actual textures, one coloration and
one surface perturbation choice per texture.  This would allow rippled wood,
or dented granite combinations, etc., but, keep in mind that any texture
transformations applied to one texture (i.e. TRANSLATE or SCALE) will also
transform the other one in the same fashion.


As of version 2.10, it is possible to create layered textures. If you use more
that one texture block, the raytracer will compute the colour of the last
texture and if there's any transparency in the colour (i.e., any alpha), it
will mix in some of the colour from the underlying textures.

IMPORTANT NOTE:  As of version 2.10, the keywords in this following section
                 CANNOT be used outside of a TEXTURE-END_TEXTURE structure.
                 This is a change in the input language from prior versions.

The following object surface lighting characteristics are available:

6.2.6.1)    AMBIENT value

Ambient light is light that is scattered everywhere in the room.  An object
lit only by ambient light will appear to have the same brightness over the
entire surface.  The default value is very little ambient light (0.3).  The
value can range from 0.0 to 1.0.

6.2.6.2)    DIFFUSE value

Diffuse light is light coming from a light source that is scattered in all
directions.  An object lit only by diffuse light looks like a rubber ball with
a spot light shining on it.  The value can range from 0.0 to 1.0.  By default,
there is mostly diffuse lighting (0.7).

6.2.6.3)    BRILLIANCE value

Objects can be made to appear more metallic by increasing their brilliance.
This controls the tightness of the basic diffuse illumination on objects and
minorly adjusts the appearance of surface shininess.  The default value is
1.0.  Higher values from 3.0 to about 10.0 can give objects a somewhat more
shiny or metallic appearance.  This is best used in concert with either the
SPECULAR or PHONG highlighting.

6.2.6.4)    REFLECTION value

By setting the reflection value to be non-zero, you can give the object a
mirrored finish.  It will reflect all other objects in the room.  The value
can range from 0.0 to 1.0.  By default there is no reflection.

6.2.6.5)    REFRACTION value

By setting the refraction value to be non-zero, the object is made transparent.
Light will be refracted through the object like a lens.  The value can be set
between 0.0 and 1.0.  There is no refraction by default.

NOTE 1:  New for 2.10:  In order to refraction to work properly, you must have
         some ALPHA component in the surface colour.  In the places where the
         ALPHA is high, the refracted light can get through.  In places where
         the ALPHA is low, the refracted light is suppressed.  This is a
         change in the input language from prior versions.

NOTE 2:  The refracted light is filtered by (takes on) the surface colour.

NOTE 3:  In layered textures, the REFRACTION and IOR keywords MUST be in the
         last texture, otherwise they will not take effect.

NOTE 4:  If a texture has an ALPHA component and no value for REFRACTION was
         supplied, the renderer will simply transmit the ray through the
         surface with no bending.

6.2.6.6)    IOR value

If the object is refracting light, then the IOR or Index of Refraction should
be set.  This determines how dense the object is.  A value of 1.0 will give no
refraction.  The Index of Refraction for air is 1.0, water is 1.33, glass is
1.5, and diamond is 2.4.

6.2.6.7)    PHONG value

Controls the amount of Phong Specular Reflection highlighting on the object.
Causes bright shiny spots on the object, the colour of the light source that
is being reflected.  The size of the spot is defined by the value given for
PHONGSIZE below.  PHONG's value is typically from 0.0 to 1.0, where 1.0 causes
complete saturation of the object's colour to the light source's colour at the
brightest area (center) of the highlight.  There is no PHONG highlighting
given by default.

6.2.6.8)    PHONGSIZE value

Controls the size of the PHONG Highlight on the object, sort of an arbitrary
"glossiness" factor.  Values range from 1.0 (Very Dull) to 100 (Highly
Polished).  Default PHONGSIZE is 40 (plastic?) if not specified.  This is
simulating the fact that slightly reflective objects, especially metallic
ones, have microscopic facets, some of which are facing in the mirror
direction.  The more that are facing that way, the shinier the object appears,
and the tighter the specular highlights become.  Phong measures the average of
facets facing in the mirror direction from the light sources to the viewer.

6.2.6.9)    SPECULAR value

Very similar to PHONG Specular Highlighting, but a better model is used for
determining light ray/object intersection, so a more credible spreading of the
highlights occur near the object horizons, supposedly.  PHONG is thus included
for mostly academic reasons, but try them both and you decide which you like
better.  This effect is most obvious for light sources behind objects.  The
size of the spot is defined by the value given for ROUGHNESS below.  Like
PHONG, SPECULAR values are typically from 0.0 to 1.0 for full saturation.
Default is no SPECULAR highlighting.

Note that Specular and Phong highlights are NOT mutually exclusive.  It is
possible to specify both and they will both take effect.  Normally, however,
you will only specify one or the other.

6.2.6.10)   ROUGHNESS value

Controls the size of the SPECULAR Highlight on the object, relative to the
object's "roughness".  Values range from 1.0 (Very Rough) to 0.001 (Very
Smooth).  The default value, if not specified, is 0.05 (Plastic?).  The
roughness or average directional distribution of the microfacets facing in the
same direction as the perpendicular surface "normal" cause the most notable
reflection of the highlight to the observer.


6.2.6.11)   METALLIC

This keyword indicates that the colour of the specular and phong hightlights
will be the surface colour instead of the lightsource colour.  This creates
a metallic appearance.  When using this feature, you should set AMBIENT to
about 0.5 and set DIFFUSE to 0.0.


The following advanced procedural textures are available:

6.2.6.12)   CHECKER - A colouring texture.

CHECKER texturing gives a checker-board appearance.  This option works best on
planes.  When using the CHECKER texturing, you must specify two colours
immediately following the word CHECKER.  These colours are the colours of
alternate squares in the checker pattern.  The default orientation of the
CHECKER texture is on an X-Z plane (good for ground work, etc.) but to use it
on an object which has mostly X-Y orientation (such as a sphere, for
instance), you must ROTATE the texture.

To rotate the CHECKER texture onto an X-Y plane:

     TEXTURE
          CHECKER COLOUR White COLOUR Red
          SCALE <10.0 10.0 10.0>
          ROTATE <-90.0 0.0 0.0>   { Checkers now in the X-Y plane... }
     END_TEXTURE

6.2.6.13)   CHECKER_TEXTURE - A colouring texture.

I've had many requests for a checker pattern to allow you to alternate between
wood and marble or any other two textures.  So, in version 2.10, I've added a
texture called CHECKER_TEXTURE that takes two textures instead of two colours.

In order to support layered textures, I've made the syntax a bit more verbose
than it would be otherwise.  The syntax is:

    TEXTURE
       CHECKER_TEXTURE
          TEXTURE ... put in a texture here ... END_TEXTURE
          TEXTURE ... add optional layers on top of that one ... END_TEXTURE
       TILE2
          TEXTURE ... this is the second tile texture END_TEXTURE
          TEXTURE ... a texture layered on top of the second tile END_TEXTURE
       END_CHECKER_TEXTURE
       AMBIENT ...
       DIFFUSE ...
   END_TEXTURE

Note that the textures in CHECKER_TEXTURE only use the surface colouring
texture information.  Information about AMBIENT, DIFFUSE, REFLECTION, etc.
and surface normal information (WAVES, RIPPLES) are ignored inside the
CHECKER_TEXTURE. (hey, what do you want for a 10 minute change?)


6.2.6.14)   BOZO - A colouring texture.

BOZO texture basically takes a noise function and maps it onto the surface of
an object.  This "noise" is well-defined for every point in space.  If two
points are close together, they will have noise values that are close
together.  If they are far apart, their noise values will be fairly random
relative to each other.

As mentioned above, for coloration textures such as WOOD, MARBLE, and BOZO,
etc., you may change the colouring scheme by using a colour map.  This map
allows you to convert numbers from 0.0 to 1.0 (which are generated by the ray
tracer) into ranges of colours. For example, the default BOZO colouring can be
specified by:

     TEXTURE
          BOZO
          COLOUR_MAP
               [0.0 0.4 COLOUR White COLOUR White]
               [0.4 0.6 COLOUR Green COLOUR Green]
               [0.6 0.8 COLOUR Blue COLOUR Blue]
               [0.8 1.0 COLOUR Red COLOUR Red]
          END_COLOUR_MAP
     END_TEXTURE

The easiest way to see how it works is to try it.  With a good choice of
colours it produces some of the most realistic looking cloudscapes you have
ever seen indoors!  Try a cloud color map such as:

     TEXTURE
          BOZO
          TURBULENCE 1.0      { A blustery day.  For a calmer one, try 0.2 }
          COLOUR_MAP
               [0.0 0.5  COLOUR RED 0.5 GREEN 0.5 BLUE 1.0  {blue to blue}
                    COLOUR RED 0.5 GREEN 0.5 BLUE 1.0]
               [0.5 0.6  COLOUR RED 0.5 GREEN 0.5 BLUE 1.0  {blue to white}
                    COLOUR RED 1.0 GREEN 1.0 BLUE 1.0]
               [0.6 1.001 COLOUR RED 1.0 GREEN 1.0 BLUE 1.0 {white to grey}
                    COLOUR RED 0.5 GREEN 0.5 BLUE 0.5]
          END_COLOUR_MAP
          SCALE <800.0 800.0 800.0>
          TRANSLATE <200.0 400.0 100.0>
     END_TEXTURE

The color map above indicates that for small values of texture, use a sky blue
color solidly until about halfway turbulent, then fade through to white on a
fairly narrow range.  As the white clouds get more turbulent and solid towards
the center, pull the color map toward grey to give them the appearance of
holding water vapor (like typical clouds).

Check out sunset.dat for a really neat (but slow) sky pattern using ALPHA.


6.2.6.15)   SPOTTED - A colouring texture.

Spotted texture is a sort of swirled random spotting of the colour of the
object.  If you've ever seen a metal organ pipe up close you know about what
it looks like (a galvanized garbage can is close...) Play with this one, it
might render a decent cloudscape during a very stormy day (?).  No extra
keywords are required.  Should work with colour maps.  With small scaling
values, looks like masonry or concrete.

6.2.6.16)   AGATE - A colouring texture.

This texture is similar to Marble, but uses a different turbulence function.
The TURBULENCE keyword has no effect, and as such it is always very turbulent.

6.2.6.17)   GRADIENT - A colouring texture.

This is a specialized texture that uses approximate local coordinates of an
object to control colour map gradients.  This texture ONLY works with colour
maps (one MUST be given!) and has a special <X, Y, Z> triple given after the
GRADIENT keyword, which specifies any (or all) axes to perform the gradient
action on.  Example: a Y gradient <0.0 1.0 0.0> will give an "altitude colour
map", along the Y axis.  Values given other than 0.0 are taken as 1.0.

For smooth repeating gradients, you should use a "circular" colour map, that
is, one in which the first colour value (0.0) is the same as the last one
(1.001) so that it "wraps around" and will cause smooth repeating gradient
patterns.  Scaling the texture is normally required to achieve the number of
repeating shade cycles you want.  Transformation of the texture is useful to
prevent a "mirroring" effect from either side of the central 0 axes.  Here is
an example of a gradient texture which uses a sharp "circular" color mapped
gradient rather than a smooth one, and uses both X and Y gradients to get a
diagonally-oriented gradient.  It produces a dandy candy cane texture!

     TEXTURE
          GRADIENT < 1.0 1.0 0.0 >
          COLOUR_MAP
               [0.00 0.25  COLOUR RED 1.0 GREEN 0.0 BLUE 0.0
                    COLOUR RED 1.0 GREEN 0.0 BLUE 0.0]
               [0.25 0.75  COLOUR RED 1.0 GREEN 1.0 BLUE 1.0
                    COLOUR RED 1.0 GREEN 1.0 BLUE 1.0]
               [0.75 1.001 COLOUR RED 1.0 GREEN 0.0 BLUE 0.0
                    COLOUR RED 1.0 GREEN 0.0 BLUE 0.0]
          END_COLOUR_MAP
          SCALE <30.0 30.0 30.0>
          TRANSLATE <30.0 -30.0 0.0>
     END_TEXTURE

You may also specify a TURBULENCE value with the gradient to give a more
irregular colour gradient.  This may help to do neat things like fire or
corona effects.


6.2.6.18)   GRANITE - A colouring texture.

This texture uses a simple 1/f fractal noise function to give a pretty darn
good grey granite texture.  Typically used with small scaling values (2.0 to
5.0).  Also looks good with a little dithering (texture randomness).  Should
work with colour maps, so try your hand at pink granite or alabaster!

6.2.6.19)   RIPPLES - A surface perturbation texture.

As mentioned earlier, you may specify a surface perturbation texture which
can be used in conjunction with the above coloration textures.  RIPPLES makes
a surface look like ripples of water.  The RIPPLES option requires a value to
determine how deep the ripples are:

     TEXTURE
          WOOD
          RIPPLES 0.3
          TRANSLATE < 1.0 2.0 3.0 >
          ROTATE < 0.0 10.0 40.0 >
          SCALE < 10.0 10.0 10.0 >
     END_TEXTURE

(In this case, the WOOD, MARBLE, or BOZO, etc. keywords are optional).  If a
different colouring is specified (WOOD, MARBLE, or BOZO), then the COLOUR
parameter is ignored (except for light sources where it gives the light colour
or when rendering with a low -q option).


6.2.6.20)   WAVES - A surface perturbation texture.

Another option that you may want to experiment with is called WAVES.  This
works in a similar way to RIPPLES except that it makes waves with different
frequencies.  The effect is to make waves that look more like deep ocean
waves. (I haven't done much testing on WAVES, so I can't guarantee that it
works very well).

Both WAVES and RIPPLES respond to a texturing option called PHASE.  The PHASE
option allows you to create animations in which the water seems to move.  This
is done by making the PHASE increment slowly between frames.  The range from
0.0 to 1.0 gives one complete cycle of a wave.

The WAVES and RIPPLES textures also respond to a keyword called FREQUENCY.  If
you increase the frequency of the waves, they get closer together.  If you
decrease it, they get farther apart.


6.2.6.21)   BUMPS - A surface perturbation texture.

Approximately the same turbulence function as SPOTTED, but uses the derived
value to perturb the surface normal.  This gives the impression of a "bumpy"
surface, random and irregular, sort of like an orange.  After the BUMPS
keyword, supply a single floating point value for the amount of surface
perturbation.  Values typically range from 0.0 (No Bumps) to 1.0 (Extremely
Bumpy).  Values beyond 1.0 may do weird things.

6.2.6.22)   DENTS - A surface perturbation texture.

Also a surface normal perturbing texture.  Interesting when used with metallic
textures, it gives impressions into the metal surface that look like dents.  A
single value is supplied after the DENTS keyword to indicate the amount of
denting required.  Values range from 0.0 (Showroom New) to 1.0 (Insurance
Wreck).  Use larger values at your own risk, they will raise your rates,
anyway... ;-) Scale the texture to make the pitting more or less frequent.

6.2.6.23)   WRINKLES - A surface perturbation texture.

This is sort of a 3-D (normal perturbing) GRANITE.  It uses a similar 1/f
fractal noise function to perturb the surface normal in 3-D space.  With ALPHA
values of greater than 0.0, could look like wrinkled cellophane.  Requires a
single value after the WRINKLES keyword to indicate the amount of wrinkling
desired.  Values from 0.0 (No Wrinkles) to 1.0 (Very Wrinkled) are typical.

6.2.6.24)   IMAGEMAP - A colouring texture.

This is a very special coloration texture that allows you to import a
bitmapped file in DUMP format (the format output by the ray-tracer), IFF
format or Compuserve GIF format and map that bitmap onto an object.  In the
texture of an object, you must give the IMAGEMAP keyword, the format, and a
file name.  The syntax is:

          IMAGEMAP [gradient] DUMP "filename" [ONCE]
     or   IMAGEMAP [gradient] IFF "filename" [ONCE]
     or   IMAGEMAP [gradient] GIF "filename" [ONCE]

The texture will then be mapped onto the object as a repeating pattern.  The
ONCE keyword places only one image onto the object instead of an infinitely
repeating tiled pattern.  When ONCE is used, the colour outside the mapped
texture is set to transparent.  You can use the layered textures to
place other textures or colours below the image.

In version 2.10 and up, you can specify the ALPHA values for the colour
registers of IFF or GIF pictures (at least for the modes that use colourmaps).
You can do this by putting the keyword ALPHA immediately following the
filename followed by the register value and transparency.  If the ALL keyword
is used instead of a register number, then all colours in that colourmap get
that alpha value.

Eg.
          IMAGEMAP <1.0 -1.0 0.0> IFF "mypic.iff"
             ALPHA ALL 0.0

   ...or     ALPHA 0   0.5
             ALPHA 1   1.0
             ALPHA 2   0.3
             ...

          ONCE
          ...


By default, the image is mapped onto the X-Y plane in the range (0.0, 0.0) to
(1.0, 1.0).  If you would like to change this default, you may use an optional
gradient <x, y, z> vector after the word IMAGEMAP.  This vector indicates
which axes are to be used as the u and v (local surface X-Y) axes.  The vector
should contain one positive number and one negative number to indicate the "u"
and "v" axes, respectively.  You may translate, rotate, and scale the texture
to map it onto the object's surface as desired.  Here is an example:

     INCLUDE "shapes.data"

     OBJECT
          QUADRIC Plane_XY END_QUADRIC
          TRANSLATE <0.0  -20.0  0.0>

          TEXTURE
               { make this texture use the x and z axes for the mapping. }
               IMAGEMAP <1.0  0.0  -1.0> GIF "image.gif"
               SCALE <40.0 40.0 40.0>
          END_TEXTURE
     END_OBJECT

Filenames specified in the IMAGEMAP statements will be searched for in the home
(current) directory first, and if not found, will then be searched for in
directories specified by any "-l" (library path) options active.  This would
facilitate keeping all your imagemaps (.dis, .gif or .iff) files in a
"textures" subdirectory, and giving an "-l" option on the command line to where
your library of imagemaps are.

When I was bored with nothing to do, I decided that it would be neat to have
turbulent texture maps.  So, I said - "what the hell!"  You can specify
TURBULENCE with texture maps and it will perturb the image.  It may give some
bizarre results.  Is this useful?  I dunno.  It was easy to do so I did it.
Try it out and see what you get.


6.2.7)  Composite Objects

Often it's useful to combine several objects together to act as a whole.  A
car, for example, consists of wheels, doors, a roof, etc.  A composite object
allows you to combine all of these pieces into one object.  This has two
advantages.  It makes it easier to move the object as a whole and it allows
you to speed up the ray tracing by defining bounding shapes that contain the
objects.  (Rays are first tested to see if they intersect the bounding shape.
If not, the entire composite object is ignored).  Composite objects are
defined as follows:

     COMPOSITE
          OBJECT
               ...
          END_OBJECT

          OBJECT
               ...
          END_OBJECT
          ...

          SCALE < 2.0 2.0 2.0 >
          ROTATE < 30.0 45.0 160.0 >
          TRANSLATE < 100.0 20.0 40.0 >
     END_COMPOSITE

Composite objects can contain other composite objects as well as regular
objects.  Composite objects cannot be light sources (although any number of
their components can).  This is because it is nearly impossible to determine
the true "center" of the composite object, and our light sources are pinpoint
ray sources from the center of the light source object, wherever that may be.


6.3)    Bounding Shapes

Let's face it.  This program is no speed demon.  You can save yourself a lot
of time, however, if you use bounding shapes around any complex objects.
Bounding shapes tell the ray tracer that the object is totally enclosed by a
simple shape.  When tracing rays, the ray is first tested against the simple
bounding shape.  If it strikes the bounding shape, then the ray is further
tested against the more complicated object inside.

NOTE:  Don't use bounding shapes instead of CSG to clip objects.  You will not
       get the result you want.  For the raytracer to work properly, you must
       have the entire object inside the bounding shape.

To use bounding shapes, you simply include the following lines into the
declaration of your OBJECT or COMPOSITE_OBJECT:

     BOUNDED_BY
          a shape
     END_BOUND

An example of a Bounding Shape:

     OBJECT
          INTERSECTION
               SPHERE <0.0 0.0 0.0> 2.0 END_SPHERE
               PLANE <0.0 1.0 0.0> 0.0 END_PLANE
               PLANE <1.0 0.0 0.0> 0.0 END_PLANE
          END_INTERSECTION

          BOUNDED_BY
               SPHERE <0.0 0.0 0.0> 2.0 END_SPHERE
          END_BOUND
     END_OBJECT

The best bounding shape is a SPHERE since this shape is highly optimized.  Any
shape may be used, however, if more convenient.



7)  Displaying the Images

When the ray tracer draws the picture on the screen, it doesn't make good
choices for the colour registers.  Without knowing all the needed colours
ahead of time, only approximate guesses can be made.  Usually, a post-
processor is really needed to view the final image correctly.

7.1)    Amiga Systems

A post-processor has been provided for the Amiga which scans the picture and
chooses the best possible colour registers.  It then redisplays the picture.
For the Amiga, "DumpToIFF" can optionally save this picture in IFF format.
The syntax for the DumpToIFF post-processor is:

     DumpToIFF filename

where the filename is the one given in the -o parameter of the ray tracer.  If
you didn't specify the -o option, then use:

     DumpToIFF data.dis

If you want to save to an IFF file, then put the name of the IFF file after
the name of the data file:

     DumpToIFF data.dis picture

This will create a file called "picture" which contains the IFF image.


An alternative approach is to buy the commercial package called "The Art
Department" from ASDG.  You can then use the +fr option of the raytracer to
produce raw files which can be read in to TAD using Sculpt mode.  You can also
render using +fd to produce a dump format file, and use d2iff to convert this
to a 24-bit IFF image to load into TAD.


7.2)    IBM Systems

For the IBM, you will probably want to use the +ft option (default if +f is
given) and write the image out in Targa-24 format.  If you have a Targa or
compatible display adapter, you may view the picture in the full 16 million
colors (that's why they still cost the big $$ bucks, but Hercules and Everex,
notably, are introducing their lower-priced SVGA-compatible 24-bit color display
systems for the IBM PC and compatibles).  If you don't have one of these, there
are several different post-processing programs available to convert the TARGA
true-color image into a more suitable color-mapped image (such as .GIF).  If
you have a VGA/MCGA or SVGA adapter capable of 320x200 by 256 colors or better,
then you may use the +d option which will display the image as it generates
using only approximate screen colors.  The +d option will Autodetect the type
of display adapter card you have and briefly say what kind it found before
displaying the picture.  If you say +dx where x is one of the predefined IBM
(S)VGA display adapter types, no hardware test is performed, so if you don't
have that type of (S)VGA card, -> DON'T <- use that particular +dx option!

When displaying the image to screen, a HSV conversion method is used (hue,
saturation, value).  This is a convenient way of translating colors from a
"true color" format (16 million) down a "colour mapped" format of something
reasonable (like 256), while still approximating the color as closely as the
available display hardware permits.  As mentioned previously, the tracer has
no way of knowing which colors will be finally used in the image, nor can it
deal properly with all of the colors which will be generated (up to 16M), so
only 4 shades each of 64 possible hues are mapped into the palette DAC, as
well as black, white, and two grey levels. The advantage a post-processor has
in choosing mapped colors is that it can throw away all the unused colors in
the palette map, and thereby free up some space for making better gradient
shades of the colors that are actually used.

There are several available image processing programs that can do this, a
public domain one that is very good is PICLAB, by the Stone Soup Group (the
folks who brought you FRACTINT).  The procedure is to load the TARGA file,
then use the MAKEPAL command to generate a 256 color map which is the
histogram-weighted average of the most-used colors in the image (You could
also PLOAD a palette file from FRACTINT or one you previously had saved using
PSAVE).  You then MAP the palette onto the image one of two ways:

     1)   If the DITHER variable is OFF, a nearest-match-color-fit is used,
          which can sometimes produce unwanted "banding" of colored regions
          (called false contours).
     2)   If the DITHER variable is ON, then a standard dither is used to
          determine final color values.  This is much better at blending the
          color bands, but can produce noise in reflections and make mirrors
          appear dirty or imperfect.

Then you would typically SHOW the image or GSAVE it into GIF format.  While
the picture is still in the unmapped form (TARGA, etc.) you can perform a
variety of advanced image processing transformations and conversions, so save
the .TGA or .RAW files you make (in case you ever get a TARGA card, or give
them to a friend who has one!).

A commercial product that also does a good job of nearest-match-color-fit is
the CONVERT utility of The AutoDesk Animator.  However, the dither effect is
not as good as that of PICLAB.  To convert the file in AA's CONVERT, you LOAD
TARGA, then in the CONVERT menu, go to the SCALE function and just hit RENDER.
Click on the DITHER (lights up with an asterisk when on) if you want it to use
it's dithering.  CONVERT will scale (if asked to) and then do a histogram of
total used colors like PICLAB, but then makes 7 passes on the color map and
image to determine shading thresholds of each hue.  This nearly eliminates the
color banding (false contours) in a lot of cases without resorting to good 'ol
dithering.  By now you must get the feeling DITHER is a 4-letter word.  If
you have a low-resolution display, it is.  If you have too few colors,
however, it can be a saving grace.  At resolutions of 640x400 or higher the
"spray paint" effect of dithering and anti-aliasing is much less noticeable,
and effects a much smoother blending appearance.

A new package to show up in the public domain/shareware circles for the IBM
is something called Image Alchemy, by Handmade Software.  It will convert
TARGA format to GIF files and do a decent job of palette selection and
dithering.  To use it simply say "ALCHEMY file.tga file.gif -g -8 -c256".
It also features a quick-and-dirty display mode where it uses a standardized
palette in much the same way DKB's +d option does, but offers dithering of the
image while using the pre-defined palette, for a somewhat better quick display.


7.3)    Unix Systems

I don't have many details on Unix systems, but I hear that the FBM utilities
work well to convert the Dump format files into various formats of images.
For people with access to anonymous FTP over USENET, the FBM utilities are
available from nl.cs.emu.edu (128.2.222.56) in directory /usr/mlm/ftp.



8)  DKBTrace Utilities

In many cases, creating data files for DKBTrace is difficult and tedious.  To
help remedy this problem, I and various other people have developed some
utilities to create data files.  These utilities are described below.

As well, there are some utilities that perform operations on the image files
created by DKBTrace.  These utilities convert between various formats and
allow you to modify or merge output files together.

I'd like to thank all the people who wrote these utilities and sent them to
me.  If anybody else comes up with other utilities, please let me know and
I'll include them in the distribution.

Some of these utilities are written in BASIC in IBM systems.  As such, they
are not easily portable from system to system.  If anyone wants to convert
them to C, let me know and I'll post the C versions.

8.1)    Data File Creation Utilities

The data creation utilities fall into two categories:  Those that convert from
some other format into DKB format, and those that generate DKB files using
algorithmic techniques.  These utilities are described below.

8.1.1)  SA2DKB

This program converts Sculpt-Animate 3D & 4D data files into DKB format.  It
currently only supports the basic triangles and textures. It doesn't support
smooth triangles (it treats them like normal triangles), light sources,
cameras, or floors.

(This utility was formerly called "Sculpt2DKB" but the IBM systems out there
kept calling it "SCULPT2D", then couldn't figure out what a 2D program had to
do with raytracing or what the nonexistent Amiga program called "Sculpt-2D"
was :-)

8.1.2)  DXF2DKB

This utility converts AutoCAD DXF (Drawing eXchange Format) files into
DKBTrace format scene description files.  It was written by Aaron Collins.  It
does not support all of the DXF primitives, but will suffice for simple
objects and scenes after EXPLODE'ing and DXFOUT'ing then in AutoCAD.

8.1.3)  ShellGen

ShellGen is a BASIC program written by Dan Farmer.  It's based on a short code
fragment from Clifford Pickover's book "Computers, Pattern, Chaos, and Beauty"
(St. Martin's Press).  This code fragment was reprinted in Ray Tracing News
Issue 3.3.

As far as I know, the BASIC program only works on IBM's.  It does, however,
allow you to change the parameters and see a quick outline of what the result
will look like.

For those people without IBM's, I've changed the original code fragment to at
least output a DKB-format file.  No user interface has been provided, however.

8.1.4)  Twister

Twister is a C program written by Drew Wells (CIS 73767,1244).  It creates
data files for twisted shapes.  The program uses a text interface and prompts
the user with a question/answer format.

8.1.5)  Chem2DKB

Chem2DKB is an IBM BASIC program written by Dan Farmer.  It takes models
generated by the CHEM.EXE program written by Larry Puhl.

8.1.6)  Lissajou

This is an IBM BASIC program written by Dan Farmer.  It creates data files for
lissajous figures.  The basic algorithms were from Clifford Pickover.  See
Scientific American Jan. '91 and Omni Feb '90 for examples.


8.2)    Output File Manipulation Utilities

These utilities perform some useful manipulations on the dump format and Targa
format output files from DKBTrace.  I'd like to thank the people who wrote
these utilities and provided them for general distribution.

8.2.1)  dump2i24   (DumpToIFF24)

This program was written by Helge E. Rasmussen ([e-mail]).  It converts
the dump format files produced by DKBTrace into 24-bit IFF format files.
These files can then be read by a variety of programs including "The Art
Department" by ASDG.

8.2.2)  catdump

This utility was written by Ville Saari [e-mail] (and copyright
by the Ferry Island Pixelboys.)  It takes two or more partially rendered files
in DKBTrace's dump format and merges them into one file.  This is useful for
all sorts of things like rendering different parts on different computers and
combining the results.

NOTE:  Be careful if you combine pictures produced on different systems.  If
the random number generator works differently between the two systems, the
textures may look completely different from one another.  So long as you
use the same executable, you should be fine.

8.2.3)  combdump  (combine dump)

This utility was also written by Ville Saari.  It takes two images generated
with DKBTrace with slightly different viewpoints, and creates one dump-format
image file to be viewed with RED-BLUE or RED-GREEN 3D glasses.  The program
allows you to compensate for the exact filtering characteristics of your
glasses to get the best possible result.

8.2.4)  dump2mtv

This is yet another utility written by Ville Saari.  This one converts
DKBTrace dump format files onto MTV format used by the MTV and RayShade
raytracers.

8.2.5)  dump2raw

The dump2raw utility was written by Aaron Collins to convert the dump format
output of DKBTrace into three separate files for red, green, and blue.  On the
IBM, the extensions for these files are "r8", "g8", and "b8".  On the other
systems, they are "red", "grn" and "blu".

Version 2.10 of the raytrace allows you to use the +fr option to output raw
format files directly without the need for a conversion program like this.

8.2.6)  halftga

The halftga utility (written by Aaron Collins) shrinks a Targa-format file to
exactly half its original size.  This file can then be converted into a GIF
image and used in an IMAGE_MAP statement.  For systems with little memory
available for imagemaps, this command can be a life-saver.

8.2.7)  gluetga

This utility (by Aaron Collins) is similar to catdump but works for Targa
format files.  It takes several partially-rendered Targa files and glues them
together into one image.

8.2.8)  tga2dump

This utility was written by Aaron Collins.  It converts Targa format 16, 24,
and 32 bit images into DKB's dump format for use in image-mapping.


8.3)    Animation Utilities

One of the most frequent questions I'm asked is whether or not DKBTrace
supports animation.  The answer is no, not directly.  However, I have made
some changes to the program to provide frame-to-frame consistency so you can
use it for animation if you want to.  The problem, then, is creating the data
files for each individual frame.  That's what this section is all about.

8.3.1)  RayScene

Although RayScene is not being distributed with this raytracer, I thought I'd
at least mention it and tell you where you can get it.  RayScene is a program
that creates data files for DKBTrace based on a high-level (higher-level?)
description of the motion of the camera and the objects.  It was written by
Jari K{hk|nen ([e-mail]) and Panu Hassi ([e-mail]) and
is available by anonymous FTP from tolsun.oulu.fi (128.214.5.6) in the
directory /pub/rayscene or from iear.arts.rpi.edu in the directory
/pub/graphics/ray/rayscene.


This explanation of RayScene was sent to me by Panu Hassi;

   "I've tried animation with DBW before DKBTrace2.0 was released.
    The procedure was this: First I wrote the first scene file, copied it
    for NUMBER_OF_FRAMES times and then edited some parts of those files
    to create movement etc.  If something went wrong (I accidentally edited
    wrong value etc), I had to edit all those scene files again to make the
    changes.  Not so nice if there are 100 files to edit...

    So a friend of mine, Jari K{hk|nen, and I decided to write RayScene to
    make that process even a little easier.  With RayScene the process
    goes like this:  you create a scene file and mark the places that
    should be changed with a variable, like:

    BOUNDED_BY
         SPHERE <0.0 0.0 0.0> #sphere_size# END_SPHERE
    END_BOUND

    Then you create another file where the values for these variables are
    listed.  Rayscene simply creates N scene files inserting current value of
    each variable to proper place.  That's all :D

    We have included couple of simple utilities that help with creating
    those variable values, but the original scene files are still created
    'manually'.  Still, the results have been really nice.  There are
    several animations for Amiga and PC in tolsun.oulu.fi."

9)  How it All Works (or How to Get What You Want)

The information in this section is designed for people who are reasonably
familiar with the raytracer and want more information on how things work so
they can push it to its limits.  You probably don't need this level of detail
to make interesting data files, but if you suddenly get confused about
something the program did, this section may help you figure it out.

9.1)    Viewpoints

Viewpoints can be completely defined by four vectors.  The LOCATION is easy.
That's where the camera is.  The DIRECTION is a vector that starts at the
LOCATION and points to the center of a window.  The UP vector starts at the
center of the window and points to the center of the top edge.  The RIGHT
vector starts at the center of the window and points to the center of the
right edge.

                              |\
                              | \
                              |  \
                              |   \
                              |  ^ \
                              |  |Up|
                              |  |  |
                              |  |  |
    Location *------------------->  |
                Direction     |   \ |Right
                              |    \|
                              \     |
                               \    |
                                \   |
                                 \  |
                                  \ |
                                   \|

The window is then divided up according to the resolution you specified and
rays are fired through the pixels out into the world.  For an eye ray,
therefore, the equation of the ray is:

   Location + t (Direction + ((height - y)*UP) + (x*RIGHT))

where "t" is a parameter that determines the distance from the eye to the
object being tested.  The Y coordinate is inverted by subtracting it from
height because most graphics systems put 0,0 in the top left corner of the
screen.

This viewpoint model is very flexible.  It allows you to use left-handed or
right-handed coordinate systems.  It also doesn't require that the DIRECTION,
UP, and RIGHT vectors be mutually orthogonal.  If you want, you can distort
the camera to get really bizarre results.

Once the basic four vectors are specified, it's possible to use the SKY and
LOOK_AT vectors to point the camera.  You must specify the SKY vector first,
but let me describe the LOOK_AT vector first.  LOOK_AT tells the camera to
rotate in such a way that the LOOK_AT point appears in the center of the
screen.  To do this, the camera first turns in the left-to-right direction
(longitude in Earth coordinates) until it's lined up with the LOOK_AT point.
It then turns in the up/down direction (latitude in Earth coordinates) until
it's looking at the desired point.

Ok, now we're looking at the proper point.  What else do we have to specify?
If you're looking at a point, you can still turn your camera sideways and
still be looking at the same spot.  This it the orientation that the SKY
direction determines.  The camera will try to position itself so that the
camera's UP direction lines up as closely as possible to the SKY direction.

Put another way - in airplane terms, the LOOK_AT vector determines your
heading (north, south, east, or west), and your pitch (climbing or
descending).  The SKY vector determines your banking angle.

9.2)    Ray-Object Intersections

For every pixel on the screen, the raytracer fires at least one ray through
that pixel into the world to see what it hits.  For each hit (well, almost),
it calculates rays to each of the light sources to see if that point is
shadowed from that light source.  For reflecting objects, a reflected ray is
traced.  For refracting objects, a refracting ray is traced.  That all adds up
to a lot of rays.

Every ray is tested against every object in the world to see if the ray hits
that object. This is what slows down the raytracer.  You can make things
easier by using simple bounding shapes on your objects.

Fortunately, all ray-object intersections for all shapes in DKBTrace can be
solved by a simple quadratic equation.  This is why QUADRICs are used in
DKBTrace.  Solving for things like B-Splines, Bezier Splines, NURBS, Torus',
etc. is a lot more complicated.  That's why I haven't implemented primitives
for these shapes.

9.3)    Transparency and Refraction

This section get really complicated because of the way transparency and
refraction are implemented.  If you don't really care, skip to the next
section. If you don't mind slogging through this and getting confused, then
read on.

- you've been warned -

The way that transparency and refraction work has changed slightly from
previous versions.  Now, transparency and refraction work together instead of
separately.

First, let me distinguish between reflected light and filtered light.  Suppose
you painted a table with patches of colour.  You then took some red sand and
sprinkled it on top of the various colours.  The red sand will tint the
colours red, but you will still see some of the original colour.  If, instead,
you took a sheet of red plexiglass and put it on top of the table, all you
could see would be shades of red.  That's because the plexiglass filter ONLY
allows the red colour to show through.

In DKBTrace, the layered textures work like the red sand - the colours on top
mix with the underlying colours depending on the density (ALPHA) of the
distribution.

Refraction, however, works like a filter.  The surface colour determines that
colours of light are allowed to pass from the inside of the object to the
outside, and vice versa.  Here are some filter colours:

   RED 1.0  GREEN 0.0  BLUE 0.0   ALPHA 1.0    - a red filter
   RED 1.0  GREEN 1.0  BLUE 1.0   ALPHA 1.0    - clear glass
   RED 0.0  GREEN 0.0  BLUE 0.0   ALPHA 1.0    - a dark filter - this will
                                                 appear black.

Now, consider the following layered textures:

   TEXTURE COLOUR Green ALPHA 0.6 END_TEXTURE
   TEXTURE COLOUR Yellow ALPHA 0.3 REFRACTION 0.5 END_TEXTURE

(Keep in mind that the last texture is on top.)

NOTE: In layered textures, only the REFRACTION component of the LAST entry has
any effect.

The colour you get is calculated like this:

         ____  Full Brightness
         |
         |
         |
         |
         |
         |   7/10 of pixel's colour is Yellow
         |
         |
         |
         |
         |
         |---
         |
      -  |   3/10 (alpha) left over for underlying colour
     |   |
     |   |
     |   ----  Full Darkness
     |
     |
     |
     |
     |   ____  From the 3/10 available:
     |   |
     |   |
     |-> |   4/10 is green
         |
         |
         |---6/10 (alpha) is available for refraction
         |
         |
         |
         |
         |-- 5/10 of that (6/10) is passed through from refraction
         |        and filtered by the combined filter colour
         |        (yellow filtered by green).
         |
         |
         |
         ----



So, the top texture layer supplies some fraction of the light that reflects off
the surface of the object.  If the ALPHA was non-zero, it allows the lower
textures to supply the remainder.  If, after all the textures are processed,
there's still some fraction left over, it is applied to the light that's
refracted through the object.

This algorithm probably doesn't coincide with reality, but neither does the rest
of the raytracer, so I'm not terribly concerned about it.

9.4)    Textures, Noise, and Turbulence

If there's one thing that DKBTrace is known for, it's textures.  Here's how
they really work.  If you want some good reading material, check out "An Image
Synthesizer" by Ken Perlin in the SIGGRAPH '84 Conference Proceedings.

Let's start with a marble texture.  Real marble is created when different
colours of sediments are laid down one on top of another and compressed to
form solid rock.

For example, take a simple block of marble:
          ___________
         /          /|
        /          / |
       /__________/  |
       |   Red    | /|
       |----------|/ |
       |  White   | /|
       |----------|/ |
       |   Red    | /|
       |----------|/ |
       |  White   | /
       |__________|/

If you carve a shape put of this block of marble, you will get red and white
bands across it.

Now, consider wood.  The rings in wood are created when the tree grows a new
outer shell every year.  Hence, we have concentric cylinders of colours:

                ______
               /      /
              /      / \
             /      /   \
            /      /     \
           /      /      |
          /______/       |
         / _____ \       |
        / / ___ \ \      |
       / / / _ \ \ \     /    (how do you draw a log in ASCII??!!)
      / / / / \ \ \ \   /
      | | | | | | | |  /
      | | | |O| | | | /
      | | | | | | | |/
      \ \ \ \_/ / / /
       \ \ \___/ / /
        \ \_____/ /
         \_______/

Cutting a shape out of a piece of wood will tend to give you rings of colour.

Now, this is fine, but the textures are still a bit boring.  For the next
step, we blend the colours together to create a nice smooth transition.  This
makes the texture look a bit better.  The problem, though, is that it's too
regular - real marble and wood aren't so perfect.

Before we make our wood and marble look any better, let's look at how we make
noise.  Noise (in raytracing) is sort of like a random number generator, but
it has the following properties:

   1) It's defined over 3D space i.e., it takes x, y, and z and returns the
      noise value there.
   2) If two points are far apart, the noise values at those points are
      relatively random.
   3) If two points are close together, the noise values at those points are
      close to each other.

You can visualize this as having a large room and a thermometer that ranges
from 0.0 to 1.0.  Each point in the room has a temperature.  Points that are
far apart have relatively random temperatures.  Points that are close together
have close temperatures. The temperature changes smoothly, but randomly as we
move through the room.

Now, let's place an object into this room along with an artist.  The artist
measures the temperature at each point on the object and paints that point a
different colour depending on the temperature.  What do we get?  BOZO texture!

Another function used in texturing is called DNoise.  This is sort of like
noise except that instead of giving a temperature, it gives a direction.  You
can think of it as the direction that the wind is blowing at that spot.

Finally, we have a function called turbulence which uses DNoise to push a
particle around a few times - each time going half as far as before.

         P ------------------------->
                  First Move        /
                                   /
                                  /
                                 /Second
                                /  Move
                               /
                        ______/
                        \
                         \
                          \
                           Q - Final point.

This is what we use to create the "interesting" marble and wood texture.  We
locate the point we want to colour (P), then push it around a bit using
Turbulence to get to a final point (Q) then look up the colour of point Q in
our ordinary boring wood and marble textures.  That's the colour that's used
for the point P.

(Did you really want to know all that?  Do you really care?  I dunno.)

9.5)    Layered Textures

As of version 2.10, DKBTrace supports layered textures.  Here's how that
works.

Each object and each shape has a texture that may be attached to it.  By
default, shapes have no texture, but objects have a default texture.
Internally, textures are marked as being constant or variable.  A constant
texture is one that was DECLAREd as a texture and is being shared by many
shapes and objects.  Variable textures are textures that have been declared
totally within the object or have used a DECLAREd texture and modified it in a
destructive way.  The idea here is that we want to save on memory by sharing
textures if possible.

If you have several texture blocks for an object or a shape, they are placed
into a linked list (First-in Last-out).  For example, take the following
definition:

   OBJECT
      SPHERE <0 0 0> 1 END_SPHERE
      TEXTURE WOOD END_TEXTURE
      TEXTURE MARBLE END_TEXTURE
   END_OBJECT

Here's what happens while parsing this object:  Since this is an object (as
opposed to a shape - SPHERE, PLANE, etc.), it starts out with the default
texture attached.

   ________      _________
   |      |      |       |
   |      |----->|Default|
   |Object|      |Texture|
   |      |      |_______|
   |      |
   |______|

When the parser sees the first TEXTURE block, it looks to see what it has
linked.  Since the thing that's linked is the default texture (not a copy), it
discards it and puts in the new texture.

   ________      _________
   |      |      |       |
   |      |----->| WOOD  |
   |Object|      |Texture|
   |      |      |_______|
   |      |
   |______|

On the next texture, it sees that the texture isn't the default one, so it
adds the second texture into the linked list.

   ________      _________      _________
   |      |      |       |      |       |
   |      |----->|MARBLE |----->| WOOD  |
   |Object|      |Texture|      |Texture|
   |      |      |_______|      |_______|
   |      |
   |______|


Now for a problem.  If you want to specify the REFRACTION of the texture, the
raytracer must first calculate the surface colour.  It does this by marching
through the texture list and mixing all the colours.  When it's finished, it
checks the ALPHA value of the surface colour and decides whether it should
trace a refracting ray.  Where does it get the REFRACTION value and the index
of refraction?  It simply takes the one in the topmost (the last one defined)
texture.  I don't see any reason to have refraction values for any other
textures in the layer as it applies to the whole object.

9.6)    Image Mapping

One major problem people have when designing data files for DKBTrace is how to
position images onto the desired surfaces.  With version 2.10, this problem
becomes slightly easier since the image can be mapped onto the object in the
object's natural coordinate system.  Thereafter, when the object is
translated, rotated, or scaled, the image map will follow it.

The image mapping that DKBTrace currently supports is called a "parallel
projection" mapping.  This technique is simple (that's why I implemented it
:-), but it's not perfect.  It works like a slide projector casting the
desired image onto the scene.  The difference, however, is that the image
never gets larger as you move further away from the slide projector.  In fact,
there is no real slide projector.  Consider the following cross section:


Image to Map
    |                 _________
    V                 \       /            /\        ___________________
                       \     /            /  \       \                 /
----A-------------------A   A------------A    A-------A---------------A-->
    B                    B B            B      B       BB           BB
    C                     C            C        C        CCCC   CCCC
    D                                 D          D           DDD
    E                                E            E
    F                               F              F
----G------------------------------G                G-------------------->
                                  /                  \
                                 /____________________\

This two dimensional example shows an image with colours A,B,C,D,E,F, and G
being mapped onto three objects.  The raytracer performs a similar operation
to map a 2D picture onto a 3D object.  Note that objects cannot shadow each
other from the image being mapped.  This means that the image will also appear
on the back of the object as a mirror image.

The mapping takes the original image (regardless of the size) and maps it onto
the range 0,0 to 1,1 in two of the 3D coordinates.  Which two coordinates is
specified by the gradient vector provided after the image.  This vector must
contain one positive number, one negative number, and one zero.  The positive
number identifies the u axis (the left-right direction in the image) and the
negative number represents the v axis (the picture's up-down direction).  Note
that the magnitude of the number is irrelevant.

For example:

    IMAGEMAP <1 -1 0> GIF "filename"

will map the GIF picture onto the square from <0 0 0> to <1 1 0> like this:

        Y
        ^
        |
        |
        |
      1 |----------
        |   Top  R|
        |L       i|
        |e       g|
        |f       h|
        |t       t|
        | Bottom  |
        ----------------> X
                  1

If we reversed the vector, the picture would be transposed:

    IMAGEMAP <-1 1 0> GIF "filename"

produces:

        Y
        ^
        |
        |
        |
      1 |----------
        |B Right  |
        |o       T|
        |t       o|
        |t       p|
        |o        |
        |m  Left  |
        ----------------> X
                  1

Once the image orientation has been determined, it can be translated, rotated,
and scaled as desired to map properly onto the object.



9.7)    Output File Formats

People always ask me to describe the output file formats of DKBTrace.  I
received so many requests for this that I decided to put it into the document.

The normal "default" output format is "dump" format.  This is based on QRT
format and goes like this, where each character is a hex digit:

Header:
     wwww hhhh          - width, height (16 bits each, LSB first)

For each data line:
     llll               - line number (16 bits, LSB first, 0 to LINES-1)
     rr rr rr rr rr ... - the red components for that line
                          (8 bits each - 0=dark, 255=bright)

     gg gg gg gg gg ... - the green components for that line
                          (8 bits each - 0=dark, 255=bright)

     bb bb bb bb bb ... - the blue components for that line
                          (8 bits each - 0=dark, 255=bright)

Note that this format is slightly different from QRT's.


The "+fr" option of the raytracer produces "raw" files.  These are simply
three files with no header information and no line number information - just
the raw data.

The "+ft" option writes out Targa format.  Specifically, the fields are:

Header:
   00 00 02 00 00      - Fixed header information for uncompressed type 2 image
   00 00 00
   0000                - Horizontal offset always is at 0000
   llll                - Vertical offset (1st line number, 16 bits, LSB first)
   wwww hhhh           - width, height of image (16 bits each, LSB first)
   18 20               - 24 bits per pixel, Top-down raster

For each line:
   bb gg rr bb gg rr ... - blue, green, and red data, 8 bits for each pixel.




10) Common Questions and Answers

I often get asked the same questions again and again.  I usually take this to
mean that the documentation is not complete or not sufficiently clear.  In
order to correct this problem, I've added some sections to the document
describing the features in more detail.  I've also collected some of the more
popular questions and answered them here:

     Q: Will you be implementing radiosity?
     A: I don't expect so.  The techniques for radiosity are quite involved
        and time consuming (although they are getting faster).  The amount of
        effort required to implement radiosity is beyond my current plans.

     Q: Do you intend make DKBTrace RenderMan compatible?
     A: Probably not.  RenderMan is a specification that requires much more
        functionality than DKBTrace currently provides.  The camera models,
        modelling primitives, and shading language of RenderMan are all very
        involved and difficult to implement.  As well, RenderMan is not well
        suited to a raytracing approach.  Don't expect to see DKBTrace
        RenderMan compatible in the near (or distant) future.  Note, though
        that several of the DKBTrace textures are similar to those obtainable
        by RenderMan.

     Q: I defined a light source but the shadows and lighting are all wrong.
     A: Light sources must be defined at the origin (0,0,0) and translated to
        the proper place.  The reason for this is to allow the diffuse lighting
        calculations to quickly determine where the center of the light source
        is.  It's a very difficult task to calculate the center of an object
        (in general), so I simply take the place that the object was translated
        to as the center of the light source.

     Q: I keep running out of memory.  What can I do?
     A: Buy more memory :-)  But seriously, you can decrease the memory
        requirements for any given picture in several ways:
          1) DECLARE texture constants and use them (textures are shared).
          2) Don't modify the texture that you are sharing.  On the first
             modify, the texture is copied and (therefore) takes up more space.
          3) Put the object transformations before the texture structure.  This
             prevents the texture from being transformed (and hence, copied.
             This may not always be desirable, though).
          4) Use UNIONS instead of COMPOSITE objects to put pieces together.
             (previous versions of the raytracer didn't allow this because
             the texture applied to the entire object.  Version 2.10 and up
             allow you to change the texture on a per-shape basis.)
          5) Use fewer or smaller image maps.
          6) Use GIF or IFF (non-HAM) images for image maps.  These are stored
             internally as 8 bits per pixel with a colour table instead of
             24 bits per pixel.

     Q: I get a floating point exception error on certain pictures.
        What's wrong?
     A: Oh no! Not another one!  The raytracer (obviously) performs MANY
        floating point operations when tracing a scene.  If I had to check
        each one for overflow or underflow, the program would be much longer
        and I would be much closer to going insane trying to locate all
        possible cases.  If you get this problem, I'd suggest that you
        first look through your data file to make sure you're not doing
        something stupid like:

          - Scaling something by 0.0 in ANY dimension
          - Making the LOOK_AT point the same as the LOCATION
          - Defining triangles with two points the same (or nearly the same)
          - Using the zero vector for normals.

        If it doesn't seem to be one of these problems, let me know, but there
        may not be a lot I can do because overflows can occur almost anywhere.
        Sorry.  If you do have such troubles, you can try to isolate the
        problem in the input data file by commenting out objects or groups
        of objects until you narrow it down to a particular section that
        fails.  Then try commenting out the individual characteristics of the
        offending object.

     Q: No matter how much I scale a Cylinder, I can't make it fit on the
        screen.  How big is it and how much do I have to scale it?
     A: Cylinders (like most quadrics) are infinitely long.  No matter how
        much you scale them, they still won't fit on the screen.  To make a
        capped cylinder, you must use CSG:

           INTERSECTION
              QUADRIC Cylinder_Y END_QUADRIC
              PLANE <0.0 1.0 0.0> 1.0 END_PLANE
              PLANE <0.0 -1.0 0.0> 1.0 END_PLANE
           END_INTERSECTION

        Cylinders CAN be scaled in cross-section, the two vectors NOT in the
        name of the cylinder (X and Z, in our example above) can be scaled
        to control the width and thickness of the cylinder.  Scaling the Y
        value (which is normally infinite) is meaningless, unless you have
        "capped" it as above, then scaling the entire INTERSECTION object
        in the Y dimension will control the height of the cylinder.

     Q: Why don't you define a primitive for a 6-sided box?
     A: Because you can do it so easily with CSG:

           INTERSECTION
              PLANE < 1.0  0.0  0.0> 1.0 END_PLANE
              PLANE <-1.0  0.0  0.0> 1.0 END_PLANE
              PLANE < 0.0  1.0  0.0> 1.0 END_PLANE
              PLANE < 0.0 -1.0  0.0> 1.0 END_PLANE
              PLANE < 0.0  0.0  1.0> 1.0 END_PLANE
              PLANE < 0.0  0.0 -1.0> 1.0 END_PLANE
           END_INTERSECTION

     Q: Are planes 2D objects or are they 3D but infinitely thin?
     A: Neither.  Planes are 3D objects that divide the world into two
        half-spaces.  The space in the direction of the surface normal is
        considered outside and the other space is inside. In other words,
        planes are 3D objects that are infinitely thick.

                            ^
                            |
                            |
                            |  Outside
                     _______|_______
                               Inside


     Q: Can DKBTrace render soft shadows?
     A: No.  This would require a lot more programming work and a lot more
        calculation time.  You can place an unturbulated WOOD texture
        "filter" over a lamp in a can, and use a colour map going from dark
        (ALPHA 0.0) around the edges to clear (ALPHA 1.0) at the center,
        and get a soft-shadow-like effect for a "spotlight".

     Q: I'd like to go through the program and hand-optimize the assembly code
        in places to make it faster.  What should I optimize?
     A: Don't bother.  With hand optimization, you'd spend a lot of time to
        get perhaps a 5-10% speed improvement at the cost of total loss of
        portability.  If you use a better ray-surface intersection algorithm,
        you should be able to get an order of magnitude or more improvement.
        Check out some books and papers on raytracing for useful techniques.
        Specifically, check out "Spatial Subdivision" and "Ray Coherence"
        techniques.

     Q: Objects on the edges of the screen seem to be distorted.  Why?
     A: If the DIRECTION vector of the viewpoint is not very long, you may
        get distortion at the edges of the screen.  The reason for this is that
        the viewpoint's screen is flat:


                               | /\  This object looks small
                               | \/
                               |
                               |
                               *   <---- * = Projection of objects onto screen.
                               |
                               |
               Viewpoint --> V * /\  This object looks big
                               * \/
                               |
                               |
                               |
                               |<---- viewing screen.
                               |
                               |

     Q: How do you position image maps without a lot of trial and error?
     A: By default, images will be mapped onto the range 0,0 to 1,1 in the
        appropriate plane.  You should be able to translate, rotate, and
        scale the image from there.

     Q: What's the difference between ALPHA and REFRACTION?
     A: The difference is a bit subtle.  Alpha is a component of a colour that
        determines how much light can pass through that colour.  Refraction is
        a property of a surface that determines how much light can come from
        inside the surface.  See the section above on Transparency and
        Refraction for more details.

     Q: How do you calculate the surface normals for smooth triangles?
     A: When I implemented smooth triangles, I never really expected anyone to
        manually calculate the surface normals.  There are two ways of getting
        another program to calculate them for you.

          1) Depending on the type of input to the program, you may be able to
             calculate the surface normals directly.  For example, if you have
             a program that converts B-Spline or Bezier Spline surfaces into
             DKB-format files, you can calculate the surface normals from the
             surface equations.

          2) If your original data was a polygon or triangle mesh, then it's
             not quite so simple.  You have to first calculate the surface
             normals of all the triangles.  This is easy to do - you just use
             the vector cross-product of two sides (make sure you get the
             vectors in the right order).  Then, for every vertex, you average
             the surface normals of the triangles that meet at that vertex.
             These are the normals you use for smooth triangles.

     Q: When I render parts of a picture on different systems, the textures
        don't match when I put them together.  Why?
     A: The appearance of a texture depends on the particular random number
        generator used on your system.  DKBTrace seeds the random number
        generator with a fixed value when it starts, so the textures will be
        consistent from one run to another or from one frame to another so
        long as you use the same executables.  Once you change executables,
        you will likely change the random number generator and, hence, the
        appearance of the texture.  There is an example of a standard ANSI
        random number generator provided in IBM.C, include it in your machine-
        specific code if you are having consistency problems.

     Q: What's the difference between a COLOUR declared inside a TEXTURE
        and one that's in a shape or an object and not in a texture?
     A: The colour in the texture specifies the colour to use for qualities
        5 and up.  The colour on the shape and object are used for faster
        rendering in qualities 4 and lower and for the colour of light sources.
        See the -q option for details on the quality parameter.


     Q: I created an object that passes through its bounding volume.  At times,
        I can see the parts of the object that are outside the bounding volume.
        Why does this happen?
     A: Bounding volumes are NOT designed to change the shape of the object.
        They are strictly a realtime improvement feature.  The raytracer trusts
        you when you say that the object is enclosed by a bounding volume.  The
        way it uses bounding volumes is very simple:  If the ray hits the
        bounding volume (or the ray's origin is inside the bounding volume),
        then the object is tested against that ray.  Otherwise, we ignore the
        object.  If the object extends beyond the bounding volume, anything goes.
        The results are undefined.  It's quite possible that you could see the
        object outside the bounding volume and it's also possible that it could
        be invisible.  It all depends on the geometry of the scene.

     Q: Will you be writing a Graphical User Interface for DKB?
     A: No, but several other people have expressed an interest in writing
        one.  I'd like to form a mailing list to get all these people in touch
        with each other, so if you have an interest in this, please let me
        know.

     Q: When will the next version be available?
     A: If I told you, I'd be lying because I don't know.  I'm finding that
        releasing an official version of a program like this is a major
        effort.  It requires not only the changes to the code, but also
        changes to the documentation.  Sometimes (as with this release), I
        have to change the older data files to conform to the new syntax.
        Usually, I have to spend a lot of time re-rendering scenes that used
        to work to make sure they still do.  That combined with sending the
        files to beta testers, getting feedback, making fixes, and re-issuing
        the changes adds up to a lot of work.  I don't expect I'll be doing
        it terribly often.

        Bottom line - If I say "next week", don't believe me.  I'm probably
        wrong.



11) Converting Data Files from Versions Prior to 2.10

Unfortunately, version 2.10 changed the format of the data files.  These
changes were mostly to avoid confusion - especially in the case of layered
textures.  There were also some changes that were made to allow more flexible
library objects.  This section details the changes in the data file format and
why it was necessary to make those changes.  I'm sorry that you have to go
back through all your old data files and edit them all, but I think you'll
agree (I hope you'll agree :-) that the changes are for the better.

   1) The following keywords are no longer accepted outside of a TEXTURE block:
        AMBIENT, DIFFUSE, BRILLIANCE, REFLECTION, REFRACTION, IOR, PHONG,
        PHONG_SIZE, SPECULAR, ROUGHNESS

      Reason: For layered textures, it's not clear which texture these keywords
              apply to if they're not in a TEXTURE block.  I was really getting
              messed up in the implementation trying to locate the proper
              references for these keywords.  It's much cleaner to only allow
              them inside a TEXTURE block.

   2) A new texture called COLOUR (or COLOR) has been added.  This texture
      simply specifies a simple colour to use.

      Reason:  It's useful to be able to declare a TEXTURE with the colour
               embedded inside it.  Besides, I had to provide some way of
               specifying a simple colour after I made the following change:

   3) The keyword "COLOUR" or "COLOR" when used outside of a TEXTURE block
      is only used to provide a colour for low-quality renderings (ones where
      the -q value is 5 or below.

      Reason:  This is the same reason as for change 1.  For layered textures,
               it wasn't clear what the object or shape colour meant when the
               texture itself contained colour information.  Rather than have
               a convoluted searching scheme (which I tried at first, then
               abandoned due to difficulties in explaining it), I decided to
               keep it simple.  If you want a simple colour, put it in a
               TEXTURE block.

   4) When an object or shape is transformed, the textures attached to it are
      transformed as well.

      Reason:  Previously, you couldn't DECLARE objects with textures, then
               create identical copies of them in different places.  This was
               especially annoying when you create an object that has an image
               mapped onto it.  As soon as you moved the object, the image was
               left behind.  Unfortunately, this means that the texture trans-
               formations inside TEXTURE blocks in old data files would double
               transform the texture, and must be removed.

   5) The interaction between ALPHA colours and REFRACTION has changed.
      Previously, there was no interaction at all.  If you had a surface that
      contained an ALPHA colour, you could see through the surface.  If the
      surface had refraction, you could also see through.  With the new
      release, ALPHA and REFRACTION in combination tell you how much light
      is passed through from the inside of the object.

      To make things a bit easier, if an object has an ALPHA component but the
      REFRACTION is 0.0 (or unspecified), the renderer will simply transmit the
      ray through the object without any refractive bending.

      Reason:  It seemed to make sense.  The code for ALPHA was doing the same
               work as the code for REFRACTION except for actually bending
               the ray.  Now, you can create objects that are partially opaque
               and partially transparent. Where they are transparent, the light
               passing through the object is bent by the index of refraction.
               Makes sense, no?

   6) When you use an IMAGEMAP with the ONCE option, the colour outside the
      mapped image is transparent (RED 1.0 GREEN 1.0 BLUE 1.0 ALPHA 1.0).

      Reason:  This allows you to see the underlying textures.


   7) I've remove "BasicShapes.data" and replaced it with "shapes.dat",
      "colors.dat", and "textures.dat".


      Reason:  The old name didn't apply any more (since it contained more than
               just shapes).  Also, I was tired of the IBM people using the
               name "BASICSHA.DAT" :-).

   8) The textures in textures.dat (formerly BasicShapes.data) were previously
      scaled to <10.0 10.0 10.0>.  This scaling has been removed.

      Reason:  The factor of 10.0 seemed to be a totally arbitrary scale factor
               that someone used.  I'd like to keep the scaling factors up to
               the users.

12) Handy Hints

     -    To see a quick version of your picture, use -w64 -h80 as command
          line parameters on the Amiga.  For the IBM, try -w80 -h50.  This
          displays the picture in a small rectangle so that you can see how
          it will look.

     -    Try using the sample default files for different usages - QUICK.DEF
          shows a fast postage-stamp rendering (80x50, as above) to the
          screen only, LOCKED.DEF will display the picture with anti-aliasing
          on (takes forever) with no abort (do this before you go to bed...).
          The normal default options file TRACE.DEF is read and you can
          supersede this with another .DEF file by specifying it on the
          command line, for example:

          trace -iworld.dat -oworld.out quick.def

     -    When translating light sources, translate the OBJECT, not the
          QUADRIC surface.  The light source uses the center of the object as
          the origin of the light.

     -    When animating objects with solid textures, the textures must move
          with the object, i.e. apply the same ROTATE or TRANSLATE functions
          to the texture as to the object itself.  This is now done automatic-
          ally in version 2.10 if the transformations are placed _after_ the
          TEXTURE block.

     -    You can declare constants for most of the data types in the program
          including floats and vectors.  By combining this with INCLUDE files,
          you can easily separate the parameters for an animation into a
          separate file.

     -    The amount of ambient light plus diffuse light should be less than
          or equal to 1.0.  The program accepts any values, but may produce
          strange results.

     -    When using ripples, don't make the ripples too deep or you may get
          strange results (the dreaded "digital zits"!).

     -    Wood textures usually look better when they are scaled to different
          values in x, y, and z, and then rotated to a different angle.

     -    You can sort of dither a colour by placing a floating point number
          into the texture record:

          TEXTURE
               0.05
          END_TEXTURE

          This adds a small random value to the intensity of the diffuse
          light on the object.  Don't make the number too big or you may get
          strange results.  You generally won't want to use this if you are
          rendering frames for animations, as this "dithering" is random.

          Better results can be obtained, however, by doing proper dithering
          in a post-processor.

     -    You can compensate for non-square aspect ratios on the monitors by
          making the RIGHT vector in the VIEWPOINT longer or shorter.  A good
          value for the Amiga is about 1.333.  This seems ok for IBM's too at
          320x200 resolution.  If your spheres and circles aren't round, try
          varying it.

     -    If you are importing images from other systems, you may find that
          the shapes are backwards (left-to-right inverted) and no rotation
          can make them right.  All you have to do is negate the terms in the
          RIGHT vector of the viewpoint to flip the camera left-to-right (use
          the "right-hand" coordinate system).

     -    By making the DIRECTION vector in the VIEWPOINT longer, you can
          achieve the effect of a tele-photo lens.

     -    When rendering on the Amiga, use a resolution of 320 by 400 to
          create a full sized HAM picture.



13) Compiling the Code

If you want to compile the source code on a supported platform, do the
following:

    1) Copy or rename the file called <system>conf.h to config.h
         eg.  rename amigaconf.h config.h

    2) Copy or rename the appropriate make file to "makefile"
         eg.  rename amigamake makefile

    3) Edit the makefile to make sure all compiler options are set up
         properly for your system.

    4) Type "make"




14) Porting to Different Platforms

I've taken great pains to make DKBTrace as portable as possible.  So far, it's
working out fairly well.  For the most part, the core of the raytracer will
compile with any decent C compiler.

If you want to port the raytracer to another system, please try to modify the
core of the raytracer as little as possible.  Each system will have its own
makefile, config file, and C file.  The config file is included by all of the
raytrace modules and can be used to perform special #defines for that system.
The C file should contain all system-specific code.  It must implement the
following functions:

   void display_init ();    /* Open the graphics device and initialize it */
   void display_close();    /* Close the graphics device                  */
   void display_finished(); /* Perform any operations required after      */
                            /* finishing the rendering but before quitting*/
   void display_plot (x, y, Red, Green, Blue)
                            /* Display the specified colour at point x,y  */


In your config file, you may customize the following things:

   #define FILE_NAME_LENGTH    (default 150)
   #define DBL_FORMAT_STRING   (the string to use to read a double)
   #define DEFAULT_OUTPUT_FORMAT ('d', 'r' or 't' - default output file format)
   #define TEST_ABORT          (the operation to perform while tracing to see
                                if we should abort the trace.)
   #define RED_RAW_FILE_EXTENSION
   #define GREEN_RAW_FILE_EXTENSION
   #define BLUE_RAW_FILE_EXTENSION
                               (the default extensions for the +fr mode)

   #define STARTUP_DKB_TRACE   (the code to call immediately after starting
                                the main program. - useful if you don't have
                                a command-line interface)

   #define PARAMS(x)           ("(x)" if you have prototypes, "()" otherwise)



15) References

I'm always asked about good books on raytracing and graphics in general.
This section address that issue by listing several good books or periodicals
that you should be able to locate in your local computer book store or your
local university library.

    "An Introduction to Raytracing"
    Andrew S. Glassner (editor)
    Academic Press
    1989

    "Image Synthesis:  Theory and Practice"
    Nadia Magnenat-Thalman and Daniel Thalmann
    Springer-Verlag
    1987

    "The RenderMan Companion"
    Steve Upstill
    Addison Wesley
    1989

    "Graphics Gems"
    Andrew S. Glassner (editor)
    Academic Press
    1990

    "Fundamentals of Interactive Computer Graphics"
    J. D. Foley and A. Van Dam
    Addison-Wesley
    1983

    "Computer Graphics:  Principles and Practice (2nd Ed.)"
    J. D. Foley, A. van Dam, J. F. Hughes
    Addison-Wesley,
    1990

    "Computers, Pattern, Chaos, and Beauty"
    Clifford Pickover
    St. Martin's Press

    "SIGGRAPH Conference Proceedings"
    Association for Computing Machinery
    Special Interest Group on Computer Graphics

    "IEEE Computer Graphics and Applications"
    The Computer Society
    10662, Los Vaqueros Circle
    Los Alimitos, CA 90720

    "The CRC Handbook of Mathematical Curves and Surfaces"
    David von Seggern
    CRC Press
    1990

    "The CRC Handbook of Standard Mathematical Tables"
    CRC Press
    The Beginning of Time


16) Concluding Remarks

It seems that in any project like this, as soon as you fix some bugs, some
more appear.  I expect that the new features I provided in this release will
cause some problems somewhere.  There's only so much you can do to get all the
bugs out.  For the next little while, I intend to keep the program stable
feature-wise and just tackle major bugs.  Hopefully things will stablize this
way (and I can take a much needed breather).

Thanks go out to Alexander Enzmann for generously providing the code for the
QUARTIC surface algorithms, and for his assistance in implementing it and
for helping squash a couple of other bugs.

I would like to thank all the people who used versions 2.01 and 2.04 and
provided useful comments and helpful suggestions.  The program has been much
improved with your help.

I would also like to thank my beta testers for all the help, bug reports,
suggestions, comments, and time spent.  I'd like to say a special thank-you to
Aaron Collins who has fielded many of the questions on the raytracer and has
been invaluable in debugging, testing, and generally improving the program.
Thanks guys.

David Buck