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From: erich@eye.com (Eric Haines) Date: Thu, 1 Jul 93 16:26:57 GMT Organization: 3D/EYE, Inc. Ithaca, NY Message-ID: <1993Jul1.122657.27332@eye.com> Newsgroups: comp.graphics _ __ ______ _ __ ' ) ) / ' ) ) /--' __. __ , --/ __ __. _. o ____ _, / / _ , , , _ / \_(_/|_/ (_/_ (_/ / (_(_/|_(__<_/ / <_(_)_ / (_</_(_(_/_/_)_ / /| ' |/ "Light Makes Right" July 1, 1993 Volume 6, Number 2 Compiled by Eric Haines, 3D/Eye Inc, 2359 Triphammer Rd, Ithaca, NY 14850 erich@eye.com All contents are copyright (c) 1993 by the individual authors Archive locations: anonymous FTP at princeton.edu (128.112.128.1) /pub/Graphics/RTNews, wuarchive.wustl.edu:/graphics/graphics/RTNews, and many others. Contents: Introduction New People Ray Tracer Races, Round 2, by Eric Haines Simple, Fast Triangle Intersection, part II, by John Spackman Review: _Photorealism and Ray Tracing in C_ (and others), by Eric Haines Comments on Various Ray Tracing Speedups, by Andrew Woo (awoo@alias.com) Errata to _Photorealism and Ray Tracing in C_, compiled by Eric Haines InterChange Plus Model/Texture Data CD-ROM, by John Foust Ray Tracing Roundup ==== Net cullings follow =============================================== Re: Intersection Between a Line and a Polygon (UNDECIDABLE??), by Allen B Obfuscated Postscript Ray Tracer, by Takashi Hayakawa ------------------------------------------------------------------------------- Introduction Ugh, what a backlog! I've tried for a month to find time to catch up with the deluge but seem to be running on a treadmill (so how many mixed metaphors is that?). Anyway, I'm going to put out what I've got - think of this issue as coming out in April. The "Roundup" is huge, I tried to whittle what I could, but there's been a lot of activity out there. SIGGRAPH: yes, there will be another gathering of the clans, i.e. the seventh meeting of the Ray Tracing Roundtable. Sounds impressive? Well, it's simply an excuse to have a chance to meet other people interested in ray tracing and put names to faces. As usual, I'll give a brief intro, people go around the room and briefly introduce themselves, then we split up and talk about whatever. This year we'll meet as a Birds of a Feather group (BOF), so look at the BOF sign at Registration for what room we're in. I plan on a 5:15 pm meeting on Thursday after the papers. By the way, we're not a SIG this year because SIGGRAPH is charging $100 or so for setup/cleanup fees or somesuch from SIGs, but BOFs still seem to be free. ---- So who invented ray tracing? Most people will say Appel in 1968, though twelve years later Whitted did the paper that brought it all together, and Doug Kay also was working along similar lines at the time. On the net the idea was floated that ray tracing came out of nuclear weapon testing. True, rays were used in simulations, but this would be called ray casting at best - it was not used to render realistic images. By the same logic, explorers of analytic geometry and ray/object intersections could be considered the inventors. Watt and Watt propose that Descartes was one of the first ray tracers because of his analysis of the rainbow. By widening the definition of ray tracing even more, it's maintained that Durer or one of his contemporaries was the inventor of ray tracing (you know, all those frustum and vanishing point drawings from around the Renaissance). This question does bring up another that's a bit more profound: would computer science have any existence without computers? Some universities with a strong theory department would have us believe that computers are irrelevant to computer science. Sure, there was Boolean logic and finite math before computers, but it's interesting to contemplate how much (data structures, sorting, networks, languages, you name it...) would not exist if there was no hardware to make the theory have a point to it. Computer science would be a disparate set specialities in mathematics and nothing more. A lot of computer graphics would go away, with some linear algebra and analytic geometry being all that would be of interest. Certainly the idea of figuring out a pixel's color would be up there with figuring out the next decimal place of pi as far as usefulness went. What would people have thought of Foley & Van Dam & Feiner & Hughes _Computer Graphics_ if it were sent back 50 years? Anyway, I like the answer that Appel invented ray tracing, then rightly ignored it as too expensive for the computers of 1968. ------------------------------------------------------------------------------- New People # John Foust # Syndesis Corporation # PO Box 65 # 235 South Main St # Jefferson, WI 53549 # (414) 674-5200 # (414) 674-6363 FAX Syndesis Corporation makes InterChange Plus, a system of translators for exchanging data between 3D modeling programs such as AutoCAD DXF, Wavefront, Imagine, LightWave, 3D Studio and many others (see announcement in this issue). ------------------------------------------------------------------------------- Ray Tracer Races, Round 2, by Eric Haines Back in RTNv3n1 I timed Craig Kolb's Rayshade, Mark Vandewettering's MTV, and my own commercial code against each other. Three years have passed and many new ray tracers are out there. I recently received from Eduard Schwan a modified SPD package, with new code by Alexander Enzmann and him. SPD stands for Standard Procedural Databases, and is a set of programs I created for testing ray tracer efficiency schemes (available at princeton.edu:/pub/Graphics and other places). The modified code allows output in formats other than NFF, such as POV, Vivid, RTrace, QRT, Rayshade, etc. I hope to modify this code a little and distribute it with the next SPD release. Since these new formats were now available, I decided to have a race between the various ray tracers for just raw rendering speed. I did not bother with QRT because I couldn't easily find it on the net, it's pretty old, and it does not have any efficiency speedups (so almost everything will beat it). I ran all tests on an HP 720 RISC workstation and compiled all ray tracers with optimized and profiler options. Instead of using Vivid, I used "Bob", which is essentially Vivid and which had source code available (unlike Vivid, I believe). The source code is in _Photorealism and Ray Tracing in C_ (but not on the net), reviewed elsewhere in this issue. Rayshade runs fairly slow if the user does not take any action to improve efficiency. However, it is simple enough to add a spatial subdivision grid to the input data. I added a grid of resolution == ceil( cube-root( # of primitives ) ) to each database, but did not include the ground polygon (if present) to the grid. POV 1.0 has minimal efficiency support (user defined bounding boxes) which were too much work to use, so I avoided these. Vivid and RTrace both have automatic efficiency schemes (the only way to go, in my humble opinion). Vivid/Bob and RTrace are descendents of MTV's efficiency scheme and use Kay-Kajiya space sorting to get a bounding volume hierarchy. Note that if you have Bob, you should definitely get the errata from wuarchive at graphics/graphics/books/errata, which has code which makes Bob 5% faster than the original code. Two sets of tests were done: one with SPD using a size factor of 1, which creates databases with from 4 to 147 primitives, the other with the default size factors, which gives 4000 to 10,000 primitives. Small, level 1 databases (from 4 to 147 primitives), times in seconds: balls gears mount rings teapot tetra tree POV 1.0 377.32 31609.4 697.62 1853.09 1103.54 62.74 408.01 Rayshade 4.0.6 140.34 2126.6 143.38 472.45 330.24 32.94 116.18 Rayshade w/grid 98.41 380.2 110.00 111.30 112.84 35.26 85.71 Bob (Vivid) 97.16 733.9 88.67 161.76 141.15 30.72 76.56 RTrace 114.55 867.2 141.96 183.59 (no go) 39.77 93.67 Notes: Something screwy happened with converting cylinders for the rings database for POV (this is probably the converter's fault, not POV's), so this database did not render correctly. The cones for the tree database seemed weird at the ends, too, though they did render. RTrace did not render the teapot at size one as it (reasonably enough) balked when it encountered the degenerate polygons with (0,0,0) normals. These polygons have no area (so can't be seen), but their data is indeed bad. POV and ungridded Rayshade can be compared for raw object intersection speed; Rayshade wins by 2x or more. Adding the efficiency grid to Rayshade makes performance increase by up to 6 times, even with these simple scenes (the exception is tetra, which has only four primitives, and in which the grid slows down performance). Bob edges out RTrace by a little bit (maybe 20%), and is sometimes better, sometimes worse than gridded Rayshade. I should mention that I ran Rayshade with all objects casting opaque shadows so as to be comparable with POV (and Bob and RTrace, near as I can tell). True filtered shadows would take awhile longer to compute for the gears database. Default size SPD databases, time in seconds: balls gears mount rings teapot tetra tree POV 1.0 191000 1775000 409000 260000 45000 31000 250000 Rayshade w/grid 173.04 326.7 158.22 327.38 133.75 54.43 147.05 Bob (Vivid) 398.83 1060.5 224.79 831.71 245.12 48.42 272.87 RTrace 667.25 1488.6 805.65 (fail) 347.15 156.78 371.39 Notes: The POV times are approximate, made by extrapolating the time for an 8x8 pixel rendering minus the time for a 1x1 rendering (i.e. minus file read-in time). The record for POV goes to gears, which would take about 3 weeks to render. RTrace had a "runtime - too many SURFACES" on rings and so did not render it. If you were off the planet for the past decade and didn't think efficiency schemes would gain you much, these timings would change your mind. Since POV 1.0 doesn't have any efficiency scheme, its speed is a tad slow. A good grid makes Rayshade run like a speed demon, outperforming almost everything every time. Bob outperforms RTrace by a higher margin at this point. Conclusions: If you are willing to get your hands a little dirty with setting up the gridding, use Rayshade (I hope Craig will make gridding default in the next version). For painless rendering, Bob/Vivid is good, though RTrace is in the running and supports some interesting primitives and all sorts of other support (see the Roundup in this issue). POV is fun but slow. The good news is that version 2.0 of POV will have automatic efficiency generation and will be out in a few months. It will also fix a shading bug I noticed (strange bright lines at the light silhouette edges of shiny spheres). In the meantime you can add bounding boxes by hand if you want (ugh) - it does make a significant difference in speed. If anyone else has filters for SPD output for ART or any other competitors, please do pass them on to me and I'll give them a whirl. ------------------------------------------------------------------------------- Simple, Fast Triangle Intersection, part II, by John Spackman (spackman@lightwork.co.uk) [This is in response to last issue's article by Chris Green, Steve Worley and myself on half-plane testing for the inside-outside test for ray tracing triangles. John has a good illustration for what the barycentric coordinates mean - EAH] When the maths are boiled away, the barycentric test IS the half plane test - with the extra advantage that the half plane 'heights' values are normalised o to the range [0,1] over the triangle's extent. o to sum to 1 within the triangles supporting plane [ good for interpolation ] Taking a barycentric [alpha,beta,gamma] coordinate system for the triangle T:- beta=0 \ gamma=0 beta=1 \ / \ \ / gamma=1 \ \ / / \ \ / / \ \ / / \ \A / / alpha=1 ___________\_____________\/_____________/________________ \ /\ / \ /TT\ / \ /TTTT\ / \ /TTTTTT\ / \ /TTTTTTTT\ / alpha=0 \ /TTTTTTTTTT\ / _________________________\/____________\/_______________________ B/\ /\C / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \/ \ T = { [alpha,beta,gamma] : alpha>0,beta>0,gamma>0 } eg: A = [1,0,0], B=[0,1,0], C=[0,0,1] Notice that 'alpha' is simply height above the 'alpha=0' half-space plane 'beta' is simply height above the 'beta=0' half-space plane 'gamma' is simply height above the 'gamma=0' half-space plane In effect, the triangle is simply the intersection of [0,1] slabs in alpha, beta and gamma. Of course, it is true that taking [alpha,beta,gamma] over a projected 2D space may be faster than in full 3D space - but that's something else again. [in a later note:] With the Half-spaces you only get an early get-out if alpha < 0.0. With the Barycentric coordinates, you get an early get-out if alpha < 0.0 OR alpha > 1.0. In other words, the former regards a triangle as an intersection of singly bounded three half spaces, whereas the second regards a triangle as an intersection of doubly bounded slabs. -------- John also points out: But the half space test is just a homogeneous dot-product:- height = [x,y,z,1] . [s,t,u,v] for the plane with outward normal [s,t,u] displaced at distance v from the origin in this direction. Therefore height = [x,y,z,1] . [s,t,u,v] ----- -------------------- normalise normalise = [x,y,z,1] . [s',t',u',v'] where s' = s / normalise t' = t / normalise u' = u / normalise v' = v / normalise is the same as the Barycentric test. So just store [s',t',u',v'] instead of [s,t,u,v]. All normalisation is then precomputed, the Barycentric test becomes as cheap as the half space test, and the Limeys have saved the world again. -------- Eric Haines replies: True that you get an early out with the bounding slab, and I thought this would be a big win. [I included a lot of statistics here, which basically come up with the result that the two tests are pretty similar in performance under a variety of conditions. I will not bore you with the minutiae... However, doing the precomputation is certainly a win, vs. using the straight barycentric test (see RTNv5n3 for code).] ---- One interesting speedup that Steve Worley and I discussed for Chris Green's method is sorting the edges of each triangle by its length. Longer triangles will tend to cut larger parts of the area of the bounding box surrounding the triangle away, and so will cause earlier rejections of points outside the triangle. The long and short of it was that this trick indeed decreases overall testing time in general and is simple to add to the preprocess for creating triangle half-plane sets. Steve points out that just getting the longest edge first should help a fair bit and be an even faster preprocess, though I did find that the full sort helped a tad more. Sorting the two edges touching the anchor vertex for the Barycentric test helps a bit, too. Some interesting related sorting possibilities exist for convex polygon testing. If the triangle test is used, then the largest triangles should be tested first in order to maximize the chance of an early hit. If the exterior edge test (test the point against all edges; if it is outside any edge then you are done) is used then there is an optimal ordering of edges to test in order to cut off the maximum amount of area per edge tested. Getting this optimal ordering looks like an NP-complete kind of a problem, though. This is pretty surprising, given that the problem appears fairly simple on the face of it. ------------------------------------------------------------------------------- Review: _Photorealism and Ray Tracing in C_ (and others), by Eric Haines _Photorealism and Ray Tracing in C_ is by Christopher Watkins, Stephen Coy, and Mark Finlay. It's available through M&T Books in paperback and comes with two PC 5 1/4" HD disks of code and data. 482 pages, 48 color plates, $44.95, ISBN 1-55851-247-0. This book discusses most facets of ray tracing with a hands on perspective. There are many code fragments scattered throughout, along with a fully functional ray tracer, Bob, which is a descendant of Vivid. A simple modeler and a back end to dither and display images on a PC are also provided. Though the code is PC oriented, I had very little difficulty compiling the ray tracer on my UNIX workstation. Not a lot of space of the book is devoted to PC specific topics, maybe 40 pages. The disks include polygon models for a human skull, an egyptian mummy head, a human face, a heart, a duck, a column, Venus de Milo, some cars, chess pieces, and other objects. There are also a bunch of little programs which generate various procedural models which are enjoyable in their own right. Also included are some texture maps. The basics are covered along with some additional topics such as procedural modeling, color and bump texturing, depth of field effects, soft shadows, height fields, and others. There is not much heavy theory presented, as the book strives to teach the lone hobbyist or student without risking losing them. The color plates are a good mixture of educational and just for fun images, and some of the renderings are excellent. I believe the data to render all of the plates is present on the disks. There are a few shortcomings with the book. One is common to many computer paperbacks, that of listing pages and pages of uninterrupted code. This book is nowhere near the worst offender I've seen, but there are a fair number of pages of code which have little reason for being on the printed page (e.g. does anyone really want to read noise function code?). Sampling every 20th page (20,40,60...) of the book and seeing what was there, I found 11 out of the 24 pages were code - a fairly high ratio. This translates to about 220 pages of code. Some is useful to publish, the rest is just bulk. Another problem which is more serious is non-standard terminology. The ones I noticed: - height fields are referred to as "z-buffers". - the translation factors in a 4x4 matrix are presented in the first column, with W in the top row, instead of last row/column. - the function to transform normals, trans_normal(), works, but using the transpose of the inverse of the matrix would be faster and more readable. An errata listing for this book is included elsewhere in this issue, and the most current listing is kept at wuarchive.wustl.edu:graphics/graphics/books. I was dismayed to see under "Where to Now?", a section at the very end of the book, that the only books listed as places to go next were those sold by M&T Books. However, at least there were references to some related papers and books (though beware of typoes) in the Bibliography. There are some other minor problems, but the book seems pretty solid otherwise. Stephen Coy sent me a list of corrections which I will try to edit up and get put in the graphics book errata area at wuarchive. If you wish to understand the basics of ray tracing and quickly get a ray tracer going on your machine, consider getting this book. Of the "disk in the back" trade books out there, this one is reasonable in its approach and covers a wide range of topics. From what I can tell, it seems to be the best "with code" book currently on the market. BOB/VIVID is the fastest "free" (well, you have to get the book if you want the source) ray tracer available today (Rayshade datafiles can be tweaked to be made faster, but this involves sometimes complicated user intervention). There are a few other trade books on ray tracing. Roger T. Stevens' _Fractal Programming and Ray Tracing with C++_ is fairly old and nowhere near as good (see RTNv4n2 for a brief, scathing review). A book I have not had the opportunity to read (i.e. I don't want to fork out $$$ for it...) is Craig Lindley's _Practical Ray Tracing in C_ (around $49.95) from Wiley, which has a disk of software for DKB Trace, the ancestor of POV. What little I glanced at was not quite right. For example, someone pointed out his ray definition is a little odd. Indeed, he says the "t" in point = origin + t * direction stands for "time". Not really, it's just a parameter and it certainly does not stand for time (unless your name is Ping-Kang Hsiung and you're doing relativistic ray tracing). I also have not seen the book _The Image Lab_ from Waite Group Press, so cannot say much about it. This book is a collection of shareware/freeware programs such as the POV ray tracer, the PICLAB image processing program, CSHOW for viewing graphics files, IMPROCES super VGA paint program, and Image Alchemy image converter (all of these programs can be found on the net). It seems unlikely that the book has much of a chance to go into any detail about POV's basis given the number of programs included. As an aside, Bob is faster than the current POV 1.0 and does not show any serious rendering bugs (see the timings test article in this issue). For more advanced or textbook type material, there are a few good choices, though none have any code provided with them. _An Introduction to Ray Tracing_ by Glassner et al (including myself) is a bit old but still a comprehensive overview of the theory, though it is a little disjoint at times and weak in some areas of interest (e.g. texture mapping). I should mention this book is now in its fourth printing and all the typos and mistakes we know about have been corrected. Watt & Watt's new book, _Advanced Rendering and Animation Techniques: Theory and Practice_, is a good unified guide to advanced rendering in general and I highly recommend it. Think of it as a condensed and simplified "Best of SIGGRAPH" for the past decade and you won't be too far wrong. I hope to review it next issue. Foley and Van Dam and Feiner and Hughes' _Computer Graphics_ includes an overview of ray tracing, if you don't feel like learning too much; other recent textbooks also include summaries of the algorithms involved. ------------------------------------------------------------------------------- Comments on Various Ray Tracing Speedups, by Andrew Woo (awoo@alias.com) With respect to Steve Worley's speedup idea with multiple grid orientations ["An Easily Implemented Ray Tracing Speedup", RTN v.6 n.1] Our raytracer at Alias raytraces in eye-space (i.e. eye is at (0,0,0), staring perpendicularly into the scene), Andrew Pearce did this to be consistent with our non-raytrace renderers. This requires an initial transform of everything at the beginning (lights, geometry, etc). However, this has turned out to be quite advantageous for our raytracer. Working in eye-space means that most of our primary rays will benefit from Steve's multi-grid idea (i.e. most primary rays are almost in the grid orientation). According to Steve's assumption, working in eye-space is then most idea for primary rays for orthographic cameras. However, I have found little performance increase with this - maybe because our raytracer already has ray bounding boxes (ala Snyder & Barr, Siggraph 87) and the advantages of Steve's approach have already been accounted for by the ray bounding boxes. Maybe not, keep on hacking, Steve - interesting idea you have here. Onto the bounding areas for ray-polygon intersection, by Steve Worley and Eric Haines... The general ray-polygon process that I find useful is very similar to yours: 1) back-face culling (same as you suggested). 2) intersect with the polygon plane and determine a distance value T. This evaluation is simply T = (d - N.O) / N.D, where N, d form the plane equation, O = ray origin, D = ray direction. 3) check that T > epsilon and T < an already hit polygon's T value. 4) check that the intersection point O + TD is inside the polygon bounding box. 5) perform the inside-outside test. There is no need to intersect with the ray-intersect the polygon bounding box - that's too expensive. And I do step #4 with respect to the 3d polygon bounding box because I already have those for the ray bounding box approach. [This is actually identical to what I use. Steve's 2D bounding test is just a slightly faster way to do step #4 - since you can precompute once which plane to cast the polygon upon, you can also precompute once which 2D box to use, and you can combine the two (this is, of course, if you like longwinded, duplicated code for speed - me, though I can see its use, I haven't implemented the 2D test since it's just too much hacking). - EAH] Now here's the neat extension to eye-space raytracing (for perspective) again... Since the primary rays always have a ray origin at (0,0,0), the evaluation of T just becomes d/N.D, and the intersection point is now just TD. This can be advantageous for some traversal schemes as well (where O + TD needs to be evaluated quite often). I was also hacking with reducing the T evaluation for future generation rays. I was able to reduce the floating point count, but found little improvement - sigh. Ok, I will stop shooting off my mouth and get some work done. ------------------------------------------------------------------------------- Errata to _Photorealism and Ray Tracing in C_, compiled by Eric Haines book contact: Stephen Coy (70413.136@compuserve.com) Compiled by Eric Haines (erich@eye.com) from Stephen Coy's notes and my own. The newest version of this errata listing (with all the code patches) is in wuarchive.wustl.edu:graphics/graphics/books/errata. version 1.0 date: 6/23/93 -------- plate 2 : Image should be rotated and returned to correct aspect ratio. plate 17 : Text should be "Varying texture amplitude on spheres" plate 18 : Text should be "Varying texture terms on spheres" plate 34 : "Sphereflake" not "Sphere Lake" pg 124 #define NLAMBDA has the comment "not used anywhere" - true, this is just left over from Mark Vandewettering's code, upon which Bob is based. pg 157 Equation 6-1 is totally messed up. Should be: REFL_DIR = RAY_DIR + 2*(RAY_DIR _dot_ NORMAL) * NORMAL pg 164 "is simply to cast more than one ray per screen pixel (in other words, subsampling)." should say "supersampling." pg 168 top "...in the code as parallax projection." should be "flat projection." pg 168 Note that most of the samples have up= 0 0 1 not 0 1 0 and the "left" vector is calculated from up and the to and from points. pg 168-169 Seems to imply that spherical projection differs from fisheye. It doesn't. pg 169 Replace "Parallax" with "NoParallax" pg 170 The sphere in plates 9 & 10 is reflective not transparent. pg 173 Bob's adaptive supersampling does not cast a ray through the center of the pixel. It first looks at the corners. pg 176 Where it says "Figure 7-3 shows..." it should say "Plate 20 shows..." pg 221 Replace "baricentric" with "barycentric" pg 230 The reference to figure 8-6 should be 8-5. pg 232 top "For example, a list of 10 requires on average five intersection calculations per ray." WRONG the correct answer is 10 + #lights*5 + reflected + refracted... pg 234 paragraph three: "Now compare the maximum of the tnear values and the minimum of the tfar values. If the ray intersects the volume, then tmax is greater than tmin." No; correct this to: "Now compare the maximum of the tnear values (tmax) and the minimum of the tfar values (tmin). If the ray intersects the volume, then tmax is less than tmin." pg 241 2nd paragraph "if the value of t for the bounding volume of the node is less that the current tmin value..." should say "greater than" pg 274 near bottom "The reflecting sphere would be next to impossible without great additional cost if solid texturing were not used." Huh? What sphere? This sentence looks lost. pg 333 Replace "Kunni" with "Kunii". pg 351 A less overloaded term than "z-buffer" would be "heightfield" pg 473 Replace "Carpender" with "Carpenter" pg 474 Replace "Glasner" with "Glassner", "Peachy" with "Peachey" Code patches: The patches for the code are attached at the end of this file. Tokens.c has a fix to correct a bug in the handling of numbers in scientific notation. Inter.c has been optimized in a big way and gains an additional 5% overall for the raytracer. Sponge.zip contains the correct version of the program to generate the sponge image in the book. Porting to a unix system is pretty trivial. A makefile is needed, and little in the code needs to be changed. The delimiter in file.c on line 70 may have to be modified. The code uses <string.h>, so those using <strings.h> will have some macro defines ahead of them. [patches are not included here for brevity - if you can't ftp the errata, I can send them to you. - EAH] ------------------------------------------------------------------------------- InterChange Plus Model/Texture Data CD-ROM, by John Foust / Syndesis Corporation (76004.1763@compuserve.com) [Though a tad pricey, I thought this CD-ROM and software was of sufficient interest to readers here to warrant publication. Also, note the offer of "free if you contribute to it". The text is written by a representative of the company but sounds reasonable. BTW, I'm certainly interested in noting any other commercial products out there that are related to ray tracing and are affordable by mere mortals (i.e. less than $300 is a good target, less than $100 even better) - EAH] My company makes InterChange Plus, a system for translating between many different 3D modeling file formats. We've been in the Amiga market since 1987, but we're moving to Windows later this year. The "Syndesis 3D-ROM" is a CDROM collection of more than 500 freely distributable 3D models, all present in AutoCAD DXF, 3D Studio, Wavefront .obj, Video Toaster LightWave and Impulse's Imagine PC/Amiga formats. We didn't attempt to fix the normals from objects that have random orientation. (Since InterChange doesn't do that (yet) I didn't want to mislead people about its abilities.) It's also got more than 400 tileable, wrappable texture maps. It includes a fully indexed, cross-referenced catalog of the objects. The disc includes demonstration models from companies such as Viewpoint Animation Engineering. All 28 Viewpoint demo models are present, including the yet-unreleased Siggraph 93 set. More demo objects were contributed by Noumenon Labs, VRS Media, Mira Imaging and other commercial modeling companies. The 3D-ROM is a demonstration of the translation abilities of InterChange Plus, Syndesis's system for converting between 3D file formats. InterChange Plus translates between AutoCAD DXF, 3D Studio, Digital Arts, Wavefront, Swivel, Sculpt, VideoScape, LightWave, Imagine, CAD-3D, PAGErender and Vista DEM formats. Soon to come is support for StereoLithography, Macromedia 3DGF, Super 3D, Alias StyleGuide, Topas, Softimage, Inventor and Vertigo formats. All material and hierarchy information is preserved as best as possible. We don't sell source, but we do license to several companies in executable form. This ISO-9660 disc is fully accessible from MS-DOS, Macintosh, Amiga and Unix workstations. The price is $199.95. If you'd like to find out about this CDROM, we'd be glad to add you to our mailing list. See us at Siggraph 93, booth 2244, Hall D. We're not trying to get into the 3D object business, we're trying to tell people about InterChange Plus, and to get more freely distributable objects into the hands of artists. We're going to make more editions of the 3D-ROM with new objects. In the newsletter, we'll describe how people can send us objects and then get a free CDROM that contains their objects. That's how we're going to thank everyone who contributed. I'd really like to flush out all those nifty university-created and government-created data sets and objects we're see over the years and convert them into useful, popular 3D formats. The Internet "avalon" site was kind enough to make me an 8mm Exabyte copy of the 3D collection there, and I got the DEMs from the Xerox "spectrum" site. Some of the avalon objects made it to the first disc, and more DEMs will be present on future discs. Syndesis Corporation P.O. Box 65 235 South Main Street Jefferson, WI 53549 (414) 674-5200 (414) 674-6363 FAX ------------------------------------------------------------------------------- Ray Tracing Roundup There are a few things of note in ray tracing software out there. Rayshade is getting used more and more on workstations for "serious" rendering (as in zillions and zillions of polygons, for example). POV has a ton of people cranking out utilities and whatnot. RTrace does not seem to get the attention it deserves (perhaps because of the sometimes hideous ftp connection to Portugal - George Kyriazis, any chance of mirroring this site at wuarchive?). It supports a good set of primitives and has a ton of converters to its format (including some unique ones like IRIS Inventor, IRIT, etc) - see the RTrace section below for a diagram of formats supported. -------- The site wuarchive.wustl.edu will soon mirror the entire net. At least that is how it's starting to look like - if you're having problems getting into avalon.chinalake.navy.mil or find faramir.informatik.uni-oldenburg.de too far away, they are mirrored (along with many other graphics hosts) at wuarchive in mirrors/mirrors/graphics/<hostname>. -------- For animation for any ray tracer, there is a utility called Animdat, freeware/shareware that will replace variable names in a template file and output a series of data files with the variables incremented in the right places. (hed@cats.ucsc.edu) There's also a very useful (and similar) package called RTAG. It's a PC binary only, though. It is ASP software, $20, by P. Sherrod. It supports more functions, I believe, than Animdat such as spline curves for animation paths. (If Animdat currently supports splines, I apologize. Last time I saw it it didn't.) It's worth a look if you have a PC and do animations with any of the popular raytracers--the Rtag (and Animdat) packages aren't hard-coded to deal with only POV. I've uploaded it onto wuarchive.wustl.edu (128.252.135.4) under /pub/msdos_uploads/graphics/rtag20.zip. (Russell Webb, rwebb@nyx.cs.du.edu) -------- [This commercial program has a large and devoted group of Amiga users out there, and their mailing list (requests: imagine-request@email.sp.paramax.com) is quite active. - EAH] There is a new product for the IBM'ers out there. It is called IMAGINE and it just started shipping. I can personally attest that it will blow the doors off of 3D-Studio. It is made by IMPULSE, and is in its 3rd version (1st for the IBM). It can do morphing, your standard key-framing animation, it is a raytracer (reflections & shadows), and can do/apply special FX to objects (like ripple, explode, bounce, things of that nature). Also it has algorithmic texture maps and your standard brushmapping also. You can have animated brushmaps (i.e. live video mapped on the objs), also animated backdrops (i.e. live video backgrounds), also animated reflections maps. Don't let the low price fool you, this product can do it all when it comes to 3D-animation and rendering! (Tony R. Boutwell, trb3@Ra.MsState.Edu) I finally received the information about Imagine for the PC. They are presently shipping Version 2.0 of the software and will release Version 3.0 in the first quarter of 1993 (or so they say). The upgrade from 2.0 to 3.0 is $100.00. To purchase Imagine 2.0, it costs $495.00 or if you are upgrading from another eligible (call them for info) modeler, it is only $200.00 plus shipping & handling. It requires a PC with 4 Megs, a math coprocessor, and DOS 5.0 or up and a Microsoft mouse and SVGA card. (Scott A Snowiss, sasst11+@pitt.edu) I work the same hours as Impulse so I had a friend call them for me. They told her the price was $495 but I could get it for $200 if I would send in a photocopy of the manual cover from another ANIMATION program. She asked them what animation program would do? They asked her which animation programs I had. She told them Deluxe Paint Animation and Disney's Animation Studio. They said either one would do. (Jim Nobles, usenet@ornl.gov) Impulse Inc. 8416 Xerxes Avenue North Minneapolis, MN 55444 1-800-328-0184 -------- The ray tracing and radiosity bibliographies that I maintain were updated around January of 1993 with the previous year's new references. See the computer graphics FAQ for more info, or just get them at princeton.edu: /pub/Graphics. (EAH) The 5th (and perhaps final) release of the collection of ray tracing abstracts is ready. I've put it in several ftp sites [the usual, such as princeton.edu: /pub/Graphics - ask Tom if you need one near you]. Get rtabs.4.93.shar.Z The abstracts (RTabs.tex) are only available in Latex form now. Significant changes have been made. A second file (RTnew.tex) contains just the abstracts added since the last release if you don't want to print the whole thing again. Version 5 - April 1993 Number of printed pages: RTnew - 11, RTabs - 95 Number of abstracts: RTnew - 34, RTabs - 334 (+ 45 non-unique refs) (Tom Wilson, wilson@forest.dab.ge.com) -------- In addition to the cyberware_demo.tar.Z file mentioned last issue, there is a new addition to the FTP site taurus.cs.nps.navy.mil:/pub/dabro. The file cyber.tar.Z contains some ASCII translations of a few of the 3D data sets that I did for someone who wanted a lower resolution data base. It contains several polygonal descriptions of a head, face, skull, vase, etc. The format of the files is a list of vertices, normals, and triangles. There are various resolutions and the name of the data file includes the number of polygons, eg. phred.1.3k.vbl contains 1300 polygons. (George Dabrowski, Cyberware Labs, dabro@taurus.cs.nps.navy.mil) -------- Polyray is a ray tracing program written by Alexander Enzmann It is at uni-oldenburg (it's also mirrored at wuarchive in mirrors/mirrors/graphics/...). It only comes in executable form for the PC but has some neat features that PoV does not have. It also supports animation within the script file for the scene. -------- There is a utility called KALEIDO which generates the coordinates/edge and face lists for 80 different objects. My favourites are the dodecahedron, icosahedron, soccer football and other exotic polyhedra made from the combination of triangles, squares, and hexagons(#18 and #33). It also includes the basic objects like the tetrahedron, cube and hexahedron. The author is Dr. Zvi Har'El (rl@gauss.technion.ac.il). KALEIDO is available from: wuarchive.wustl.edu:graphics/graphics/kaleido and at gauss.technion.ac.il. One slight problem is that the polygon vertex lists are not ordered for polygon rendering/Gouraud shading. I had to write a utility to do this automatically. (Michael S. A. Robb, michaelr@spider.co.uk) -------- Rayshade related: A font consisting of upper and lowercase letters and numbers formed from cylinders, spheres and torii is available, font.rh. There are no restrictions on its use. There is also a program, text_to_rayshade.c. (Paul Chamberlain, tif@austin.ibm.com) (Daniel Peisach, peisach@hydra.rose.brandeis.edu) ---- I have placed the new rsdefs (v2.0) on weedeater.math.yale.edu in the incoming directory. Changes include new objects (chessboards; text characters (font.rh); rounded boxes, cylinders, and discs; bathroom objects -- soap, soap-dish, drinking glass, toothbrush, and glass holder; jewels), a better interface for using objects and surfaces in scene files, and more example files. For those who have never heard of the rsdefs package -- the package is a group of files for use with rayshade that are #included into a scene file. The files define commonly used settings, constants, macros, surfaces and objects inorder to make them commonly accessible to the user and to help reduce the amount of work necessary for creating new scenes. There are also several example files that show the use of the predefined "creations" that also serve as general examples for the use of rayshade. The "creations" have been defined so that they impart no extra overhead in the way of memory to rayshade unless specifically invoked in a scene file. The creations only exist in the C-preprocessor's memory. Objects and surfaces can be used either as instances or as named objects (the "name" declaration for objects and "surface" declaration for surfaces). The objects can also be used inside aggregates (CSG, list, grid) and can be followed by transformation calls that will transform the whole object. Currently there are 57 surfaces, 184 superprimitives, 29 constants, viewing parameters for several different output media and several macros and textures defined. (Larry Coffin, lcoffin@clciris.chem.umr.edu) ---- By request, I have placed the source for the stereo image pairs I generated a while back on weedeater.math.yale.edu in the "incoming" directory. The file is called "ster.src.tar.Z" and contains the source for the "subs", "pipes", "chains" and "view" images. (Stuart Warmink, sw@groucho.att.com) ---- Joy over joy: there's a new Inetray version out. Apart from fixing a few un-niceties it has one major advantage over version 1.0.1: it can be used in pipes and with stdin redirection. This means that access to .ray files is no longer necessary in the normal case. Everything which is presented to inetray on stdin is automatically sent to all worker machines. That means that something like this works: $ echo "sphere 2 0 0 0" | inetray > sphere.rle Again, NO remote file access is required!!! Inetray is an application allowing you to concurrently raytrace an image using a lot of machines. The task is dynamically distributed to all machines offering this service. Inetray is based on the Rayshade 4.0 libraries. It does not require any modification to the rayshade source and is compatible with all patches (known to me). As usual, I uploaded inetray.1.1.0.tar.Z to maggia.ethz.ch where it can be collected by anonymous ftp. If you have any questions and/or comments please send mail to Andreas Thurnherr (ant@bernina.ethz.ch). ---- The February '93 issue of National Geographic Magazine features a 3 page foldout generated with Rayshade. The image shows the surface of Venus near a large double-vented volcano named "Sappas Mons." The picture was generated from NASA Magellan radar and altimetry data using Rayshade.4.0 modified to deal with large (~256Meg) heightfields and image files. The May issue of Scientific American has a short article on pp 26-27 which includes one of our Venus Landscapes. The cover of the April 23 issue of Science Magazine features yet another Venus landscape generated with Rayshade. The image shows the surface of Venus near a large circular feature called "Miarlaidji Corona." The rayshade heightfield used is 3556x3556 by 32 bit floats and an 8bit SAR radar image the same size was texture mapped onto the surface. This was done on a 4 headed SPARC 6/40 with 64Meg of RAM and a couple Gig of disk space, and took about 6 hours to render at size of 2200 by 2800 pixels. (David P. Anderson, dpa@io.isem.smu.edu) ---- Check out the June issue of Omni Magazine, page 52. The "computer-generated image of HIV created on a Cray Super Computer" was done with Rayshade. It really looks much larger in person :-):-). A larger version of this image may be found on fconvx.ncifcrf.gov in tmp/rayshade as virion.rle.Z. For more info you can contact me at mcgregor@ncifcrf.gov or Connor McGrath at mcgrath@ncifcrf.gov. (Please see the acknowledgment.txt file for a few more details). (George McGregor, mcgregor@ncifcrf.gov) ---- SCO Open Desktop has been using Rayshade rendered images in their demonstrations. (Robert Walsh, robertwa@sco.COM) ---- The following files are (temporarily, at least) available for anonymous ftp at ftp.ncsa.uiuc.edu in /outgoing/marca/natural-textures: NTRL-TXTRS.README grass-rocks.rle.Z grass02.rle.Z ivy-rocks02.rle.Z bark.rle.Z grass01.rle.Z ivy-rocks01.rle.Z ivy-stucko.rle.Z (David DeBry, ddebry@dsd.es.com) -------- Vivid/BOB and POV related: I have a new modeler out called Sculptura that you might want to try. It has Vivid and POV output, and it can read in DXF files, so you can use it to model new shapes, or you can use it as a pathway for DXF to POV or Vivid. There is a demo version at wuarcive.wustl.edu in /mirrors /mirrors/win3/demo/demo3d.zip (Michael Gibson, gibsonm@stein.u.washington.edu) -------- POV related: POVCAD and PV3D are two modelers for POV. faramir.informatik.uni-oldenburg.de is a good site for both (this site is mirrored at wuarchive - see note at the beginning of the roundup). The newest PV3D tends to be in /pub/dkbtrace/incoming as file pv3dv100.zip. There also exist a GUI called aewire, by Alexander Enzmann. Contact him (70323.2461@compuserve.com) for more information. ---- Ville Saaris expression evaluator code for PoV allows very easy animation generation using formulas on framenumber or time. Another but more complicated solution is Rayscene. (Andre Beck, beck@irzr17.inf.tu-dresden.de) ---- The Graphics Alternative BBS (510-524-2780) carries many POV related software packages, etc. ---- I wrote a PM (for IBM's OS/2) interface for DKB. The file is dkbpm.zip or dkbpm2.zip and is available at hobbes.nmsu.edu, in a graphics directory somewhere, sorry I can't remember the exact path. It has a statistics window with time stats, a bitmap image viewing window and a transcript window for progress reporting. Menus and dialogs to set all the options. Source is also included. I'm working on the next release of POV for PM and NT. The beta I have for OS/2 is pretty similar to the DKB version. The NT beta I have has a quantization thread that constantly quantizes the image and adjusts the palette accordingly. It also can launch multiple render threads if you have a multiprocessor NT machine. I'm in the process of migrating the quant and palette stuff back to OS/2. I'll let you know when povpm and povnt are available. (Michael Caldwell, mcaldwel@netcom.com) ---- Daniel Gross <entropy@Panix.Com> writes: I gave up on the Transputers -- sent 'em back -- and am now building a new parallel processor based on 386 motherboards. Cheaper, better performance, easier to port software. Plus, in a pinch, if I get lazy, I could just run Win4Workgroups or NT on each of 'em and get no-code concurrent multiprocessing. For now, though, I'm still trying the harder way -- i.e. modifying PoVRay code to optimize for parallel execution. ---- One of the best utilities I've found for POV it called SP - Dave's Spline- Path Generator. You can find this on the You Can Call Me Ray BBS. Basically, you make a data file of a number of points and some other information, and SP will calculate position and rotations for your camera. You can do acceleration/deceleration, etc... with it as well. Its downfall (at least as of version 0.3) is that it only does one frame at a time (you tell it which of the N frames to compute). It's relatively easy to make a batch file for this, though. (Jason Barile, barilejb@ctrvax.vanderbilt.edu) ---- I produce POV 3D fonts and have a range of about 500 so far. Price is about 65 UK pounds or 90 for two. The data is about 3-4 meg uncompressed for each font and each letter has to be #included and assigned a texture, details and examples are included with the font. The level of detail is very high, and looks good even when flying through the bowl of a "P" for example. I decided on a standard where the baseline of the font is at zero, with the leading height at 1, with the font being 1 unit deep. This makes changing fonts easier, though still a little fiddly adjusting kerning... There is as yet no easy way of making them - the process takes several hours of hard work with W4W macros. Available in Vivid format too. (Andrew Haveland-Robinson, andy@osea.demon.co.uk) -------- RTrace related: There is a new version of the RTrace ray-tracing package (8.2.0) at asterix.inescn.pt [192.35.246.17] in directory pub/RTrace. Check the README file. [Most, perhaps all, of this is mirrored at wuarchive in graphics/graphics/ray/RTrace. - EAH] The MAC RTrace 1.0 port is in directory pub/RTrace/Macintosh Thanks to Reid Judd (reid.judd@east.sun.com) and Greg Ferrar (gregt@function.mps.ohio-state.edu). For all the Mac users of RTrace, there is a Compact-Pro HQX file called movies.cpt.hqx in pub/RTrace/Macintosh, at asterix.inescn.pt [192.35.246.17]. In this file I've put 2 small animations to be played with SimplePlayer or any similar program (in the Mac, of course). For all the users of RTrace, there is a specification of the format RTrace uses in a Postscript compressed file called sffv8.ps.Z. [SFF is something like NFF, vastly extended to handle splines, textures, etc. - EAH] There is also a 3D Studio 1.0 file converter in pub/RTrace/scene-conv called 3ds2scn.awk. You must have a reasonably good AWK program (preferably gawk 2.14) to process the ASCII files that 3D Studio creates and convert them to SCN format. RTrace now can use the SUIT toolkit to have a nice user interface. Compile it with -DSUIT or modify the Makefile. SUIT is available at suit@uvacs.cs.virginia.edu I have binaries of RTrace with SUIT for SUN Sparc, SGI Indigo and DOS/GO32. Please contact me if interested. Here goes a short description of current converters from CAD/molecular/chemistry packages to the SCN format. The package programs are related as below (those marked with * have been modified) irit2scn IRIT ----------------| | NFF (nffclean, nffp2pp) sol2scn | | ACAD11 ---------------| | nff2sff | | mol2scn v scn2sff* v rtrace* ALCHEMY -----------> SCN -----------> SFF ----------> PIC or PPM ^ cpp | pdb2scn | picmix PDB -----------------| picblend | ppmmix* chem2scn | ppmblend* CHEMICAL --------------| | 3ds2scn* | 3D STUDIO --------------| | iv2scn* | IRIS Inventor -----------| The DOS port of RTrace is in pub/RTrace/PC-386 (rtrac820.arj, utils820.arj and image820.arj). See the README file there. Requires DJGPP GO32 DOS extender (version 1.09 included), which can be found in directory pub/PC/djgpp (and in many sites around netland). There are also demo scenes, manuals and all the source code... (Antonio Costa, acc@asterix.inescn.pt) ======== USENET cullings follow =============================================== Re: Intersection Between a Line and a Polygon (UNDECIDABLE??), by Allen B (ab@nova.cc.purdue.edu) Curiously, in modern PostScript, the point in a polygon problem can be solved even more easily. To wit: %! %%Title: Point in Polygon %%Creator: Allen B (ab@cc.purdue.edu) %%For: the amusement of comp.graphics regulars %%LanguageLevel: 2 %%DocumentNeededResource: humor sense thereof %%EndComments % This program will test whether a point is inside a given polygon. % Currently it uses the even-odd rule, but that can be changed by % replacing ineofill with infill. These are Level 2 operators, % so if you've only got Level 1 you're out of luck. % % The result will be printed on the output stream. % % Caution: only accurate to device pixels! % Put a huge scale in first if you aren't sure. % Point to test % PUT X AND Y COORDINATES HERE 50 75 % Vertices of polygon in counter-clockwise order % PUT ARRAY OF PAIRS OF COORDINATES HERE [ [ 0 0 ] [ 100 0 ] [ 100 100 ] [ 67 100 ] [ 67 50 ] [ 33 50 ] [ 33 100 ] [ 0 100 ] ] dup 0 get aload pop moveto dup length 1 dup 3 1 roll sub getinterval { aload pop lineto } forall closepath ineofill { (Yes!) } { (No!) } ifelse = ------------------------------------------------------------------------------- Obfuscated Postscript Ray Tracer, by Takashi Hayakawa (h-takasi@isea.is.titech.ac.jp) [This was an entry in the Obfuscated Postscript contest some time back. A pretty minimal piece of work and the image looks decent, too. - EAH] # This is a shell archive. Remove anything before this line, # then unpack it by saving it in a file and typing "sh file". # # This archive contains: # Tiny_RayTracing.HINT Tiny_RayTracing.ps # LANG=""; export LANG PATH=/bin:/usr/bin:$PATH; export PATH echo x - Tiny_RayTracing.HINT cat >Tiny_RayTracing.HINT <<'@EOF' Tiny_RayTracing.ps by Takashi Hayakawa (h-takasi@isea.is.titech.ac.jp) is a ray tracing program in only 762 bytes (plus header)! BEST OBFUSCATED ARTWORK -- 1st prize -- The 2nd most coveted prize. These combine obfuscation with great artwork. Don't send this one to a printer. It will take too long. Display it on the screen and be ready to wait a while. The picture is well worth it. If you want to print the picture much faster, use this version: %! Tiny RayTracing by HAYAKAWA,Takashi<h-takasi@isea.is.titech.ac.jp> /p/floor/S/add/A/copy/n/exch/i/index/J/ifelse/r/roll/e/sqrt/H{count 2 idiv exch repeat}def/q/gt/h/exp/t/and/C/neg/T/dup/Y/pop/d/mul/w/div/s/cvi/R/rlineto{load def}H/c(j1idj2id42rd)/G(140N7)/Q(31C85d4)/B(V0R0VRVC0R)/K(WCVW)/U(4C577d7)300 T translate/I(3STinTinTinY)/l(993dC99Cc96raN)/k(X&E9!&1!J)/Z(blxC1SdC9n5dh)/j (43r)/O(Y43d9rE3IaN96r63rvx2dcaN)/z(&93r6IQO2Z4o3AQYaNlxS2w!)/N(3A3Axe1nwc)/W 270 def/L(1i2A00053r45hNvQXz&vUX&UOvQXzFJ!FJ!J)/D(cjS5o32rS4oS3o)/v(6A)/b(7o) /F(&vGYx4oGbxSd0nq&3IGbxSGY4Ixwca3AlvvUkbQkdbGYx4ofwnw!&vlx2w13wSb8Z4wS!J!)/X (4I3Ax52r8Ia3A3Ax65rTdCS4iw5o5IxnwTTd32rCST0q&eCST0q&D1!&EYE0!J!&EYEY0!J0q)/V 3 def/x(jd5o32rd4odSS)/a(1CD)/E(YYY)/o(1r)/f(nY9wn7wpSps1t1S){[n{( )T 0 4 3 r put T(/)q{T(9)q{cvn}{s}J}{($)q{[}{]}J}J cvx}forall]cvx def}H K{K{L setgray moveto B fill}for Y}for showpage You can change the "3" in "3 def/x" on line 10 to be 1 for more resolution (but a much slower print) or "6" for a faster print (your printer might be able to handle this) with less resolution. @EOF chmod 644 Tiny_RayTracing.HINT echo x - Tiny_RayTracing.ps cat >Tiny_RayTracing.ps <<'@EOF' %!OPS-1.0 %%Creator: HAYAKAWA,Takashi<h-takasi@isea.is.titech.ac.jp> /A/copy/p/floor/q/gt/S/add/n/exch/i/index/J/ifelse/r/roll/w/div/H{{loop}stopped Y}def/t/and/C/neg/T/dup/h/exp/Y/pop/d/mul/s/cvi/e/sqrt/R/rlineto{load def}H 300 T translate(V2L&1i2A00053r45hNvQXz&vUX&UOvQXzFJ!FJ!J!O&Y43d9rE3IaN96r63rvx2dcaN G&140N7!U&4C577d7!z&&93r6IQO2Z4o3AQYaNlxS2w!!f&nY9wn7wpSps1t1S!D&cjS5o32rS4oS3o Z&blxC1SdC9n5dh!I&3STinTinTinY!B&V0R0VRVC0R!N&3A3Axe1nwc!l&993dC99Cc96raN!a&1CD E&YYY!F&&vGYx4oGbxSd0nq&3IGbxSGY4Ixwca3AlvvUkbQkdbGYx4ofwnw!&vlx2w13wSb8Z4wS!J! c&j1idj2id42rd!X&4I3Ax52r8Ia3A3Ax65rTdCS4iw5o5IxnwTTd32rCST0q&eCST0q&D1!&EYE0!J &EYEY0!J0q!x&jd5o32rd4odSS!K&WCVW!Q&31C85d4!k&X&E9!&1!J!v&6A!b&7o!o&1r!j&43r!W) {( )T 0 4 3 r put T(/)q{T(9)q{cvn}{s}J}{($)q{[}{]}J}J cvx}forall 270{def}H K{K{L setgray moveto B fill}for Y}for showpage @EOF chmod 644 Tiny_RayTracing.ps exit 0 ------------------------------------------------------------------------------- END OF RTNEWS