Ray Tracing News

"Light Makes Right"

September 5, 1988

Volume 1, Number 8

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

All contents are copyright (c) 1988, 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.



Well, I'm back from my honeymoon, I've just moved into a new house, and I have returned to work and am confronted with a heavy duty schedule. However, the workstation's on the fritz for a few hours so here's my chance to compile an issue of the RT News.

Other major changes around here are that Michael Cohen (of radiosity fame, and a subscriber) has begun his cross-country drive from Ithaca to Salt Lake City. He'll be continuing his education at the University of Utah's computer graphics facility. Roy Hall is taking over Michael's place at the Cornell Program of Computer Graphics, and should be added to this mailing list soon. Andrew Glassner is now with Xerox PARC, and his new address should be available by next issue, too.

I plan to get another issue out within a week, as there is also an interesting research idea that I need to talk about with a few people before presenting it here. Stay tuned...and please feel free to submit to the next issue.

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Capsule Biographies

What follows are short self-descriptions by various new people at the roundtable at SIGGRAPH. These are simply in the order I received them. The latest address list (email and physical) is attached at the end of this issue.

By the way, if you never submitted an autobiographical sketch, (or if you are doing something that's different from your last sketch) please feel free to send one on to me for the next issue.

# Russ Tuck - SIMD parallel algorithms and architectures for ray tracing
# Computer Science Dept, Univ. of North Carolina

My dissertation research is on parallel methods of programming SIMD parallel computers. I have developed a measure of program portability, and a system which lets the programmer specify in advance how portable a program must be. The compiler can then provide (and enforce) this amount of portability. I call this an "optimally portable" programming system. I'll be presenting my work at "Frontiers 88: The 2nd Symp. on the Frontiers of Massively Parallel Computation" in October. Thinking about ways to do ray tracing (and radiosity) on massively parallel SIMD machines is a fun sidelight. (Some of my ideas were in the June '88 hardcopy Ray Tracing News.)

# Greg Ward - accuracy and realism, daylight, efficient light sources.
# Lawrence Berkeley Laboratory

The purpose of my work is the development of more accurate calculations for lighting design and engineering. Electric lighting contributes directly or indirectly to about 20% of the nation's energy consumption. Although significant progress has been made in the area of energy-efficient light sources, wasteful installations frequently result from poor building design rather than low fixture efficiency. It is hoped that with better computational tools, architects and engineers will produce more energy-efficient designs. I am currently working on a validated reflection model and method for measuring surface properties using a digitizing camera. By streamlining the measurement process, it should be possible to obtain accurate simulations of designs using a realistic variety of construction materials. I am also comparing the accuracy and applicability of different classes of lighting calculation, and exploring the use of animation in design visualization.

# Pete Litwinowicz -- realistic image sythesis, etc.
# Apple Computer, INC

Working on 3D animation, rendering and modelling at Apple.

# Tom Malley - parallelism, complex scenes, space subdiv., shading methods
# Evans & Sutherland Computer Corporation

My interests are primarily in how to make ray traced images that are significantly more realistic than the computer generated images we often see now. The complexity of the models must increase for realism. If we want to ray trace large databases on many processors, we must determine efficient ways to make pieces of the data set available dynamically to processors as they perform intersection searches. Additionally, I'm interested in analysis of reflection models to see where the typical simplifying assumptions steer us wrong, and what the alternatives may be. I'd also like to see more closed loop comparisons of computer generated images with real scenes.

# Chuck Grant - tracing fewer rays, coherency, antialiasing
# Lawrence Livermore National Laboratory

I am interested in algorithms and data structures for most areas of image synthesis: visible surface algorithms, volumetric visualization, antialiasing, texturing, shading, etc., etc... Ray tracing is a big part of my interests but not all. I am currently working on a comparison of all existing visible surface algorithms, and have invented several new ones as a result. I am not interested in "Scientific Data Visualization" but the demands of my job make me spend a lot of time doing just that. I am finishing my PhD. in computer graphics at the University of California at Davis.

# Steve Stepoway -- efficient intersection calc., parallelism

My interests in ray tracing these days are centering around finding more efficient ray-object intersection calculations, as well as issues of parallelism in rendering. I am working with Sam Uselton (U. Tulsa) and Mark Lee (AMOCO) on developing some new space sub-division techniques (next year's SIGGRAPH paper).

# Daniel Bass - Realism, diffraction & wavelength effects
# Apollo Computer Inc.

[no autobiographical note]

# Ken Joy - intersection tests, efficiency, coherency
# Computer Graphics Research Lab, Computer Science Division,
# University of California, Davis

[no autobiographical note]

# Fred Fisher - realism, radiosity enhancements, ray tracing manufacturing
# databases

Hello. I'm now working at DEC doing electronics design for a geometry pipeline. My interest in ray tracing has involved rendering polygonal databases (presumably ones similar to those used in a quick-Gouraud-render CAD environment ). I've been writing a lot of software on my own (ray-tracing and otherwise) to understand the image synthesis process better, with the intent of designing hardware to help the rendering phase.

# Pierre Poulin - illumination models, natural phenomenon
# University of Toronto
# Department of Computer Science

I am a graduate student working right now on a model for anisotropic reflection that would save the world and computing time. This should be my introduction in the fascinating science of the simulation of natural phenomenon (or how to deceive the eye with less than 1 million polygons...).

# Andrew C. Woo - intersection culling algorithms and complexity
# University of Toronto
# Department of Computer Science

I am currently a first year (fast approaching second year) master's student at the University of Toronto. My current thesis work is on a new approach to shadow acceleration (beyond trans-warp drive, of course) and comparing it to existing shadow accelerators (eg. the impulse-power "light buffer" --> just kidding, Eric).

# Chuan Chee - natural phenomena, ray tracing, animation
# University of Toronto
# Department of Computer Science

I am finishing my first year as a master's student at the University of Toronto. I currently do not have a thesis topic.

# Robert E. Webber, Prof. - ray tracing large databases of volume density data.
# Computer Science Department
# Rutgers University, Busch Campus

Am currently tuning a ray tracer that handles hierarchically arranged voxel data. The basic unit of organization is a 16 by 16 by 16 ``voxel'' block where each voxel contains 32 bits of information. This information is interpreted as either a density description of the contents of that voxel or a pointer to another voxel block representing a recursive decomposition of the current block. 16 by 16 by 16 times 4 bytes means that my basic block is 16k, which is a size that fits our local disk system rather well from the point of view of i/o overhead. The program is organized to allow the database to be spread over a number of files (max 255) thus avoiding the 4 gigabyte unix file size problem (since the pointers only have to be able to address the start of each 16k block, 32 bit pointers can address a terabyte of data -- should we ever be lucky enough to have it) as well as the problem of finding alot of space inside of a single disk partition. Rutgers currently organizes its computing around a cluster of a hundred networked Sun workstations including 2's, 3's, and 4's.

The current status of the system is that 5 megabyte scenes (roughly 400 blocks) representing densities at the 256 by 256 by 256 level have been ray traced. Surface interpolation permitted images of demonstrating shadows, shading, and inter-reflection to be generated. Various techniques for determining the surface represented by a local cluster of voxel densities are being experimented with. Will soon be running the ray tracer in parallel (don't expect much bus contention as the system is currently extremely cpu bound). We are also installing some WORM drives locally and so soon expect to have yet another layer of memory hierarchy to fiddle with.

# Michael Natkin
# Brown University

No current paragrapho for now, as i'm rewriting our whole environment at the moment, no time for ray-tracing.


That's all for now, with about 6 people who are new but haven't contacted me yet.

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SIGGRAPH '88 RT Roundtable Summary, by Paul Strauss and Jeff Goldsmith

0.  Women don't talk about ray tracing.
1.  It would be nice to have something that does both ray tracing and
2.  It would be nice to have caustics.
3.  It would be nice to do analytical anti-aliasing.
4.  Motion blur is a Good Thing.
5.  Adaptive subsampling don't work good.
6.  There are many ways to minimize ray-object intersection tests.
7.  Hardware would be nice.  Maybe later.
8.  We should use ray tracing for real applications.

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Commercial Ray Tracing Software and SIGGRAPH, by Eric Haines and others

Last issue I listed all the commercially available ray tracers I knew as of SIGGRAPH. There were a few new entries I saw this year:

        - ElectroGIG, from England, shown at the Meiko booth, is the first
          commercial ray tracer based on using constructive solid geometry
          that I've seen.

        - SoftImage, (the people with the nice rocks image) from Montreal,
          had a nice looking Wavefront/Alias/etc-looking package with a ray
          tracer.  They claim it was the fastest ray tracer on the floor (it
          runs on a number of machines) and seemed to use octree subdivision.
          I never got to see the demo, but people tell me that it was fast,
          and that the programmer is a very careful and efficient coder.

        - Shima-Seiki, from Japan.  They claim to have a ray-tracer with
          hardware assistance (whatever that means), though they're not
          marketing it yet and couldn't tell us anything about it.  The
          realtime texturing system from Mars, with lots of cool buttons and
          knobs, was pretty impressive though.  System cost is $500K, $300K,
          or "we haven't decided", depending on when you talked with them.

        - Ray Tracing Corp is now Ray Tracing Research Corp, and they released
          a ray tracer for the Mac II for $895.

        - Apollo: not a product, but their ray tracer was fun to watch as a
          demo of both the speed of their new DN10000 (not sure about the
          number of zeros in that one) super-mini-super-workstation and of
          Apollo's networking abilities.  Darn fast.

        - Silicon Graphics: also not a product, they had a very nice demo
          (which, sadly, a number of their marketing people didn't know about)
          showing a scene from a god's-eye point of view, with rays shooting
          through the image plane and bouncing around.  The image would build
          up scan line by scan line on both the image plane in the scene and
          in a separate window.  You could also change the god's-eye view
          interactively as the scene was being ray-traced.  Nice.

Other things of interest: AT&T Pixel Machines' ray tracer is now even faster, purely due to software tuning. They plan to cut even more time by further changes. "Sphereflake", which ran at about 30 seconds last year, now runs at around 16 seconds. There is a public domain modeller which should be out in mid-October which will run on the Iris 3130 and on the Pixel Machine. It was developed by NASA (demoed at AT&T), and since they're governmental they can't make it a for-profit product. In a month and a half contact their distributor, "COSMIC" (which stands for something), at 404-542-3265. They won't really know much about it until then.

SGI showed radiosity images on the floor, though there is no announced product yet. They seemed to have developed their own adaptive refinement technique. HP showed ray tracing film loops and stills, and radiosity images and on-the-fly adaptive refinement (which will be a product sometime this winter). The new radiosity technique introduced by Cornell this year has the promise of being "radiosity for the rest of us".

Those were my major impressions (other than the usual "the art show was better this year", "course lunches were worse", etc) - anyone else care to add their two cents?

Jeff Goldsmith points out:

Cray Research has "Oasis," Gray Lorig's ray tracer, available, I think, for free. Of course, you have to buy a Cray at $20 million first....

I don't get it. Why doesn't every CG Software vendor supply a ray tracer. It's definitely the easiest renderer to write. Yes, they are slo-o-o-o-o-o-w, but they sound glitzy and (I bet) would stimulate sales, even if buyers never used them.

Gray Lorig responded to my query for info on Oasis:

The current status of the Oasis package, which is basically a raytracing animation package, is it's an unsupported product. What that really means is that we will give it to Cray customers for free, give them updates every once and a while, and provide support only when I feel like it.

John Peterson says:

I would add RenderMan to your list of commercial ray tracers - I think you can explicitly implement classical ray tracing by writing some code in their magic shading language.

Also, the ray tracer I wrote at Utah is (or at least may be) commercially available. It specializes in ray tracing NURB (B-spline) surfaces, and supports the usual suspects of features (refract/flection, shadows (with penumbra), texture mapping, anti-aliasing (with stochastic sampling) and motion blur). It comes bundled with a geometric modelling system called Alpha_1, distributed by Engineering Geometry Systems in Salt Lake City.

The contact is:
        Engineering Geometry Systems
        275 East South Temple, Suite 305
        Salt Lake City, UT, 84111

I think the price is something like $10K for commerical sites and < $1K for government or university sites. The ray tracer isn't available separately, but the modelling package is so full of goodies it's worth looking at in its own right.

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A Letter, by Jeff Goldsmith

[my response is in brackets]

1) A student of mine found a typographical error in your "Intro to Ray Tracing" notes. (I gave him some pages from same to teach him about texture mapping; good job!) In Equation set E11, the third line should read: Qvy = -Nb/Dv2 rather than Nc. I noted that you didn't catch it in this years' issue. (Better typesetting, though.) Thanks for publishing that.

[Thanks! If anyone else notices typoes, omissions, or anything else that bugs them in the "Intro" SIGGRAPH notes, please contact Andrew Glassner or me or the individual author ASAP.]

2) Does anyone know where I can obtain 2D wood texture maps? FTP, email, tape, disc, whatever, is fine.

[Any leads, anyone? I'm interested, too.]

-- Jeff Goldsmith

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Best of USENET

[What follows are things posted to USENET that might be of interest here. Many readers either don't receive USENET or haven't the time to perform chaff separation. What follow are my own winnowings. - EAH]


Thomas Palmer writes:

Has anyone done any work on vectorizing ray-object intersection calculations? The vectorizing C compiler on a Cray X/MP will not (automatically) vectorize loops smaller than about 5 or 6 iterations (nor should it - the vector register load time outweighs the gain). Typical ray tracing vector operations involve vectors of length 3 or 4.


 Thomas C. Palmer       NCI Supercomputer Facility
 c/o PRI, Inc.          Phone: (301) 698-5797
 PO Box B, Bldg. 430    Uucp: ...!uunet!ncifcrf.gov!palmer
 Frederick, MD 21701    Arpanet: [email protected]


>From: [email protected] (Stephen Spencer)
Subject: Re: Vectorizing ray-object intersection calculations
Organization: Ohio State Computer & Info Science

There was an article in IEEE CG&A about four years ago about vectorizing ray-sphere intersections on a Cyber which included an algorithmic workup of how it worked.

As far as ray-polygon intersection goes, the article in SIGGRAPH '87 dealing with tesselation of polygonal objects (it had the pictures of grass and the Statue of Liberty in it) included the algorithm for fast ray-polygon intersection, and I did implement it and it did vectorize quite nicely. I unfortunately no longer seem to have that piece of code, but it wasn't difficult. Of course you still have to do the sorting of the intersection points but the heavy intersection calculations can be done quickly.


>From: [email protected] (John M. Olsen)
Newsgroups: comp.graphics
Subject: Polygon teapot ftp'able
Summary: Come 'n get it.
Organization: University of Utah, Computer Science Dept.

One of the kind and generous People In Charge compressed the Utah Teapot and has made it available (for a week or so) as ~ftp/pub/teapot.Z so those who want the polygon version of it can get it now. It compressed to about 270K from 990K, so it's not too bad to transfer. The machine name is cs.utah.edu. Have fun with it, and let me know if you have any problems getting it transferred.

Just so I don't get hate mail, and you don't think your software is broken: The Utah teapot was designed with a hole in the bottom. I had forgotten about this, but was reminded by someone (Jean Favre?) who rendered it.


From: [email protected] (Mark VandeWettering)
Newsgroups: comp.graphics
Subject: Ray Tracer: Part 01/01
Organization: University of Oregon, Computer Science, Eugene OR
Lines: 2353

Here is the first release of my totally whiz-bang ray tracer. Okay, so it isn't TOTALLY whiz bang, but it does have some nice features. It uses bounding volumes, has cones, spheres, polygons and cylinders as primitives, reads Eric Haines NFF file format images and more....

Use it, abuse it, sell it, but be sure to have fun with it. I had alot of fun hacking on it. If any of you find bugs, or better yet fix bugs and add features, send them to me, and I will try to get them worked into a future release which I hope might make it into comp.sources.unix.

[ code not included here: either get it from USENET, or you can write Mark or myself for a copy. The source weighs in at about 55K bytes.]


Reply-To: [email protected] (John K. Counsulatant)
Organization: RICH Inc. , Franklin Park,IL

If anyone is interested in *other* ray tracers, I have source to DBW Render (an excellent ray tracer ported from the VAX to the Amiga) and Tracer (a crude spheres only (but a good starter :-) tracer for the Amiga). I am in the process of obtaining QRT (quick ray tracer (if there is such a thingee ;-)) source (also for the Amiga).

I can be reached at:

RealTime (prefered): 1(312)418-1236 (6pm to 10:30pm central time)

USmail: John Kjellman E-Mail: [email protected] 17302 Park Ave. Lansing IL 60438


Reply-To: [email protected] (Sean Casey) Organization: The Leaning Tower of Patterson Office @ The Univ. of KY

In article ([email protected]) [email protected] (Mark VandeWettering) writes:
> Isn't DBW Render copyrighted? I believe the source code may not
> be redistributed, I tried to obtain the sources, but aborted
> because of the restriction on use/redistribution.

The first release of DBW Render was freely redistributable. I believe it even found it's way to a Fish disk. The story I hear is of an evil employer seeing $$$ and telling Dave that since he wrote it on the company computer it belongs to the company and that no further releases may be given away.

The current release uses "Look Up A Word In The Manual" type copy protection, the most annoying kind I have experienced to date.

If someone really wants to pay for an Amiga ray tracer, I'd send him in the direction of one of Turbo Silver, Videoscape 3D, or Sculpt 3D, all excellent products. These products are in fierce competition with each other, and get better all the time. I saw a pamphlet in Turbo Silver that had an ad for a fascinating terrain generator module. Just think, combine a high quality terrain generator and the logistics of a board wargame...

Oh yeah, I hear that some of the commercial Amiga ray tracing software is being ported to the Mac II. These products have been around for a while, so it's a good chance for Mac users to get their hands on some already-evolved ray-tracing software.

***  Sean Casey                        [email protected],  [email protected]
***  (Looking for his towel)           {backbone|rutgers|uunet}!ukma!sean
***  U of K, Lexington Kentucky, USA   Internet site? "talk [email protected]"
***  ``With a name like Renderman, you know it's good jam.''


Reply-To: [email protected] (George Kyriazis)
Organization: RPI CS Dept.

Hello world! I have been using ray tracers for quite some time now, and I have made many changes to some of them, so I though it was time for me to write a ray tracer. So there it is! It is not supposed to be fast or anything, but I think it is well commented and easy to understand. It is very simple also. I am willing to give it to anyone that wants it. Unfortunately, I don't think I can put it in a place where people can ftp to, so if you want it, please send me mail. I'm sure I can put it in some public place later. The ray tracer currently supports only spheres, with ambient, diffuse, specular lighting, together with reflections and refractions. I don't use any in-line code for the vector routines, but subroutines, for readability. Hope someone will want to play around with it.

George Kyriazis

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Postscript Ray Tracer, John Hartman and Paul Heckbert

[This was published in the last hardcopy RT News. Here it is again, for those not inclined to type a lot]
Reply-To: [email protected] (John H. Hartman)
Organization: University of California, Berkeley

Ever worry about all those cycles that are going to waste every night when you shut off your laserwriter? Well, now you can put them to good use. Introducing the world's first PostScript ray tracer. Just start it up, wait a (long) while, and out comes an image that any true graphics type would die laughing over. As it is currently set up it will trace a scene with three spheres and two lights. The image resolution is 16x16 pixels.

Warning: the code is a real kludge. I'm not sure there is much you can change without breaking it, but you're welcome to try. If, by chance, you are able to improve the running time please send us the improved version.

psray.ps is the ray tracer. result.ps is what a 16x16 image should look like.

Have fun.

John H. Hartman [email protected]
UCB/CSD ucbvax!ernie!jhartman

# to unpack, cut here and run the following shell archive through sh
# contents: psray.ps result.ps
echo extracting psray.ps
sed 's/^X//' <<'EOF10807' >psray.ps
X% Copyright (c) 1988  John H. Hartman and Paul Heckbert
X% This source may be copied, distributed, altered or used, but not sold for
X% profit or incorporated into a product except under licence from the authors.
X% This notice should remain in the source unaltered.
X%   John H. Hartman [email protected]
X%   Paul Heckbert   [email protected]
X%    This is a PostScript ray tracer. It is not a toy - don't let the kids
X%  play with it. Features include: shadows, recursive specular reflection
X%  and refraction, and colored surfaces and lights (bet you can't tell!).
X%  To use this thing just send it to your favorite Postscript printer.
X%  Then take a long nap/walk/coffee break/vacation. Running time for
X%  a recursive depth of 3 and a size of 16x16 is about 1000 seconds
X%  (roughly 20 minutes) or 4 seconds/pixel.
X%    There are a few parameters at the beginning of the file that you can
X%  change.  The rest of the code is pretty indecipherable. It is translated
X%  from a C program written by Paul Heckbert, Darwyn Peachey, and Joe Cychosz
X%  for the Minimal Ray Tracing Programming Contest in comp.graphics in
X%  May 1987.  Some changes have been made to improve the running time.
X%  Don't even bother trying to figure out how this works if you are looking
X%  for a good example of a ray tracer.
X/starttime usertime def
X/DEPTH 3 def   % recursion depth
X/SIZE 16 def   % image resolution
X/TIMEOUT SIZE dup mul 10 mul cvi 120 add def  % approximately 10 sec/pixel
X/AOV 25.0 def    % angle of view
X/AMB [0.02 0.02 0.02] def  % ambient light
X% list of spheres/lights in scene
X%            x    y    z     r   g   b   rad  kd   ks  kt   kl  ir
X/SPHERES [[[ 0.0  6.0  0.5] [1.0 1.0 1.0] 0.9 0.05 0.2 0.85 0.0  1.7]
X          [[-1.0 8.0 -0.5] [1.0 0.5 0.2] 1.0 0.7  0.3 0.0  0.05  1.2]
X          [[ 1.0 8.0 -0.5] [0.1 0.8 0.8] 1.0 0.3  0.7 0.0  0.0   1.2]
X         [[ 3.0 -6.0 15.0] [1.0 0.8 1.0] 7.0 0.0  0.0 0.0  0.6  1.5]
X         [[-3.0 -3.0 12.0] [0.8 1.0 1.0] 5.0 0.0  0.0 0.0  0.5  1.5]
X        ] def
Xstatusdict begin
XTIMEOUT setjobtimeout
X/waittimeout TIMEOUT def
X/initpage {
X   /Courier findfont
X   10 scalefont setfont
X} def
X/X 0 def
X/Y 1 def
X/Z 2 def
X/TOL 5e-4 def
X/BLACK [0.0 0.0 0.0] def
X/WHITE [1.0 1.0 1.0] def
X/U 0.0 def
X/B 0.0 def
X% index of fields in sphere array
X/cen 0 def
X/col 1 def
X/rad 2 def
X/kd 3 def
X/ks 4 def
X/kt 5 def
X/kl 6 def
X/ir 7 def
X/vec {3 array} def
X/VU vec def
X/vunit_a 0.0 def
X% dot product, two arrays of three reals
X/vdot {
X   aload pop
X   4 -1 roll
X   aload pop
X   4 -1 roll mul
X   2 -1 roll 4 -1 roll mul add
X   3 -2 roll mul add
X} def
X% vcomb, sa, a, sb, b  returns new array of sa*a + sb*b
X/vcomb {
X   aload pop
X   4 -1 roll dup dup
X   5 1 roll 3 1 roll mul
X   5 1 roll mul
X   4 1 roll mul 3 1 roll
X   5 -2 roll aload pop
X   4 -1 roll dup dup
X   5 1 roll 3 1 roll mul
X   5 1 roll mul
X   4 1 roll mul 3 1 roll
X   4 -1 roll add 5 1 roll
X   3 -1 roll add 4 1 roll
X   add 3 1 roll
X   vec astore
X} def
X/vsub {
X   aload pop
X   4 -1 roll aload pop
X   4 -1 roll sub 5 1 roll
X   3 -1 roll sub 4 1 roll
X   exch sub 3 1 roll
X   vec astore
X} def
X/smul {
X   aload pop
X   4 -1 roll dup dup
X   5 1 roll 3 1 roll mul
X   5 1 roll mul
X   4 1 roll mul 3 1 roll
X   vec astore
X} def
X/vunit {
X   /vunit_a exch store
X   1.0 vunit_a dup vdot sqrt div vunit_a smul
X} def
X/grayscale {
X   % convert to ntsc, then to grayscale
X   0.11 mul exch
X   0.59 mul add exch
X   0.30 mul add
X   255.0 mul
X   cvi
X} def
X/intersect { % returns best, tmin, rootp
X   7 dict begin
X   /d exch def
X   /p exch def
X   /best -1 def
X   /tmin 1e30 def
X   /rootp 0 def
X   0 1 NUM_SPHERES 1 sub {
X      /i exch def
X      /sphere SPHERES i get def
X      /VU sphere cen get p vsub store
X      /B d VU vdot store
X      /U B dup mul VU dup vdot sub sphere rad get dup mul add store
X      U 0.0 gt
X      {
X        /U B U sqrt sub store
X        U TOL lt
X        {
X           /U 2.0 B mul U sub store
X           /B 1.0 store
X        }
X        { /B -1.0 store }
X        ifelse
X        U TOL ge
X        U tmin lt and
X        {
X           /best i store
X           /tmin U store
X           /rootp B store
X        }
X        if
X      }
X      if
X   } for
X   best tmin rootp
X   end
X} def
X/trace {
X   13 dict begin
X   /d exch def
X   /p exch def
X   /level exch def
X   /saveobj save def
X   /color AMB vec copy def
X   /level level 1 sub store
X   p d intersect
X   /root exch def
X   /v exch def
X   /s exch def
X   -1 s ne
X   {
X      /sphere SPHERES s get def
X      /p 1.0 p v d vcomb store
X      /n
X      sphere cen get p
X      root 0.0 lt { exch } if
X      vsub vunit def
X      sphere kd get 0.0 gt
X      {
X        0 1 NUM_SPHERES 1 sub
X        {
X           /i exch def
X           /light SPHERES i get def
X           light kl get 0.0 gt
X           {
X              /VU light cen get p vsub vunit store
X              /v light kl get
X              n VU vdot
X              mul store
X              v 0.0 gt
X              p VU intersect
X              /B exch store
X              /nd exch def
X              i eq
X              and
X                 { /color 1.0 color v light col get vcomb def }
X              if
X           } if
X        } for
X      } if
X      color aload pop
X      sphere col get aload vec copy /VU exch store
X      4 -1 roll mul
X      5 1 roll
X      3 -1 roll mul
X      4 1 roll
X      mul
X      3 1 roll
X      color astore pop
X      /nd d n vdot neg store
X      /color
X      sphere ks get
X      sphere kd get color sphere kl get VU vcomb
X      0 level eq
X        { BLACK vec copy}
X        { level p 1.0 d 2 nd mul n vcomb trace vec astore }
X      ifelse
X      1.0 3 -1 roll vcomb store
X      root 0.0 gt
X        { /v sphere ir get store }
X        { /v 1.0 sphere ir get div store }
X      ifelse
X      /U 1 v dup mul 1 nd dup mul sub mul sub store
X      U 0.0 gt
X      {
X        /color
X        1.0 color sphere kt get
X        0 level eq
X           { BLACK vec copy}
X           { level p v d v nd mul U sqrt sub n vcomb trace vec astore }
X        ifelse
X        vcomb store
X      } if
X   } if
X   color aload pop
X   saveobj restore
X   end
X} def
X/main {
X   initpage
X   /data SIZE dup mul string def
X   /half SIZE 0.5 mul def
X   /i 0 def
X   /dy half AOV cvr 0.5 mul dup cos exch sin div mul def
X   /temp vec def
X   0 1 SIZE 1 sub
X   {
X      /y exch def
X      0 1 SIZE 1 sub
X      {
X        /x exch def
X         data i
X        /saveobj save def
X        VU X x cvr half sub put
X        VU Y  dy put
X        VU Z half y cvr sub put
X        DEPTH BLACK VU vunit trace
X         grayscale
X        saveobj restore
X        put
X     /i i 1 add store
X      } for
X   } for
X   gsave
X   100 300 translate 400 400 scale SIZE SIZE 8 MATRIX {data} image
X   grestore
X   100 200 moveto
X   (Statistics: ) show
X   100 190 moveto
X   (Size: ) show SIZE 10 string cvs show
X   100 180 moveto
X   (Depth: ) show DEPTH 3 string cvs show
X   100 170 moveto
X   (Running time: ) show usertime starttime sub 1000 div 20 string cvs show
X   showpage
X} def
X/main load bind
echo extracting result.ps
sed 's/^X//' <<'EOF10808' >result.ps
X/picstr 16 string def
X100 300 translate
X400 400 scale
X16 16 8 [16 0 0 -16 0 16]
X{currentfile picstr readhexstring pop} image

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Eric Haines / [email protected]