Ray Tracing News

"Light Makes Right"

May 12, 1989

Volume 2, Number 3

Compiled by Eric Haines [email protected] . Opinions expressed are mine.

All contents are copyright (c) 1989, all rights reserved by the individual authors

Archive locations: anonymous FTP at ftp://ftp-graphics.stanford.edu/pub/Graphics/RTNews/,
wuarchive.wustl.edu:/graphics/graphics/RTNews, and many others.

You may also want to check out the Ray Tracing News issue guide and the ray tracing FAQ.


Contents:


Introduction

Well, we're now at the point where there are six ray tracers for the Amiga. Interestingly, none of them have implicit efficiency schemes (i.e. where the user does not have to intervene and create the efficiency structure himself). Admittedly, efficiency schemes are more code, but I've found that I was getting a factor of three speed up for a simple scene (a ten ball sphereflake) by using an efficiency scheme vs. not using one. When your computer is the speed of an Amiga, efficiency schemes become vital.

Next time I'll include "Tracing Tricks", an article I "edited" for the latest (and last) "Introduction to Ray Tracing" course notes. The article is a "best of the RT News" compendium of efficiency tricks. By the way, the course notes should be quite a bargain: they'll consist of the book of our notes by Academic Press, plus some new tidbits and reprints of "classic" articles.

I would like to put the "Ray Tracing News" back issues somewhere that people can FTP them. Personally I don't have a computer that has an FTP site, so if there are any volunteers that would like to store the back issues, please contact me. The entire archive is about 448K at this point (not including this issue), broken into 5 parts. Can you volunteer?

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New People

# Carl Bass - hybrid shading models and quick(er) hidden surface methods
# Ithaca Software
# 902 West Seneca Street
# Ithaca, NY 14850
# 607-273-3690
alias carl_bass [email protected]

Carl is the co-founder of Ithaca Software Inc (once upon a time called "Flying Moose Inc"), which sells the HOOPS package for all kinds of computers. This is an object-oriented system which I don't know much about beyond that their debugger is called WHOOPS.

________

#
# Paul Wanuga
# Cornell Program of Computer Graphics
# 120 Rand Hall
# Ithaca, NY 14853
# (607)-255-4880
alias paul_wanuga [email protected]
Erich:

Could you please include me in your list of wiz-bango ray tracers? It appears Don has me slated for research in ray-tracing complex, realistic, non-procedural environments.

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QRT Ray Tracer (and five other Amiga Ray Tracers), by Steve Koren

This package appeared on comp.graphics a few months back. I believe the latest version of the package is available from Mark VandeWettering's FTP site (see next article). Write to Steve for more info:

        hpfela![email protected]

The software is written in C and worked just fine on my system. Below is an excerpt of the UserMan.doc file of the QRT system (which Steve extensively documented).

QRT is a ray tracing image rendering system that runs under a variety of operating systems. It has a free format input language with extensive error detection and reporting capabilities.

QRT was developed on the Amiga personal computer, so it will be compared to other Amiga ray tracers. There are, to my knowledge, five other Amiga ray tracers, each with its own strengths and weaknesses. I will describe each system briefly, and compare it to QRT. All the Amiga ray tracers can operate in HAM (4096 color) mode.

  RT: RT was the first ray  tracer  written for the Amiga, by
      Eric    Graham.  It will model  a universe made of only
      spheres, a   sky, and a checkered  or solid ground.  It
      is  relatively  fast,  but  not  generally  useful  for
      realistic modeling   because  of the sphere limitation.
      The input language  is  cryptic,  although  some  error
      checking is done.  The  system  will  only generate low
      resolution images.

 SILVER: I have never seen SILVER, so I cannot say much about
      this system.

 SCULPT-4D: This package  incorporates  an interactive editor
      for  creating  objects,   and  is  capable  of  quickly
      generating a preliminary  image  of  the scene by using
      hidden surface techniques.  However, every primitive is
      made of polygons, and some  primitives  such as spheres
      require hundreds of  polygons  for a smooth texture, so
      the ray tracing is very slow.   Also, the package takes
      a large amount of memory to run, and is prone to system
      crashes.  Its chief  feature  is  the ability to create
      arbitrary shaped objects  using  a series of triangles.
      Mirrored, dull, or shiny objects are supported.

 CLIGHT: This ray tracer also has  an interactive editor, but
      produces very poor quality  images.   It is not capable
      of any patterning or reflection characteristics.

 DBW: This is possibly the most  complete  ray tracer for the
      Amiga.  It will support objects  with arbitrary degrees
      of reflection and gloss,  depth  of field effects, some
      texturing,   wavy   surfaces,   fractals,   transparent
      surfaces, diffuse  propagation  of light from object to
      object,  and  5  primitive   types  (sphere,  triangle,
      parallelogram, fractal, and ring).  The input language,
      however,   is    so    cryptic    as   to   be   nearly
      incomprehensible, and  if  there  is  any  error in the
      input file,  it  will  crash  the  system.   It is also
      painfully slow;  some  images  take  16  to 24 hours to
      complete.

QRT is meant to be a compromise between the fast, simple ray tracers and the slow powerful systems. It compares favorably in speed to RT, and in power to Sculpt-3d or DBW. It has a very friendly input language with extensive error checking. Here are some features of QRT:

   o  Multiple primitive types, including user defined
      quadratic surfaces

   o  Arbitrary levels of diffuse reflection, spectral
      reflection, transmission, ambient lighting, and gloss

   o  User defined pattern information for objects

   o  Bounding boxes for groups of objects

   o  Shadows

   o  Multiple light sources with different characteristics

   o  Arbitrary Phong spectral reflection coefficients

   o  Color dithering to increase the apparent number of
      colors

   o  Easy to use, free format input language with error
      checking.  Parameters are by keyword and may appear in
      any order.

   o  Supports medium resolution (128k dots/screen)

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New Version of MTV Ray Tracer, by Mark VandeWettering

Mark VandeWettering's nice little ray tracer (polygons, spheres, cones and cylinders, Kay/Kajiya efficiency scheme, yacc/lex parser for NFF format, otherwise written in C) was released on USENET in three parts on March 27. Others have interesting features, but the selection of primitives and the speed of the code of the MTV ray tracer is a big plus. It's currently my favorite public domain ray tracer (the amazing BRL package I consider private).

The package is available at the usual comp.sources.unix archive sites or from Mark via anonymous ftp at drizzle.cs.uoregon.edu. Mark's address is:

    [email protected]

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Re: Ray Traced Bounding Spheres, by Earl Culham ([email protected])

Organization: University of Alberta VM/CMS

In article ([email protected]), [email protected] (Jack Ritter) writes:

>Given a cluster of points in 3 space, is there
>a good method for finding the minimum radius
>sphere which encloses all the points? If not
>minimum, at least "small"? Certainly it should
>be tighter than the sphere which encloses the
>minimum bounding box.
>
>I have a feeling the solution is iterative. If
>so, I could provide a good initial guess for the
>center & radius.

The solution is not iterative. A simple solution is available in a two step process, and is characterized by whether three, or only two of the points are on the surface of the optimal sphere.

Given the points, A, B, and C.
Searching for the center of the optimal sphere, P, with the smallest radius, R.

Checking the midpoints.

set P = point halfway between A and B
set R = 1/2 of length from A to B
If length from C to P is less than or equal to R ---> done
Repeat with line A-C, and B-C if needed.

Extending the midpoints at right angles.

build the line which intersects A-B at a right angle through the midpoint of A-B, call the line D. build the line which intersects A-C at a right angle through the midpoint of A-C, call it E. P is the point where D and E intersect. (Solve the simultaneous equations; R is the length A-P)

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Noise and Turbulence Function Code, Pascal and C, by Jon Buller, William Dirks

Re: Pixar's noise function, by Jon Buller ([email protected]) Organization: Colorado State University, Ft. Collins CO 80523

In article ([email protected]) [email protected] (Tony Apodaca) writes:
>In article ([email protected]) [email protected] (Stephen B Coy) writes:
>> ...My question: Does anyone out there know what this
>>noise function really is?
>
> Three-dimensional simulated natural textures using pseudorandom
>functions were simultaneously and independently developed by Darwyn
>Peachey and Ken Perlin in 1984-5. Both have papers in the 1985
>Siggraph Proceedings describing their systems. Perlin, in particular,
>describes in detail how noise() is implemented and can be used creatively

   [A description of the properties of the noise function goes here...]

> If you have ever been interested in realistic computer graphics, do
>whatever it takes to get a look at Perlin's paper. In 1985, his pictures
>were absolutely astounding. In 1989, they are STILL astounding.

No kidding, some of those pictures are INCREDIBLE.

Here is my code for a look-alike to the Pixar Noise function, and while I can't say anything about exactly what Pixar's looks like, I think this is probably close. After reading the 1985 SIGGRAPH papers on 3d texturing, (and seeing my prof's code to do a similar thing) I wrote this. It uses a quadratic B-Spline instead of the cubic Hermite interpolant implied in the paper. Also note that DNoise is just the x, y, and z derivatives of Noise (which are also B-Splines). The hashing functions are from Knuth's Art of Computer Programming (I don't remember which volume though).

I know the code is Pascal, and all of you will hate it, but I believe I write better Pascal than C... One final note, this was Lightspeed Pascal 2.0 for the Macintosh, but things have been reformatted slightly to get it on the net. I hope this is what you all wanted.

________

More:

One other thing you might notice, Noise is C1 continuous, DNoise is only C0. This means that DNoise will have creases in it (along the planes of the random grid. To see this, crank out a square: 0 < X < 5, 0 < Y < 5, Z=0. You will see smooth regions within each unit square, and creases between squares. To avoid this, use a cubic B-Spline, or cubic Hermite (as hinted to in the SIGGRAPH proceedings) the problem there, is that you either need more data points (64 instead of 27) for the B-Spline, or derivative info at each point of the grid (a normal plane, 4 floats instead of 1). This would take too muh time for me to code up to be worth it, and would probably run too much slower (10min for a 200x200 pixel picture now, ug.) If somebody wants to give me a cray-3 to play with, I'll write more accurate (and slower) code, until then... 8-)

Jon [email protected] ...!ncar!ccncsu!handel!bullerj
(These are my ideas (and code), nobody else SHOULD want these bugs)
I'm just trying to graduate. Apple, Pixar, HP, etc. take note, I would like your job offers, I have tired of the university life.

[NOTE: I have attached the Pascal code for the Turbulence functions. The Noise functions are in the next message in "C". Sorry about the mixed languages, but I haven't nicely translated these. -- EAH]

(* ---------- cut here ---------- cut here ---------- cut here ---------- *)

const
   MaxPts = 512;  { Must be 2^n}
   MPM1 = MaxPts - 1;
type
   PtsTyp = array[0..MaxPts] of Extended;
var
   Points: PtsTyp;

function Turb (Size: Integer;
               ScaleFactor: Extended;
               Loc: Vect;
               Pts: PtsTyp): Extended;
   var
      Scale, Result: Extended;
      Cur: Integer;
begin
   Result := Noise(Loc, Pts);
   Scale := 1.0;

   Cur := 1;
   while Cur < Size do begin
      Cur := BSL(Cur, 1);          {Cur := Cur * 2}
      Scale := Scale * ScaleFactor;
      Loc := Scale_Vect(2.0, Loc);
      Result := Result + Noise(Loc, Pts) * Scale;
   end;
   Turb := Result;
end;

function DTurb (Size: Integer;
                ScaleFactor: Extended;
                Loc: Vect;
                Pts: PtsTyp): Vect;
   var
      Result: Vect;
      Scale: Extended;
      Cur: Integer;
begin
   Result := DNoise(Loc, Pts);
   Scale := 1.0;

   Cur := 1;
   while Cur < Size do begin
      Cur := BSL(Cur, 1);
      Scale := Scale * ScaleFactor;
      Loc := Scale_Vect(2.0, Loc);
      Result := Add_Vect(Result, Scale_Vect(Scale, DNoise(Loc, Pts)));
   end;
   DTurb := Result;
end;

______________________________________

C Versions of Noise and DNoise Routines, by William Dirks ([email protected])

Organization: Ohio State University Computer and Information Science

It was suggested to me that some of you would be interested in my translated-into-C-and-corrected versions of noise() and Dnoise().

So, here they are.

Note that this is only noise and Dnoise. The turbulence routines are not included 'cause I haven't translated them yet.

Oh yeah, initnoise() fills the pts[] array with random numbers between 0 and 1. Don't forget to initialize, or noise will always return 0. (That's been experimentally verified! :-))

--Bill--

[Note that you should look over the rand() function if you use this stuff. Some rand()'s need initialization (srand()), and some give numbers from 0 to 32767, and so should use this as a divisor. -- EAH]

---------cut-here------------------------------------cut-here--------
/*
**      Noise and Dnoise routines
*
*       Many thanks to Jon Buller of Colorado State University for these
*       routines.
*/

typedef struct vector {
   double x, y, z;
} Vector;

#define NUMPTS  512
#define P1 173
#define P2 263
#define P3 337
#define phi 0.6180339
static double pts[NUMPTS]; void initnoise() { int i; for (i = 0; i < NUMPTS; ++i) pts[i] = rand() / 2.147483e9; } double noise(p) Vector *p; { int xi, yi, zi; int xa, xb, xc, ya, yb, yc, za, zb, zc; double xf, yf, zf; double x2, x1, x0, y2, y1, y0, z2, z1, z0; double p000, p100, p200, p010, p110, p210, p020, p120, p220; double p001, p101, p201, p011, p111, p211, p021, p121, p221; double p002, p102, p202, p012, p112, p212, p022, p122, p222; xi = floor(p->x); xa = floor(P1 * (xi * phi - floor(xi * phi))); xb = floor(P1 * ((xi + 1) * phi - floor((xi + 1) * phi))); xc = floor(P1 * ((xi + 2) * phi - floor((xi + 2) * phi))); yi = floor(p->y); ya = floor(P2 * (yi * phi - floor(yi * phi))); yb = floor(P2 * ((yi + 1) * phi - floor((yi + 1) * phi))); yc = floor(P2 * ((yi + 2) * phi - floor((yi + 2) * phi))); zi = floor(p->z); za = floor(P3 * (zi * phi - floor(zi * phi))); zb = floor(P3 * ((zi + 1) * phi - floor((zi + 1) * phi))); zc = floor(P3 * ((zi + 2) * phi - floor((zi + 2) * phi))); p000 = pts[xa + ya + za & NUMPTS - 1]; p100 = pts[xb + ya + za & NUMPTS - 1]; p200 = pts[xc + ya + za & NUMPTS - 1]; p010 = pts[xa + yb + za & NUMPTS - 1]; p110 = pts[xb + yb + za & NUMPTS - 1]; p210 = pts[xc + yb + za & NUMPTS - 1]; p020 = pts[xa + yc + za & NUMPTS - 1]; p120 = pts[xb + yc + za & NUMPTS - 1]; p220 = pts[xc + yc + za & NUMPTS - 1]; p001 = pts[xa + ya + zb & NUMPTS - 1]; p101 = pts[xb + ya + zb & NUMPTS - 1]; p201 = pts[xc + ya + zb & NUMPTS - 1]; p011 = pts[xa + yb + zb & NUMPTS - 1]; p111 = pts[xb + yb + zb & NUMPTS - 1]; p211 = pts[xc + yb + zb & NUMPTS - 1]; p021 = pts[xa + yc + zb & NUMPTS - 1]; p121 = pts[xb + yc + zb & NUMPTS - 1]; p221 = pts[xc + yc + zb & NUMPTS - 1]; p002 = pts[xa + ya + zc & NUMPTS - 1]; p102 = pts[xb + ya + zc & NUMPTS - 1]; p202 = pts[xc + ya + zc & NUMPTS - 1]; p012 = pts[xa + yb + zc & NUMPTS - 1]; p112 = pts[xb + yb + zc & NUMPTS - 1]; p212 = pts[xc + yb + zc & NUMPTS - 1]; p022 = pts[xa + yc + zc & NUMPTS - 1]; p122 = pts[xb + yc + zc & NUMPTS - 1]; p222 = pts[xc + yc + zc & NUMPTS - 1]; xf = p->x - xi; x1 = xf * xf; x2 = 0.5 * x1; x1 = 0.5 + xf - x1; x0 = 0.5 - xf + x2; yf = p->y - yi; y1 = yf * yf; y2 = 0.5 * y1; y1 = 0.5 + yf - y1; y0 = 0.5 - yf + y2; zf = p->z - zi; z1 = zf * zf; z2 = 0.5 * z1; z1 = 0.5 + zf - z1; z0 = 0.5 - zf + z2; return z0 * (y0 * (x0 * p000 + x1 * p100 + x2 * p200) + y1 * (x0 * p010 + x1 * p110 + x2 * p210) + y2 * (x0 * p020 + x1 * p120 + x2 * p220)) + z1 * (y0 * (x0 * p001 + x1 * p101 + x2 * p201) + y1 * (x0 * p011 + x1 * p111 + x2 * p211) + y2 * (x0 * p021 + x1 * p121 + x2 * p221)) + z2 * (y0 * (x0 * p002 + x1 * p102 + x2 * p202) + y1 * (x0 * p012 + x1 * p112 + x2 * p212) + y2 * (x0 * p022 + x1 * p122 + x2 * p222)); } Vector Dnoise(p) Vector *p; { Vector v; int xi, yi, zi; int xa, xb, xc, ya, yb, yc, za, zb, zc; double xf, yf, zf; double x2, x1, x0, y2, y1, y0, z2, z1, z0; double xd2, xd1, xd0, yd2, yd1, yd0, zd2, zd1, zd0; double p000, p100, p200, p010, p110, p210, p020, p120, p220; double p001, p101, p201, p011, p111, p211, p021, p121, p221; double p002, p102, p202, p012, p112, p212, p022, p122, p222; xi = floor(p->x); xa = floor(P1 * (xi * phi - floor(xi * phi))); xb = floor(P1 * ((xi + 1) * phi - floor((xi + 1) * phi))); xc = floor(P1 * ((xi + 2) * phi - floor((xi + 2) * phi))); yi = floor(p->y); ya = floor(P2 * (yi * phi - floor(yi * phi))); yb = floor(P2 * ((yi + 1) * phi - floor((yi + 1) * phi))); yc = floor(P2 * ((yi + 2) * phi - floor((yi + 2) * phi))); zi = floor(p->z); za = floor(P3 * (zi * phi - floor(zi * phi))); zb = floor(P3 * ((zi + 1) * phi - floor((zi + 1) * phi))); zc = floor(P3 * ((zi + 2) * phi - floor((zi + 2) * phi))); p000 = pts[xa + ya + za & NUMPTS - 1]; p100 = pts[xb + ya + za & NUMPTS - 1]; p200 = pts[xc + ya + za & NUMPTS - 1]; p010 = pts[xa + yb + za & NUMPTS - 1]; p110 = pts[xb + yb + za & NUMPTS - 1]; p210 = pts[xc + yb + za & NUMPTS - 1]; p020 = pts[xa + yc + za & NUMPTS - 1]; p120 = pts[xb + yc + za & NUMPTS - 1]; p220 = pts[xc + yc + za & NUMPTS - 1]; p001 = pts[xa + ya + zb & NUMPTS - 1]; p101 = pts[xb + ya + zb & NUMPTS - 1]; p201 = pts[xc + ya + zb & NUMPTS - 1]; p011 = pts[xa + yb + zb & NUMPTS - 1]; p111 = pts[xb + yb + zb & NUMPTS - 1]; p211 = pts[xc + yb + zb & NUMPTS - 1]; p021 = pts[xa + yc + zb & NUMPTS - 1]; p121 = pts[xb + yc + zb & NUMPTS - 1]; p221 = pts[xc + yc + zb & NUMPTS - 1]; p002 = pts[xa + ya + zc & NUMPTS - 1]; p102 = pts[xb + ya + zc & NUMPTS - 1]; p202 = pts[xc + ya + zc & NUMPTS - 1]; p012 = pts[xa + yb + zc & NUMPTS - 1]; p112 = pts[xb + yb + zc & NUMPTS - 1]; p212 = pts[xc + yb + zc & NUMPTS - 1]; p022 = pts[xa + yc + zc & NUMPTS - 1]; p122 = pts[xb + yc + zc & NUMPTS - 1]; p222 = pts[xc + yc + zc & NUMPTS - 1]; xf = p->x - xi; x1 = xf * xf; x2 = 0.5 * x1; x1 = 0.5 + xf - x1; x0 = 0.5 - xf + x2; xd2 = xf; xd1 = 1.0 - xf - xf; xd0 = xf - 1.0; yf = p->y - yi; y1 = yf * yf; y2 = 0.5 * y1; y1 = 0.5 + yf - y1; y0 = 0.5 - yf + y2; yd2 = yf; yd1 = 1.0 - yf - yf; yd0 = yf - 1.0; zf = p->z - zi; z1 = zf * zf; z2 = 0.5 * z1; z1 = 0.5 + zf - z1; z0 = 0.5 - zf + z2; zd2 = zf; zd1 = 1.0 - zf - zf; zd0 = zf - 1.0; v.x = z0 * (y0 * (xd0 * p000 + xd1 * p100 + xd2 * p200) + y1 * (xd0 * p010 + xd1 * p110 + xd2 * p210) + y2 * (xd0 * p020 + xd1 * p120 + xd2 * p220)) + z1 * (y0 * (xd0 * p001 + xd1 * p101 + xd2 * p201) + y1 * (xd0 * p011 + xd1 * p111 + xd2 * p211) + y2 * (xd0 * p021 + xd1 * p121 + xd2 * p221)) + z2 * (y0 * (xd0 * p002 + xd1 * p102 + xd2 * p202) + y1 * (xd0 * p012 + xd1 * p112 + xd2 * p212) + y2 * (xd0 * p022 + xd1 * p122 + xd2 * p222)); v.y = z0 * (yd0 * (x0 * p000 + x1 * p100 + x2 * p200) + yd1 * (x0 * p010 + x1 * p110 + x2 * p210) + yd2 * (x0 * p020 + x1 * p120 + x2 * p220)) + z1 * (yd0 * (x0 * p001 + x1 * p101 + x2 * p201) + yd1 * (x0 * p011 + x1 * p111 + x2 * p211) + yd2 * (x0 * p021 + x1 * p121 + x2 * p221)) + z2 * (yd0 * (x0 * p002 + x1 * p102 + x2 * p202) + yd1 * (x0 * p012 + x1 * p112 + x2 * p212) + yd2 * (x0 * p022 + x1 * p122 + x2 * p222)); v.z = zd0 * (y0 * (x0 * p000 + x1 * p100 + x2 * p200) + y1 * (x0 * p010 + x1 * p110 + x2 * p210) + y2 * (x0 * p020 + x1 * p120 + x2 * p220)) + zd1 * (y0 * (x0 * p001 + x1 * p101 + x2 * p201) + y1 * (x0 * p011 + x1 * p111 + x2 * p211) + y2 * (x0 * p021 + x1 * p121 + x2 * p221)) + zd2 * (y0 * (x0 * p002 + x1 * p102 + x2 * p202) + y1 * (x0 * p012 + x1 * p112 + x2 * p212) + y2 * (x0 * p022 + x1 * p122 + x2 * p222)); return v; }

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Eric Haines / [email protected]