*"Light Makes Right"*

December 12, 2005

Volume 18, Number 1

Compiled by Eric Haines, Autodesk, 10 Brown Road, Ithaca, NY 14850 [email protected] . Opinions expressed are mine, not Autodesk's.

All contents are copyright (c) 2004,2005, all rights reserved by the individual authors

Archive locations: text version at
http://www.acm.org/tog/resources/RTNews/text/

HTML at
http://www.acm.org/tog/resources/RTNews/html/

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

- Introduction
- Ray Tracing Roundup
- Newish Books, by Eric Haines
- More on Randomly Sampling Bounding Volumes, by Mateu Sbert
- Image Comparison, by Chris Cason, Eric Haines, and Greg Ward
- Real-Time GPU Spheres, by John Stone
- Plane Equations of a Tetrahedron, by Paul Kahler
- Ray/Tetrahedron Intersection, by Paul Kahler
- K-d Tree Comments, by Ingo Wald, Gordon Stoll, Vlastimil Havran, and Eric Haines
- Processor Level Optimization Verification, by Paul Kahler and Anonymous
- SIGGRAPH 2005 Report, by Eric Haines

So, the coolest things I saw at SIGGRAPH 2004 (yes, 4): the fingernail printer in the Guerilla Studio, and the Lightspace display on the exhibit floor. 20 LCDs on top of each other in a 4" deep block, cycled through at 50 frames per second. Not a perfect technology by any means, and there were some funky artifacts since only the closest object *from one direction* is displayed (what happens if you look around that object? You see a hole in space). But it was cool to see a display with lots of color, no weird technology, and that worked from a wide range of angles without special headgear, etc.

Emerging Technologies for 2004: The high dynamic range (HDR) display from Sunnybrook Technologies has been developed further from 2003's demonstration, and looked pretty cool; in 2005 it is now something you can buy. The technology for getting an overall range of more than 8 bits per channel is to add a set of LEDs for a backlight, which seems like it should be inexpensive in the long run. There were other interesting demos of other technologies and ideas, such as super-high refresh rate displays (1000 Hz) that could hide images by displaying the image and then immediately displaying its inverse. Due to persistence in the eye the two images cancelled to a gray, but you could use a pair of glasses with LCDs flickering that would then show just the hidden image. Multiple different images could be hidden this way in the same refresh set of images. There were also other oddities and artsy stuff: virtual swimming, a set of robotic floor tiles that would constantly shuffle to stay in your path of walking, mixed reality on PDAs with cameras that show you unreal objects mixed with a real scene.

Art show: I liked "All This Useless Beauty", which was a panorama over space. Imagine taking panorama shots while walking and seamlessly blending these into one very long image (15000 x 89 pixels on the web). See it here: http://www.santoroland.com/siggraph2004/artgallery.html

My favorite sketch from SIGGRAPH 2004 was "Experimental Validation of Analytical BRDF Models" by Addy Ngan et alia, MIT. It compared various lighting models with high-resolution surface reflectance data and found two interesting things: Cook-Torrance and Ashikmin models were quite good overall, LaFortune was fairly good but sometimes falls apart, and Phong- Blinn and Ward not so good (not a surprise). Second thing: the half-angle vector formula used for specular reflections is actually more in accord with real surface reflection than the mirror vector formula. Surprising. Find it and related work at http://people.csail.mit.edu/addy/research/.

SIGGRAPH 2005? Well, I've rambled enough in this introduction for now, so that article will come later in this issue.

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Recently published and available at: http://www.8dn.com/~jm/

Jeff kindly summarized some of his research for the RTNews as he went along, it was good stuff, but I kept getting distracted and never got an issue out. So if you'd like to read a really long issue of the RTN (actually, it's better than that), go check his work out. He offers, among other things, a comprehensive survey of papers and patents related to BVH and ray tracing hardware. Code for various routines are in the appendix and on the website. The thesis is somewhat oriented towards making ray tracing hardware, but there are a number of interesting theory and software bits. For example, he introduces a new ray/bounding-box intersection test based on Pluecker coordinates, and discusses one based on using the separating axis theorem. Surprisingly, these two methods appear to usually be faster than the standard slabs method. The bad news: no ray/box intersection distance is computed with the new tests, but some traversal schemes do not need this.

For bounding volume hierarchy creation (BVH), he finds that about 6 triangles per leaf bounding box is a good stopping criteria. He does some experiments with BVH traversal, changing the order in which children are traversed based on ray direction, i.e. attempting to hit the closer child first (important for eye-related rays, of course; not important for shadow rays). The speedup for some scenes is quite large. That said, it would have been interesting to compare this algorithm vs. Smit's skip pointers flattened tree traversal scheme for BVH, which gets rid of clever schemes in favor of lean and fast code (More about Smit's scheme, and a URL to it, later in this issue). But I guess Jeff wanted to graduate before he retired.

There is also much exploration of ways of representing bounding boxes as sets of integers (vs. floats), with the intent of reducing the memory footprint while speeding processing. Anyway, I won't spoil the whole thing for you; give it a look!

________

As of SIGGRAPH 2005, a noncommercial version of OpenRT will be released to the public. The version release will - for the moment - be a slightly limited, PC/Linux-only version of OpenRT. If you are interested in getting a copy, please subscribe to the "noncommercial" mailing list at

https://scihparg.cs.uni-sb.de/cgi-bin/mailman/listinfo/noncommercial

You will then receive email providing you with a download link and some additional information.

FAQ at http://www.openrt.de/GettingOpenRT/FAQ.php

________

MAXIMA: This beastie has finally been GPL'ed and made free, after too many years. This is an equation manipulation package with graphic capabilities. Not as good as Mathematica, but $1500 cheaper: http://maxima.sourceforge.net/

________

http://www.cs.utah.edu/~sparker/images.html has all sorts of heavy-duty ray-traced images, with movies at the bottom. My fave, just for the resources spent: http://www.cs.utah.edu/~sparker/images/seurat/bigcbox.jpg - a tera-ray monte-carlo rendering of the Cornell Box. This was generated in 2 CPU years on an Origin 2000. The full image contains 2048 x 2048 pixels with over 100,000 primary rays per pixel (317 x 317 jittered samples). Over one trillion rays were traced in the generation of this image.

________

Yet another free ray tracer: http://www.yafray.org/ - with OpenEXR support, lots of features, and meant to work with Blender.

________

Wouldn't it be nice to have all the tables of contents of all journals at your fingertips, in one handy place? Here you go:

http://www.math.utah.edu/ftp/pub/tex/bib/toc/index-table.html

________

You may be interested in a rewritten Quake 3 with using OpenRT. It runs in real-time using a network of 20 AMDs with 1800 MHz. I have screenshots and an impressive video on this page:

http://games.slashdot.org/games/04/06/07/2350243.shtml

-- Daniel Pohl (elchtest(at)quake(.)de)

____

I had *nothing* to do with that Quake 3 stuff entirely, I promise. It's just some of our crazy students, that don't even have the source code (only precompiled libraries and the API), who started to play around with it.

There's even a more interesting game than the entire quake/unreal thing: one of our students has created a game with lots of different effects (including sun-created caustics in shallow regions of the sea), animated objects, a sun/sky illumination model, efficient handling of hundreds and thousands of light sources, etc., etc....

Check it out: visit http://graphics.cs.uni-sb.de/~morfiel/oasen/index.html, then click on screenshots. *that* one is impressive if you see it in real time.

-- Ingo Wald (wald(at)mpi-sb(.)mpg(.)de)

________

Open source GPU ray tracers

I just wanted to inform that we (Filip Karlsson, Carl Johan Ljungstedt and Ulf Assarsson) submitted an open source GPU ray tracer to GPGPU. It is part of a master thesis project. I'm in a supervisor role nowadays, but I've been deeply involved in this project.

The practical contribution is that we actually got it working under OpenGL and Cg, which has been very messy with all driver bugs, Cg-compiler bugs, and unwritten "features" of the PixelShader 3.0-support of the NV 6800. Theoretically, it is not very hard to write a GPU-ray tracer, but in practice it was a totally different story, and we have spent at least 3 months, more or less, full time. Our hope is that people will use it as a starting place for continued research/development or whatever to boost the evolution of GPU-ray tracing. As a small research contribution, we also test standard grids vs. grids and proximity clouds. The largest model we tested was the classic Buddha of 1M triangles.

Home page with thesis report and open source here: http://www.ce.chalmers.se/edu/proj/raygpu/

There is also a very nice "competitor" work :-), by Martin Christen, published the same day at GPGPU, here: http://www.clockworkcoders.com/oglsl/rt/

[That one has lots of documentation and a Sourceforge code base. -EAH]

His version is also open source and uses Direct3D and HLSL. He also has a version running under OpenGL and GLSL. I've been testing his Direct3D ray tracer some and it works fine. He has his own implemented CPU ray tracer against which he compares performance, while we use Mental Ray.

Both Christen's and our version can import 3DS-files, although the shading of course is much more limited than in 3DStudio.

-- Ulf Assarsson (ulf(.)assarsson(at)illuminatelabs(.)com)

____

Here's a tech report that covers some of the ray-tracing-on-GPU stuff that Rodrigo Toledo's been doing:

http://www.loria.fr/~levy/php/article.php?pub=../publications/papers/2004/ray_tracing_gpu

-- John Stone (johns(at)ks(.)uiuc(.)edu)

____

The Graphics Hardware 2005 conference had one paper of relevance to ray tracing. See http://www.graphicshardware.org/program.html for the full program, along with links to PDFs and slide sets.

KD-Tree Acceleration Structures for a GPU Raytracer, T. Foley, J. Sugerman, presentation at: http://www.graphicshardware.org/presentations/foley-kdtreegpu-gh05.ppt

____

GPGPU.org has lots of great rendering news relating to cutting-edge research and the GPU. For example, included in the news area http://www.gpgpu.org/cgi-bin/blosxom.cgi/Advanced%20Rendering was the abstract of this master's thesis, among other things:

A Comparison of Acceleration Structures for GPU Assisted Ray Tracing

Recently, ray tracing on consumer level graphics hardware has been introduced. So far, most published studies on this topic use the uniform grid spatial subdivision structure for reducing the number of ray/triangle intersection tests. For many types of scenes, a hierarchical acceleration structure is more appropriate. This thesis by Lars Ole Simonsen and Niels Thrane of University of Aarhus compares GPU based traversal of kd-trees and uniform grids with a novel bounding volume hierarchy traversal scheme. The three implementations are compared in terms of performance and usefulness on the GPU. The thesis concludes that on the GPU, the bounding volume hierarchy traversal technique is up to 9 times faster than its implementations of uniform grid and kd-tree. Additionally, this technique proves the simplest to implement and the most memory efficient.

http://www.larsole.com/files/GPU_BVHthesis.pdf

Ulf Assarsson comments, "they also present some GPU source code".

________

A history of MAGI, the first production house to use ray tracing and CSG:

http://accad.osu.edu/~waynec/history/tree/magi.html

A number of its employees went on to found Blue Sky Studios. Note that this page is part of a larger site giving a history of computer graphics:

http://accad.osu.edu/~waynec/history/ID797.html

Don't miss the extensive lessons section:

http://accad.osu.edu/~waynec/history/lessons.html

There's lots of other pages around with all sorts of things, e.g. check out the index:

http://accad.osu.edu/~waynec/history/content-index.html

________

By the way, there's a wikipedia entry for ray tracing:

http://en.wikipedia.org/wiki/Ray_tracing

Feel free to go fix anything you don't like (I did, cleaning out weirdness about the definition of "backwards ray tracing"; asking what people think this term means is like asking them where they put their matrix translation values, in the right column or the bottom row; it's a religious thing.)

There's also a nice page on POV-Ray:

http://en.wikipedia.org/wiki/POV-Ray

with plenty of worthwhile links.

________

A fellow named Bruce Dawson of the Xbox advanced technology group has also published some interesting papers of good practical alternatives to the evil wicked bad epsilon tests:

http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm

-- Steve Hollasch (hollasch(at)acm(.)org)

[I should note that Steve's page, http://stevehollasch.com/cgindex/index.html, has a bunch of useful links, though it's starting to suffer a little from url-rot. That said, what is nice is that Steve has stored away a number of worthwhile articles at his site itself, so they won't get lost. - Eric]

________

I released a small raytracer that now runs on smartphones at:

- Emmanuel Viale (emmanuel(.)viale(at)wanadoo(.)fr)

____

It also had to happen someday, a ray tracer in Perl:

http://perl.plover.com/RayTracer/

____

And a ray tracer in six different languages, including LISP:

http://www.ffconsultancy.com/free/ray_tracer/languages.html

________

As mentioned last issue, the LZW (GIF) patent has expired everywhere, as of July 7, 2004: http://www.unisys.com/about__unisys/lzw/. I mention it again only because I ran across a wonderful passage at http://news.com.com/2100-1032-1014236.html, worth recording for posterity:

But Unisys credited its exertion of the LZW patent with the creation of the PNG format, and whatever improvements the newer technology brought to bear.

"We haven't evaluated the new recommendation for PNG, and it remains to be seen whether the new version will have an effect on the use of GIF images," said Unisys representative Kristine Grow. "If so, the patent situation will have achieved its purpose, which is to advance technological innovation. So we applaud that."

________

So what's your favorite mathematical theorem? Here's a list:

http://personal.stevens.edu/~nkahl/Top100Theorems.html

Personally, I love Pick's Theorem, it applies so nicely to pixel grids and is surprising and elegant: http://www.mcs.drexel.edu/~crorres/Archimedes/Stomachion/Pick.html

________

Dictionary of Algorithms and Data Structures, from NIST:

________

A wiki about computing effects of lighting:

http://lightingwiki.com/FrontPage

________

http://webexhibits.org/causesofcolor/0.html

I like the concept of "15 causes of color". If we could only stamp out just one of these causes in our lifetime! Actually, the homepage now talks about just 3 causes of color: http://webexhibits.org/causesofcolor. Anyway, a pretty site.

Interestingly enough, the Cornell Box gets used in real-life: http://webexhibits.org/causesofcolor/1H.html, and you can even change the lighting (in a javascripty way). Gosh, it seemed so much bigger in virtual reality. (Actually, I was around when the first physical Cornell box was made, around 1984, for perceptual experiments; I recall it was maybe two or three feet high).

________

A triangle mesh library that is GPL'ed and looks useful: http://www.cs.princeton.edu/gfx/proj/trimesh2/

________

I've heard good things about the Farbrausch demo tool, at http://www.farb-rausch.com/ ("demo" meaning "those tiny graphics effects programs set to music"). (recommended by Vincent Scheib)

When I tried, this site's download links failed. Some googling turned up one that worked: http://www.softonic.de/file.phtml?&id_file=35387&action=view&view=downloads

I looked over the tutorial briefly (run file werkkzeug1.exe). One cool thing here is that they have a pretty elaborate way of generating procedural textures (which is the key to having tiny demos, procedural everything). The program looks quite involved, but just walking through the tutorial gave me an appreciation of some of the elements that go into making a demo.

________

Just cool links (most of these are in my new public bookmarks list at http://del.icio.us/erich666):

http://www.pacifict.com/Story/ - best skunkworks story ever. Ken Turkowski comments on the product itself: "It's great! It's not just graphing, you know. It's also algebra and various kinds of differential calculus. One of the neatest things is direct manipulation on symbols, i.e. if you have an equation and want to move a term from one side of the equals sign to another, you just drag it over!"

http://www.krazydad.com/visco/ - a rainbow of sci-fi magazine covers. Cute.

http://www.michaelbach.de/ot - many great illusions here, old and new. My current favorite mind-fry: http://www.michaelbach.de/ot/col_lilacChaser/index.html

http://www.ianrowland.com/MiscPages/Mrangryandmrscalm.html - a new illusion. Squint. (from Ronen Barzel)

http://www.gigapxl.org/ - Imagine a single camera that takes a photo that's equivalent to 600 professional photos (or 10,000 TV screens) in terms of resolution. Pretty wild; check out the website: photos of cityscapes, which they then zoom in on a single window. (from Michael Cohen)

http://www.rendermagazine.com/ - Read the URL before clicking. What could it be? Wrong. (from Neil Gatenby)

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"Fundamentals of Computer Graphics" by Peter Shirley et alia, http://www.amazon.com/Fundamentals-Computer-Graphics-Peter-Shirley/dp/1568814690, has come out in a second edition this year. Lots of new material (270 pages worth), and lots of error cleanup of the first edition. This book seems likely to become the new "Foley & van Dam" for computer graphics (though the field has grown so much since that book, "Computer Graphics: Principles and Practice," that it's a different world). It looked worthwhile from my brief skim of the Table of Contents. Currently it is on the top of my pile of books, daring me to read it at lunchtime instead of the backlog of Wireds and Computer Gaming Worlds clogging up my valise.

"Graphics Tools: The JGT Editors' Choice", edited by Ronen Barzel, http://www.amazon.com/exec/obidos/tg/detail/-/1568812469, is a collection of articles by the editors of the "journal of graphics tools" of what they consider their favorite articles published over the past nine years. This could be thought of as the sixth "Graphics Gems" book, in some ways (since the goal of the journal is to publish tools for computer graphics, like Graphics Gems). Yes, I'm an editor; no, I don't get a dime on book sales. If you don't have back issues of JGT available to you, I recommend it, as there are some good ray tracing articles (and much else) in there.

"Foundations of Multidimensional and Metric Data Structures", by Hanan Samet, http://www.elsevier.com/wps/find/bookdescription.cws_home/706187/description#description. Each time I've run into Hanan at SIGGRAPH he's been working on this book, year after year. It's finally going to press in November. It looks to be pretty darn comprehensive, with a number of data structures relevant for computer graphics and for other multidimensional search and sort areas. He says this book will actually complement, not replace, his (now out-of-print) books on the topic from the late 80's.

Those are the ray tracing related books that come to mind. Of course, Pharr and Humphrey's "Physically Based Rendering" book has been out for more than a year now, and why don't you have one yet? See the last RTN for my brief review.

There were also some other graphics books that came out in the past year that appealed to me, but since they're not ray tracing related I won't dwell on them. "GPU Gems 2", edited by Matt Pharr (does he ever sleep?), has a lot of chewy material. I particularly appreciated seeing articles like John Owens' "Streaming Architectures and Technology Trends." Samples at http://developer.nvidia.com/object/gpu_gems_2_home.html.

"Real-Time Collision Detection", by Christer Ericson, http://www.amazon.com/exec/obidos/tg/detail/-/1558607323. It covers the topic thoroughly, and keeps focused on doing this task at interactive rates.

"Practical Linear Algebra: A Geometry Toolbox", by Gerald Farin and Dianne Hansford, http://www.amazon.com/gp/product/1568812345. This is essentially a second edition of "The Geometry Toolbox". It's a nice, approachable book on linear algebra, with many illustrations. I appreciate the authors' attempts to build up an intuition of what the various equations mean. For most graphics professionals the book won't be anything new until about Chapter 7, "Eigen Things" (and as I've said before, how can you dislike a book with a chapter title like that?). The only unfortunate bit is that the postscript files that go along with the book are no longer available on the web, the URL is dead last I checked.

"High Dynamic Range Imaging", by Erik Reinhard, Greg Ward, Sumanta Pattanaik, and Paul Debevec, http://www.amazon.com/gp/product/0125852630. Coming out soon. I've gotten a glimpse at Paul's section. Lots of practical advice and theory all pulled together, putting in all those useful bits that can't fit (and normally don't get presented) in articles; just what a book is for.

I'm interested to page through "Real-Time Cameras", by Mark Haigh-Hutchinson, http://www.amazon.com/exec/obidos/tg/detail/-/0123116341. It is more for video-game programmers, discussing techniques of camera control and response to occlusion from nearby walls, etc. I'm seen this done poorly enough times that I'm interested to learn any knowledge he has to impart.

"Advanced Game Development with Programmable Graphics Hardware", by A. Watt and F. Policarpo, http://www.amazon.com/exec/obidos/tg/detail/-/156881240X. The first four chapters look to be a good treatment of theory and practice concerning the GPU, then about a fifth of the book is focused on Policarpo's Relief Texture Map research (which does look nice, but you might end up learning more than you want about the technique). Then a quick effects chapter, and the last half of the book is on animation and game engine architecture.

"Mathematical Illustrations", by Bill Casselman, http://www.math.ubc.ca/~cass/graphics/manual/. Pretty wild book, mainly talking about controlling Postscript by using its programming language, including how to draw in 3D with hidden surfaces. It looks like a fun way to learn about Postscript's power. Also, the whole darn book is free online!

"Production Rendering: Design and Implementation" edited by Ian Stephenson, http://www.amazon.com/gp/product/1852338210. I haven't seen this one yet, but it's on my wish list; now you know what to get me for Christmas. From one of the authors: "This is the first book dedicated to teaching how to write your own RenderMan-compliant (or similar) production renderer. It includes separate chapters on shader compilers and shader interpreters, and presents a single architecture for incorporating ray tracing and global illumination into a micropolygon framework. It was written more or less equally by seven experienced graphics software developers, each of whom have published a renderer. The other authors: Mark Elendt (Mantra), Rick LaMont (RenderDotC), Jacopo Pantaleoni (Lightflow), Scott Iverson (AIR), Paul Gregory (Aqsis), and Matthew Bentham (RenderDrive)."

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- Choose a random face based on area
- Choose a random point uniformly on that face
- Choose a random direction with respect to normal N

I think, for the sake of clarity, point 3 should be changed to:

- Choose a cosine distributed random direction with respect to normal N

I'm sure this is what authors wanted to say, because (if I've checked well) the line generation they give below the algorithm corresponds to this cosine generation.

I have with my students already published in several places how to sample global lines from bounding boxes. You can find it, for example, in:

Francesc Castro, Mateu Sbert, "Application of quasi-Monte Carlo sampling to the multi-path method for radiosity", International Conference on Monte Carlo and Quasi Monte Carlo Methods '98, Claremont (USA), 1998, published by Springer Verlag

where I have described the above method, and more recently my tutorial (with Andrey Iones and S.Zhukov) on Integral Geometry in Eurographics 2001, Manchester.

It can be easily proven that the selection of pairs of random points on a sphere is a very particular case of the above technique.

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http://www.ks.uiuc.edu/Research/vmd/images/collections/openglshader/2004/spheretrace.jpg

The ray traced spheres outperform polygonal spheres using the fragment lighting in most cases, and they have the advantage of always looking spherical in profile regardless of their on-screen size, which is nice when you're displaying molecules.

One could ray trace any object inside of the bounding box, with just a few changes to the code, but spheres and cylinders are the main object types of interest in molecular visualization. With some work, I think I can gain another 2x or more in performance, which would give the ray traced spheres a significant advantage over polygonal spheres. My plan is to change the code to use a billboard rather than a full bounding box. The billboard would always be oriented so it's normal aligns with the view direction, and with this I should be able to eliminate the 2-times overdraw that occurs with the axis aligned bounding box method. Beyond that I think I can also make the shaders generally more efficient with a little work.

Once I'm done with the spheres, I'll implement cylinders, and after that I'll probably write a ray-casting volume renderer... Exciting stuff!

[Unlike other similar work I've seen, this one actually has perspective distortion, i.e., it's not just an orthogonal projection of the spheres. - EAH]

Yeah, in fact my code has to work for both perspective and orthographic projections since this is going into a real application and not just a cute one-time siggraph demo or something :-)

I'd been planning to do some sort of sphere rendering trick using GLSL for about 6 months, and finally got all of the kinks worked out of my main GLSL shader (lots of NVidia, ATI, 3DLabs driver bugs to sidestep along the way). Earlier this fall I was thinking I'd do something much simpler than this, but I decided to give ray tracing a shot after two of my colleagues mentioned they'd been working on similar things with decent results. Russell Taylor wrote a nice short paper on rendering non-polygonal objects with programmable shading:

ftp://ftp.cs.unc.edu/pub/publications/techreports/04-023.pdf

Directly Rendering Non-Polygonal Objects on Graphics Hardware using Vertex and Fragment Programs, Russell M. Taylor II, TR04-023, UNC Chapel Hill Dept. of Computer Science, 2004.

He's got a more sophisticated implementation than I have, though I think mine is faster (as a result of simplicity) and better suited to my particular purpose since my implementation is very closely tied to my application. Russell is using Cg for his stuff. Rodrigo Toledo at INRIA/Nancy has a cool piece of code he's written for ray tracing large factory models using the ARB vertex/fragment shader stuff. His implementation ray traces spheres, cylinders, and torii, and he's spent a lot of effort on tuning his performance as well as getting good results with the limited floating point precision in some programmable pipelines. See http://www.loria.fr/~levy/php/article.php?pub=../publications/papers/2004/ray_tracing_gpu

[I commented: It's a kind of wild approach; does it work for anything but bunnies and other soft stuff without hard edges?]

Their method definitely works for much more than bunnies. :-) Their approach is very similar to what I'm doing, but they've done some extra work exploring the cost of the "empty" parts of the bounding geometry, point, or billboard. Rodrigo has a nice demo which renders a huge factory model interactively using this ray tracing technique. His large model is rendered with spheres, cylinders, torii, and triangles as I recall. He and I are planning to see if we can create a molecular surface rendering implementation based on this same approach, though that's a much more complex problem for various reasons.

____

I asked John if anything has happened since he wrote me (which was around January 2005). He replied:

In the months that have passed since our emails, the code I wrote about was released in VMD 1.8.3 and a large number of my VMD users benefit from the GLSL-based GPU sphere ray tracing when making screenshots of molecules or quick movie renderings when they don't want to take the time to run one of the various software renderers that VMD can export molecular scenes to.

As is always seemingly the case, the final version of my GPU sphere ray tracing code that's in the shipping program runs a bit slower than the development version did because I had to add various workarounds for bugs in the GLSL implementations that are in the field. Also, my initial shader implementations didn't have all of the 3-D texturing code and other features that the final version has. The performance is good, but could still be improved if I broke the implementation into separate shaders for perspective and orthographic projections, 3-D texturing on/off, etc. Now that there are better shader performance analysis tools coming out for GLSL and the drivers are much improved, I plan to revisit the performance issues in my implementation and see what I can do to improve on it.

The fastest ray tracing implementations I've seen to date were hand-coded GPU assembler programs that take great pains to do just the right things for the target video board. My implementation doesn't beat these, but it's flexible and the ray tracing is only part of what the shader is doing so it's hard to compare apples-to-apples when I look at my implementation versus the others that are out there.

I've recently gotten various queries from a few CS grad students interested in working on shaders that draw perspective correct spheres in other ways, it'll be interesting to see what other GPU methods people come up with.

I had hoped to write a GPU-based ray casting volume renderer by this time, but other development tasks have distracted me from my shader work recently and I probably won't get that done until next year. Maybe that'll make an interesting topic for a future RTN if I do anything interesting/unique there.

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There are some problems with rounding on some platforms, depending on the compilation options, because we use double-precision to integer conversions in our 3d noise hash function.

Of course the question is, how do we define 'too different'? We could simply say that if any pixel is different by any amount, then it's counted in the total of different pixels.

However I am wondering if there is a more formal way to evaluate the differences, e.g. by looking at how much a given pixel differs from the reference pixel, and then somehow summing this into some sort of result.

Do you know of a specific means of doing this which can give us a number as a e.g. 'percentage difference' or something, and which has (or would have, if we used it) reasonable industry acceptance?

____

Eric replied:

Usually a "sum of squares" approach is the simplest method I know, i.e. take the difference between what's expected and what you got and square it for the pixel, add these differences up to get a total. I don't know if there's a formal way of expressing this; Greg, do you?

Greg might also be able to recommend a better metric. For example, Visual Difference Predictor, a metric Scott Daly came up with that seems to have good correlation with the perceptual difference (vs. pure numerical difference) of two images. I don't think this measure is appropriate for your task, you probably want something that's simpler since your goals are more conformance testing of the code than actual visual result. Anyway, Greg, is there some "official" way of expressing or normalizing some simple metric like distance-squared for image comparison?

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Greg Ward replied:

Mean squared error (MSE) is frequently used to compare images, though it has a poor correlation to visible differences. A better pixel-wise comparison is to use CIE Delta E* 1994, which is a complicated but manageable formula to compute color differences. Better still is Scott Daly's VDP metric, though it is rather challenging from an implementation standpoint. (I don't have an implementation myself, else I'd share it with you.) As Eric points out, this may be overkill for conformance testing, anyway, though you might consider taking the maximum error rather than the mean if you are looking for bugs. The only problem is if the round-off concerns the locations of samples, in which case your maximum error could be enormous. The eye doesn't care if an object moves one pixel to the left, but any pixel-wise comparison will show this up as a huge difference.

Your biggest problem may be with your random number generator, which you may wish to disable or replace with a low-discrepancy sequence. Even then, if POV-ray is like Radiance, round-off error in a test to determine which rays to trace can throw everything off if the random numbers are a simple sequence, since you will get out of step between machines. All correlations are lost at that point. That's why I would recommend either turning the random number generator off (i.e., returning 0.5 every time) or keying the sequence off pixel location or something repeatable.

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There is an extremely elegant way to solve the problem. Please put this in RTN.

1) A point/vertex can be represented by a column vector [x,y,z,1]. 2) A plane equation ax+by+cz+d=0 can be represented by a row vector [a,b,c,d]. 3) A point can be plugged into (tested in) a plane equation by taking the product of these (plane*point). 4) A tetrahedron can be represented by a 4x4 matrix whose columns are its vertices. 5) A tetrahedron in this point-form can be transformed by multiplication with standard transform matrices. 6) A tetrahedron can also be represented by a 4x4 matrix whose rows are the plane equation vectors. 7) A tetrahedron in this plane-matrix form can be transformed similar to the point version, as I recall, you need to use the inverse transform and perhaps multiply on the other side?

Now the magic:

8) The inverse of the point-tetrahedron-matrix is the plane-tetrahedron- matrix. You can verify this by plugging the points into the resulting plane equations. All 16 combinations can be done by multiplication of the plane and point matrices. Since the result is an identity matrix (by definition of the inverse) we see that 3 points lie on each plane. We also see that the plane equations are scaled such that the point not contained in the plane produces a value of 1 when taking the product. This indicates that the plane normals (a,b,c of each row) are pointing inward.

I believe two more things happen that are really nice:

9) The barycentric coordinates (w,x,y,z) of a point inside the tetrahedron can be determined by multiplying the plane-tetrahedron-matrix by the point. Obviously if the point is on one of the faces, one of these coordinates is zero. I believe the plane equations are such that it all just works out - you get your point as a linear combination of the 4 vertices.

10) All of this works in 2D as well.

I suspect the points can be found from plane equations in a similar way, but they would not have a W coordinate of 1 unless you scaled the plane equations properly first - or divide by W after. Obviously with the scaling above, the points are simply the inverse of the planes.

So my solution to the original question: Throw the points into a matrix and invert. Beautiful? Profound? Decide for yourself, but I think so.

________

I passed this on to Pat Hanrahan (hanrahan(at)cs(.)stanford(.)edu), who comments:

That's a neat result that I am well aware of. I use the 2D version all the time. Projective geometry and homogenous coordinates are sooo cool!

One minor point. Wherever he says "inverse" you can use the adjoint. That makes the geometry particularly elegant since the adjoint is a co-factor and that has a simple geometric interpretation. Also, the adjoint always exists.

Here is a slide that I go over in class that somewhat illustrates these ideas:

http://www.graphics.stanford.edu/courses/cs348b-04/lectures/lecture2/walk013.html

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Paul comments:

Pat is correct that you can use the adjoint instead of the inverse, the division just multiplies through all 4 plane equations by 1/determinant. However the scaling that you get from the inverse is very interesting. I believe you'll only have a zero determinant if the tetrahedron is degenerate (all points in a plane) and I suspect the determinant is actually (equal?) closely related to the volume of the tetrahedron, which means an inverse will by fine for any meaningful tetrahedron. It's not much more math when you have the adjoint already.

I have considered some interesting uses for ones that are not well formed. For example, it should be possible to negate the '1' of one vertex to create a triangular viewing frustum - truncated by the tetrahedron. This is really why I wanted to find a nice tetra-tetra intersection method. Beam tracing then becomes a bunch of tetrahedron intersection tests.

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The ray tetrahedron intersection can be done as follows: 1) Put all vertices in as columns in a matrix. (Tv for tetrahedron vertices as columns) 2) Invert to get Tp (Tetrahedron plane equations as rows) 3) Using the ray equation R=P+Lt plug R into the plane equations:

Tp*R = 0 (where * is product and R is a column vector)

Expand:

Tp*P + Tp*Lt = 0

t = -(Tp*P) / (Tp*L)

Now this is really not quite standard notation, t in this case is a 4 vector containing the distances to the 4 planes. You need to do the divide as 4 separate scalar divisions, the matrix notation is just a handy way to do 4 dot products at a time.

Now given the 4 distances, you may treat the tetrahedron as the intersection of 4 half-spaces defined by the planes. The ray will enter or exit each half space at the point of intersection. We can determine whether it enters or exits by taking the dot product of the surface normal and the ray direction; this has already been done as Tp*L. Because it is a convex object, we can take the farthest distance to an entry point and the closest distance to an exit point (this defines the extent of the intersection). If the exit is beyond the entry point, there is no intersection. Or, if ANY exit point lies in front of ANY entry point, there is no intersection. This test feels like there should be some sort of handy matrix method behind it, but I don't know.

I believe this method requires fewer calculations than Pluecker coordinates (not by much) but it does use division, which I suspect can be eliminated. Storing the inverse matrix requires less storage than Pluecker coordinates, too. In fact, because of the relation between the matrices, you may choose to only store one of them (point or plane) depending on how you expect them to be used the most.

I didn't like the Pluecker coordinates method - it is what I expected after reading the ray-triangle intersection. Very mechanical /procedural. This matrix method suffers from the same ugliness in the final part where you compare a lot of distances and check a bunch of signs. Not only does all that condition checking run slow, it's not very pretty. I like things like the ray-sphere intersection where the sign of a calculation tells you if they intersect or not. I still think ray-tetrahedron may have such a test, and that it will involve a matrix representation of the tetrahedron. But I have not found any such result... yet.

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Ingo Wald (wald(at)mpi-sb(.)mpg(.)de) writes:

There's a thick chapter about the cost function for splitting a BSP node in Vlastimil Havran's PhD thesis, and more recently (though thinner) in mine ;-) (http://graphics.cs.uni-sb.de/~wald/phd.pdf).

The same ideas can also be used for accelerating photon mapping, see http://www.sci.utah.edu/~wald/Publications/webgen/2004/VVH/download//vvh.pdf, a paper we've just had accepted at this year's (2004) Eurographics.

There is a more optimal algorithm for building the k-d tree. Sorting in every step - as you correctly mention - is O(n log n), so the total complexity is O(huge). You can, however, build the entire tree in O(n log n), which is asymptotically optimal. The algorithm for that is sketched in the vvh paper I've pointed you to - it's for points only, but applies (almost) the same for non-point primitives.

On the article itself:

I personally find the argumentation with the four probabilities (Pa, Pb, Pab, Pba) a little bit confusing, and overly complex. The original argumentation with C = C_trav + C_isec( P(a)C(a) + P(b)C(b)) is much easier to understand and implement. Thus, I don't hope anybody wants to implement the approach based on the much more complex formulae used in the text. On the other hand, that way of calculating has brought up some interesting facts that I did not know myself before, either. Like, for example, that the probability for hitting the plane doesn't change wherever you put it, or that in the one example it doesn't matter where exactly between 0.4 and 0.6 you place the split plane (which was completely surprising to me, and I'm still sure it won't hold if you consider the next-level split).

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I have a bunch of other things to say, some of them even interesting:

At SIGGRAPH 2005 in the Real-Time Ray Tracing course, Gordon Stoll gave a fascinating talk about how to make an extremely efficient ray tracing. This presentation, and many others, is available at the OpenRT project site: http://www.openrt.de/Siggraph05/UpdatedCourseNotes/course.php. I didn't expect too much from the talk: something about using SSE for shooting four rays at a polygon, some talk about cache misses, the usual new tricks for wringing more performance from the CPU. These techniques *were* covered, and it was impressive how much they could help. For example, due to ray coherence, about 95% of the rays in one of these SSE packets actually all had the same result (all hits, or all misses), so the gain from SSE was 3.5x or more. The Saarbrucken folks have said about the same thing for some time, but it was nice to hear this independently verified. Squishing a node of a k-d tree into 8 bytes resulted in a nice speed-up due to fitting the cache nicely. But he went on from there, with tip after tip. Philipp Slusallek (who has done much of this original research in the Saarbrucken group with Ingo Wald, Vlastimil Havran, and others, and who has a company on the side, http://www.intrace.com/, that is selling such a ray tracer to VolksWagen and others) half-jokingly commented to me, "He's telling all the secrets!" Other than more CPU tricks like stressing memory coherence when making the k-d tree acceleration structure, avoiding recursion and stack operations, etc., the interesting thing to me was how he stressed doing locally optimal splits of each node in the tree.

Stoll confirms what Havran and others have researched: this sort of local optimization makes a huge difference in the speed of ray traversal. This is a non-obvious result, however: on a ray tracer that hasn't had a lot of optimization of its various elements, it's a bit hard to tell what's really worth doing. The cost function's fixed cost values (cost to intersect a node, to traverse a child, to intersect a polygon, etc.) affect the cost function itself. So faster results on an experimental ray tracer can sometimes be misleading. For example, say your ray/polygon test is terrible compared to the rest of your code. In this case, algorithms stressing avoiding testing a ray against a polygon will be better for your system, but only because your original code stinks.

Stoll's group has worked very hard to optimize all the critical elements of their ray tracer. So hearing that a better k-d tree really makes a difference is exciting to me; this was supposed to be a solved problem back in 1992, that you just use some sort of simple BSP-tree (or nested grids, or bounding volume hierarchy) and it'll be good enough. Not true: more optimization can really matter, it gives a tree that's several times faster than a mediocre tree. Nice! The locally optimal trees created are quite deep (50-100 levels), many levels go by where the various splitting planes don't so much split as chop off hunks of space from a node making it bound the stuff inside the node more tightly, giving "stringy" trees where only one child continues to get subdivided, and child nodes ending with 2 triangles per cell. Another interesting tidbit of Gordon Stoll's talk: lazy evaluation is not such a good idea, since it ruins the cache's performance.

My observation on this optimized process is that it reminds me of bounding volume hierarchies. You can sort-of think of each splitting plane being generated as adding a plane of a bounding box. For example, imagine a trivial scene: two identical blobs some distance apart along a single axis, say the X axis. The global bounding box, in this case, has four sides, the Y and Z faces, that touch both blobs; each blob touches a single X face:

+-------------------------+ | # # | |#### #### | |# ## # ##| | ### ### | +-------------------------+ X axis-->

With bounding volume hierarchies say a bounding box is put around each blob. So the bounding volume hierarchy is one global box containing two. What optimized k-d trees do in this situation is to find the edges of these two blob objects, which is where you want to test to put planes. There are only two planes that need to be checked, with these planes corresponding to the "new" faces of the blob bounding box hierarchy:

+-------------------------+ | # | | # | |#### | |#### | |# ##| |# ##| | ### | | ### | +-------------------------+ X axis-->

A trivial example, but what's interesting here is that the k-d tree and the bounding box hierarchy have test planes in the *same* locations. The k-d tree is more memory efficient, as you've had to add two just two nodes, each with one splitting plane. For the bounding volume hierarchy you've had to add two complete bounding boxes. From an efficiency standpoint, k-d trees appear to have an advantage. Both k-d trees and BV hierarchy have to test the topmost global box. But then the computations for k-d trees consist of (at most) two cutting planes; for BV hierarchy you have to test two whole bounding boxes. Essentially, k-d trees, in this (contrived) case, have the advantage of coherency: 5 of the 6 planes forming each child bounding box are shared by the global bounding box. So k-d trees just have to test the sixth bounding box face of two boxes, while bounding volumes don't get to share intersection results with their parent.

You could do a similar analysis on this situation if the two blobs were displaced by an X, Y, and Z offset. In this case we've had to make six k-d tree cutting planes. Now it's less clear that k-d trees beat bounding boxes: sure, the two child bounding boxes have 12 planes total to test, and k-d only 6, but there's a bit more overhead in dealing with each plane with k-d trees.

Anyway, there are certainly many differences between k-d trees and bounding volume hierarchies, but I thought it interesting how they're similar in that the optimal k-d trees put planes in the same places that bounding boxes do, etc.

There's still more to be done in the area of efficiently forming the k-d tree, e.g. how to best form the upper levels of a BSP tree quickly is not solved (and I think there's probably no one good answer; it all depends...). Stoll pointed out that using Level-of-detail representations in ray-tracing is another tantalizing area that turns out to be hard to do in some use cases.

To address this first question, efficient k-d tree creation, there are basically two approaches I know of: sorting and binning. Say you have a million object database. It's a fair amount of work to sort the million objects, then test to find which cutting plane (along each of three axes) gives the best cost function. Recall that every object has two possible cutting planes to test for it, at its extents along each axis, so this gives 6 million planes that would need to be tested. Once you split, you now have two nodes with around half a million objects each, and each of these nodes then potentially needs 3 million plane tests to find the optimal split; 6 million tests again for a single level. Even if you use a rule of thumb (which Havran shows is worthwhile) of testing for splits only along the longest of the three axes, this is still 2 million plane tests per level. Havran also points out that you can reduce this by another factor of two by finding the object median plane (the plane that splits the set of objects' centroids in the middle) and then testing only the side of the object that is closer to this median. You're down to a full sort and then a million plane cost tests per level, still a considerable number.

So one alternative is binning, where you simply run through the objects' centroids and toss them into a regularly-space set of bins. For example, you can record each object's extents and what bins are overlapped. You can then check just the boundaries between the bins to see which of these planes is best. You've limited the number of plane tests you do, and you've avoided a sort. Gordon Stoll talked about this idea briefly during the talk and afterwards in discussions. My discussion of binning here is an "off the top of my head" idea, and I'm guessing others have studied this more thoroughly (though I don't know of any published results).

Anyway, I believe more research could be done here. The tradeoff in any of these systems is what the cost is in forming the tree vs. the speedup gained from the tree. This obviously depends on the system's use: if you plan on shooting more rays, then more time spent forming a good BSP tree may be of use. Having not done any research in this area, I'm sure I'm at the baby steps, don't know much stage of understanding what's sensible to do.

____

The original version of this text had a discussion about Smits great article on ray tracing optimization techniques, at http://www.cs.utah.edu/~bes/papers/fastRT/. The idea itself is at http://www.cs.utah.edu/~bes/papers/fastRT/paper-node12.html. The concept for bounding volume hierarchies is that you want to not bother storing the hierarchy as a hierarchy in memory, but rather as a long list of boxes and surfaces to be intersected. This list contains the whole hierarchy and all objects, in depth-first order. If you hit the box, you simply go test the next object on the list, be it a box or object, as this is the first child of the box. Each box has a single skip pointer: if you miss a box, you use the skip pointer to find out what the next object is in the list that needs to be tested. By arranging the hierarchy in this way you avoid recursion, you minimize storage, and you get excellent memory coherence among nearby objects. The cost is that you have to zip through the original tree and convert it. But this is done only once, vs. having to access parts of the original, inefficient tree for every ray.

About two minutes after sending my text out for comments, I realized this sort of thing does not apply to k-d trees, which (if created depth-first) already should have memory coherence of nearby nodes, and which have an order of evaluation which is view dependent (vs. bounding volumes, which normally do not, and so can always be evaluated in a particular order).

____

[...Much give and take among Ingo Wald, Gordon Stoll, Vlastimil Havran, and myself omitted here...]

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Eric writes:

Here's my other random thought for the day: let's say when you found that a ray pierced the cutting plane of a kd-tree that you always traversed the left one first (regardless if it's a min or max). This of course makes no sense for eye/reflection/refraction rays, since the power of the kd-tree is that ray walking is implicit. But for shadow rays, which can often make up 80% or more of the rays shot in a scene for a classical ray tracer, you just want to find any hit, not the closest hit, so traversal order doesn't matter. I don't know if there's any possible advantage to doing this with kd-trees, it really seems like there isn't, but thought I'd throw it out there. Maybe one less compare is needed? Anyway, this is then more like Smits' "same order each time" traversal idea.

____

Gordon Stoll replies:

I've thought about this a little, mostly thinking about cache performance for shadow rays in general. There are a bunch of different possible orders that you could use for shadow rays. You could do light-to- hitpoint, hitpoint-to-light, fixed order, or even SAH-based probability order. Unfortunately I can think of good and bad cases for all of those, depending on the scene and whether you do smart light culling. Hitpoint to light is probably a must if you have a big scene with occlusion and don't have smart light culling. Otherwise light to hitpoint might be good if you have a lot of occlusion by the lights (like fixtures). SAH (surface area heuristic) probability order might be interesting, but who the heck knows how that would behave or how you would do it, or how much overhead it would have.

Oh, one other comment about the flattened BVH traversal that might not come through from Smits's writeup. The traversal is *so* simple that you might profitably eliminate at least one of the unpredictable branches from the inner loop (converting into indexed or conditional moves). Could be a significant win, and maybe more so for the SSE packet tracing stuff. I vaguely remember that the Saarland guys tried to do this for kD-tree traversal way back when, but there was too much overhead for it to be profitable.

_____

In the rundown above I wrote:

> lazy evaluation is not such a good idea, since it ruins the cache's performance. ...

Gordon Stoll comments:

Hmm...don't know if I'd put it quite that way. I guess the real point is that the effect of lazy evaluation is...non-obvious :).

Looking at a straightforward depth-first kD-tree builder, think about the "frontier" of nodes where the data needed to pick a split is equal to the size of the cache (whatever cache). During the course of building, there are piles of cache misses when you're working on nodes above that frontier in the tree. Whenever you cross that frontier, there are *zero* cache misses for the entire sub-tree until you pop back above the frontier. Deciding to be lazy and stop what you're doing when you're below the frontier can only hurt your total memory traffic (can't get better than zero :).

It might not hurt as much as that implies, though. Say a ray hits a chunk of the tree that's below the frontier (i.e. smaller than the cache) for the first time in the course of the tracing. In the non-lazy scheme, the data is probably not in cache because the whole tree was built up front. So you get some misses pulling in tree data. In the lazy scheme, the data needed for building is not in cache, so you get some misses pulling that in -- but when you're done the finished tree data is right there in the cache :).

This also still leaves the possibility of being lazy above the frontier, or changing the way the builder accesses memory in general, or doing lazy evaluation for computation rather than bandwidth purposes.

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Ingo Wald (wald(at)sci(.)utah(.)edu) replies:

There're two important points about building kd-trees lazily.

1.) Assuming high occlusion / depth complexity and/or lots of triangles outside the view frustum (in other words: we're seeing only a fraction of the triangles), then lazy building will build only a fraction of the kd- tree. and this will most likely more than counter the effects of a few cache misses here and there, even *if* those should increase. Remember one important point: the finest level of the kd-tree has as many nodes as all the other ones above summed together! Thus, the impact of not even building parts of the kd-tree (which will work best at the leaves) could potentially be pretty high.

1.b.) The same actually applies to distributed rendering: in lazy building, each client could/would build different parts of the tree, so this would even kind of parallelize the building process (including distributing the cache misses over all clients).

2.) You have more information about the number of rays. Thus, you cannot only build the kd-tree *lazily*, but even *adaptively*. E.g., in the usual cost function, one argues about the "probability" of rays hitting a voxel, and use that probability to compute a estimated cost. Once you build it hierarchically you actually have some hands-on data on where the rays actually go. And of course, you could use that to decide a.) whether to subdivide a node at all (for a single active ray that probably won't make sense), and/or b.) where to put the split plane(s).

Thus, I think there is some really high potential in building kd-trees lazily. I just didn't find the time to really implement it :-(

____

We talked a fair bit about ray tracing efficiency research progress in the past 15 years. Here are some excerpted comments:

Vlastimil Havran (havran(at)mpi-sb(.)mpg(.)de) wrote:

In between there are more than 15 years of hardware improvements, so the estimated speedup from hardware advancements should be about 1000, according to Moore's law.

____

Gordon Stoll replied:

Ah, this is something I've thought about a lot. Fifteen years ago, 1990, would be (I think) a 33MHz 80486. That had onboard floating-point, which is obviously important for RT. The actual semiconductor scaling trend (including both the number of transistors and their switching speed) predicts an improvement of 3,125 times since then. Do you think that the core CPU performance of RT has actually gone up that much?

My guess is that it didn't, and that instead RT fell off of the performance curve right around then because RT breaks pretty much everything that we've put into CPUs since then (deep pipelines with branch prediction, superscalar, out-of-order, SIMD/vector operations, etc, etc, etc). I've been thinking about trying an experiment or doing a literature survey to try to support this, but for now it's just a crackpot theory. Maybe I'll try to convince Eric to figure it out. :)

Things are really good right now as far as this goes. The code is getting friendlier for the architecture (things like the packet tracing technique), and the architecture is getting friendlier for the code (shorter pipelines, multi-core, multi-threaded).

____

My wrap-up:

One other topic of conversation was about MacDonald and Booth's paper "Heuristics for Ray Tracing Using Space Subdivision" in Graphics Interface '89. The two bits that were interesting to me are related, in that they both involve the dissemination of information. First, this paper spends some time establishing the fact that the surface area of a convex object is directly related to the chance it will be hit by a ray. They use empirical testing to show that there is a correlation. This was unnecessary work, from a god's-eye view, as this result was known for some years. For example, in 1987 Goldsmith and Salmon cite L. Stone, "Theory of Optimal Search", Academic Press, 1975, pp. 27-28, as their justification for using the surface area. However, this fact hadn't really percolated out into the field of computer graphics until some time later. For example, Jim Arvo presented this fact and its proof, usually referred to nowadays as the surface area heuristic (SAH), in some SIGGRAPH 90 course notes (in http://www.ics.uci.edu/~arvo/papers/MetaHierarchies.ps), see RTNv10n1. As mentioned later in this issue, the Discrete Differential Geometry course presents this result in a formal framework of measure.

The point is that SAH had been known by some people for some time, but it took a good long while for this fact to filter out to the general graphics community, so it's hardly MacDonald's fault that he did not know of it at that time. The other interesting bit in MacDonald's paper relating to information dissemination is his own presentation of results. On the ninth page of his article he writes, "the arbitrary acyclic algorithm performed best, providing up to three orders of magnitude reduction in the number of objects tested for intersection." He even shows, in a log graph, how much better this algorithm is for one test scene. How significant is that?! He's found an algorithm (essentially what Gordon Stoll and others have also found to be great: placing kd-tree cutting planes in locally optimal locations) that works up to a thousand times faster on a particular type of scene (many small objects uniformly distributed). But then he gets distracted by his other test scenes where this algorithm does not work as well. However, these scenes are entirely unlikely, pathological cases: large overlapping objects filling a space. So he doesn't really realize he's found a critical result, and in fact spends some time trying to find a hybrid algorithm that will handle all his test scenes well, reasonable and pathological alike.

My point here is not to beat on MacDonald; he was a master's student in math who was doing his best to complete a thesis project, so did not have time to create interesting test scenes (ahhh, too bad he didn't know about the Standard Procedural Databases...). He found a great result, but didn't fully realize what he had found. What's interesting is how long it has taken for this result to percolate out. Nowadays if a new ray tracing algorithm shows a 2x speedup, it's a worthwhile result. Here MacDonald gets up to a 1000x speedup in some cases and buries the result on the ninth page of sixteen page article, because it worked for only two of his five test scenes (though for two of the remaining scenes he was getting up to a 10x improvement). The conference was relatively unknown and the proceedings not easily available, there were no pretty pictures in the article, and the most significant result is well-buried, never mentioned in the abstract, introduction, or conclusions. Amazing, really, that this result ever surfaced again at all. Heck, I certainly missed it! I mention his paper in RTNv8n2, noting that he explored this area, but never really put two and two together (or perhaps taking 5 and subtracting the 3 pathological scenes). And MacDonald was not the only person to explore this area, Fussell and Subramanian also did so, but their work never made it out past a technical report:

D. Fussell and K. R. Subramanian, "Fast ray tracing using K-D trees," Technical Report TR-88-07, U. of Texas, Austin, Dept. Of Computer Science, Mar. 1988. http://www.cs.utexas.edu/ftp/pub/techreports/tr88-07.pdf

Their conclusion was that this method was one of the fastest known, comparable to Arvo & Kirk's 5D method (a scheme that works well for coherent rays but that bogs down otherwise, and has seen little use). But they do not show their scheme was significantly faster than other schemes overall. Is it because of coding style, or the processor type, or that they used different termination criteria? We're unlikely to ever know.

The takeaway for me is that first discovering a result is important, but interpretation of the significance and validation of that result is also equally valuable. MacDonald found a useful result, but his test scenes misled him to think the result was not of interest. Also, though his advisor is well-known, MacDonald was working on his ray tracer on his own. It is very difficult for a reader to evaluate the worth of any efficiency work done by one coder in isolation: is his speedup due to a better algorithm, or just better coding of the new work? As I mentioned before, this is why I think Gordon's work is significant, as his group is optimizing every element they can, and working with realistic test data, so making their results more solid.

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I just read Stephen Bridgett's article in RTNv17n1 and wanted to comment on optimizing the point in polygon test. I've found that branching code is indeed the worst thing you can run on a modern processor. I'm still using an Athlon 700, so I'm sure the problem has gotten worse than I've seen. Anyway, while Stephen has eliminated one branch from the test there is still one left in his code fragment that can be eliminated. While it appears as an assignment it involves evaluation of a boolean >= condition which involves a conditional branch. Some processors can handle this without branching, but only with the right compiler as well.

When doing a magnitude comparison (A<B) we can replace it with a simple subtraction (A-B) and the sign of the difference can be interpreted as a flag. The great thing is you can AND, OR, or XOR multiple flags of this form using the & | ^ operators which are supported on all hardware and compilers without branches provided your operands are an integer type. There is no need to worry about the other bits - the resulting number will have no real meaning, but its sign will be the desired flag. On modern processors I've actually been able to abuse pointers to floats (recast as pointers to ints) to get a real benefit from this with floats and doubles (it works but not worth the cost to clarity). Anyway, since the flags in this case are XORed, you could take the product of the flags (differences) to get the same effect even with floating point. I'm assuming the context of the code fragment here involves several such tests and flag XORing. You could therefore compute a product of differences and test only the sign of the final result.

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He continues:

In other news, the ray tracer from rtChess has been fully separated into a library. It's now 40% faster than the implementation in the game for complex scenes.

The 40% improvement came from several small changes and one big one. I used to have the octtree nodes call each other passing the ray as a parameter. One day I moved this recursive function over to the ray class and passed the nodes as a parameter instead. I almost fell off my chair when it ran about 25% faster. I can guess that when calling the recursive function in different octtree nodes, it's changing the "this" pointer and causing something along the lines of data-dependent program flow which could stall pipelines pretty badly. That's my best guess and I never really investigated (don't look a gift horse in the mouth).

[This is backed up by Gordon Stoll's idea, mentioned in the previous article, of avoiding recursion and flattening things to a stack. - EAH]

________

[Someone who wishes to remain anonymous tried out one of the grid coherency techniques I described in RTNv12n1 and improved performance in his own ray tracer with the following. He/she writes, "I'd just as soon not have my flailing around in that space immortalized in RTN, since I think they are pretty much flailings at this point, especially since other folks have done a lot of really good work in this area lately." Personally, I'm still going to put this tidbit here, both because it's worth noting verification of the importance of striving for memory coherence, and it's nice to know that little changes in data structure storage can have a big effect. -EAH]

So how about another 15% speedup for the ray-tracer, purely due to changing the voxel grid from:

struct Voxel { ... }; Voxel *voxels = new Voxel [xres * yres * zres];

to

Voxel **voxels = new Voxel * [xres * yres * zres]; // set voxels to NULL // only allocate a Voxel structure for non-empty voxels

Doing it the latter way is the obvious right way to do it from the start, in terms of reducing memory use for all those empty voxels, but hey, by starting from a so-so implementation, it's been possible to see how much of an effect all of this stuff has due to improved cache behavior.

Presumably by doing it the better way, the cache isn't blown out by rays going through empty voxels, accessing a Voxel just to find that it's empty, but having loaded the whole thing into memory and pushed something else out to do so. This way, empty voxels are just a NULL pointer check in the voxels[] array, which is likely to already be in cache... Still, I'm surprised (as always), that this gave me a 15% speedup to the entire rendering process (for a random handful of test scenes).

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The course "Discrete Differential Geometry" was pretty interesting, at least until the equations went over my head. Equations in lectures are a tough row to hoe: if the audience already knows the equation, then the presentation is not offering all that much that is new; if they don't, then a pretty dense chunk of information appears in a single slide. Equations are wonderful, they concisely sum up this or that relationship or operation, but with no way for the recipients to put the lecture on "pause" there is a high risk of losing people. In a lecture I like presenting an equation as a "mug shot", sort of "If you see this equation in the future, you might recognize it." Then I can talk around the equation, saying what it is for and what it does. But showing many slides of equations, showing derivation after derivation, well, very few people are that quick to absorb this information. Anyway, enough on that...

The field gives a unified view of what various measurements mean and how they can be used. For example, take a box: it has a volume, a surface area, and a mean width (which, for a box, is proportional to the sum of the lengths of its edges; otherwise think of the measure as an average maximum diameter). It turns out these various measures can be used in geometric probability: the chance that an arbitrary point in space is inside the box is proportional to the box's volume (duh). However, you can go further: the chance an arbitrary ray hits a box is proportional to the box's surface area (a result known to most ray tracing type, but otherwise not commonly considered). Going a step further, the equations lead to the result that the chance the object intersects with an arbitrary plane is proportional to the mean width of the object. That's an interesting result when thinking about clipping planes, for example. It also turns out these various measures can be combined for sets of convex objects, which means the measures hold for any object (since any object can be decomposed into convex objects). Going further, you can also derive curvature values for edges and vertices (normally you find curvature only on curved surfaces), and it all falls out from theory. Anyway, look up the course notes under "Resources" at http://ddg.cs.columbia.edu/. The first two chapters, at least, are pretty approachable.

Talking with Steve Worley, it turns out another course I wish I had attended on Monday was Computational Photography. The idea here is to substitute software for high-end hardware. Instead of a camera with a $5000 lens, use a bunch of cheaper cameras and use a computer to crunch the resulting images into one high quality image. Or you could have a variety of images collected at once, e.g. some polarized and some not, and selectively choose where to reduce glare. This sort of thing is just the tip of the iceberg, and Steve raved about this course for half an hour or so. Sounded worthwhile, though I can't recall (correctly) a lot more. This field is an up-and-coming area as computer vision, photography, computer graphics, and other fields cross-pollinate. See http://photo.csail.mit.edu/ for some presentations at a different conference, in particular click on Schedule and see the talks in "What will a camera look like in 20 years".

The de rigeur event at SIGGRAPH is the Fast-Forward Papers Review. Over the course of two hours it covers the 99 papers being presented at SIGGRAPH 2005. Lightly and often humorously, but there's usually enough info to have a sense if a paper's something you'd want to see. Thankfully, only two authors gave their presentations by rapping, and only one took off some of his clothes.

Monday started early with hardware rendering related papers. The Saarbrucken folks presented their design for an RPU, a ray-tracing processing unit. It's not considerably different than today's GPUs, having just a bit more specialized hardware here and there. Interesting stat: their *software* ray tracer is about 30x faster than the freely-available POVRay ray tracer. Now, I could probably speed POVRay up by 2x by some tuning of this and that, but 30x is pretty incredible. More on this topic later in this issue.

One interesting thing: image rights. I discussed this topic with a few people, and most do not realize their rights when they have their paper published in SIGGRAPH or any other ACM journal. As I understand it, the rights to the image are mostly owned by the ACM when your article is published. You yourself can reuse your image elsewhere (i.e. in your own publications, web pages, news releases, etc.), but if a magazine or book wants to republish your image, they need permission from the ACM, not from you. The ACM charges a fairly nominal fee, $25, mostly to protect their rights.

My advice (worth exactly nothing in court) to anyone publishing nowadays is to make two images of any image to be published, one from a fairly different view, etc. In this way you can reuse and grant rights to the second, unpublished image as you wish. That said, there's an area of law where you compare one photo with another and if they match by 80% (by some eyeballing metric), then they're considered the same photo for purposes of copyright. Usually this is meant to protect one photographer's composition from being reused by another. What it means to 3D computer graphics, where it's easy to change the view, etc., remains to be seen. Still, ACM's rights to your work are less clear for a new, different image. This sort of thing is small potatoes, but taking action so that you have images and videos you fully own then removes the hassle-factor of granting permission to others wanting to use your work.

After lunch on Monday was the keynote with George Lucas. Not to be missed, of course, and fanboys were lining up at least 2.5 hours ahead. Coming in five minutes before it started, I was shunted with more than a thousand other people into a separate hall. So I can't say I saw George Lucas' real photons, but rather just a giant TV picture of his real photons, with him a few hundred feet away in the room next door. Lamest keynote ever: he was interviewed by some guy for an hour. Though it is the first time I've seen a keynote preceded by a fancy video production saying all the cool things developed under Lucas direction (and impressive they were). And, after five minutes of the interview, I left. I felt my time would be better spent getting shocked by Japanese telephone researchers. In Emerging Technologies there were a number of peculiar technologies, like the virtual straw, where you could get the impression of sucking up some drink without actually having the drink there. This one was almost always down for maintenance when I was around, so I never tried it. I did get to try the Galvanic Vestibular Stimulation device from NTT's Computer Science lab (http://www.siggraph.org/s2005/main.php?f=conference&p=etech&s=etech24, and googling on this term turns up a bunch of hits, e.g. http://jp.physoc.org/cgi/content/full/517/3/631). Sign a waiver and put on some headphones, but not for listening. No, these headphones shock you behind your left and right ears. This has the effect that, instead of thinking gravity goes straight down, you think it goes a bit to the left or right, depending on which behind-ear-area is "stimulated" (i.e. shocked). Weird effect: you're walking forward, they push the joystick left, you think you're falling and you go left to compensate! Stranger still is when you have the headphones on and you control yourself with the joystick; how self-referential can you get? Less effective was wearing the device while looking at a race game. Funniest concept was alternating left-and-right shocks in time with the beat of music: yes, you *will* have rhythm! Other than feeling shocks and tasting a metallic taste, and my inability to remember any of the year 1981, there were no side effects whatever.

Oh, from talking with others afterwards, the summary of Lucas' keynote: He's the father of digital cinema. He's developed about all the tools he needs (by pestering good people for them), though pre-visualization tools (e.g. interactive rendering of film scenes) could be handy. Voice recognition and AI in computer games could make them better. He's also spending money on education nowadays. Not sure what the other 55 minutes of the interview were about.

Monday evening I went to "Games, Beyond the Joystick" for an hour. Pretty fun to see some different interactive devices. My favorite is still the Eye Toy, which I first saw two years ago at SIGGRAPH and was one of the two reasons I then bought a Playstation 2 (the other being Dance Dance Revolution; hey, a nerd needs his exercise). Richard Marks talked more about the use of the Eye Toy with the Playstation 3. Coolest one: it quietly tracks your head. In a shooter game you can peek around a corner in a natural way, by tilting your head to one side. This sort of computing would take up about 30% of the processing power of the PS2, but only 1% of the PS3, making it cheap for developers to use in the next generation.

Sketches were generally of high quality. This venue is getting quite competitive (I've been on sketches committee the past two years), with a large percentage of submissions having additional materials such as videos. Starting in 2004, the one page sketch summaries are no longer printed in any SIGGRAPH publication, but are available only on the DVD. Sketches are currently not considered a publication. This can be a good thing, as the intent is that the appearance of the sketch should not be considered a prior publication when judging the newness of an final article submitted by the same authors. However, a side-effect of this not- publication status is that sketches are not archived in the ACM's Digital Library.

One of my favorite sketches this year was Joern Loviscach's paper on "Efficient Magnification of Bi-Level Textures". The problem is that you want to have simple bitonal images representing text on signs (for example). You want these to look good when magnified: bilinear interpolation between the texels, giving levels of gray, looks bad. Simply quantizing (display black if gray<128, white otherwise) also doesn't look that great. This is the first practical application I've seen of the Bixels concept (the idea of storing an image as both texels and the lines between texels). What was very clever was that he found you could modify the underlying texture map so as to capture the intent of a higher resolution bixel version of the sign. The resulting texture is just a simple texel texture, which can be rendered with a simple pixel program doing quantization. But, the underlying gray samples are modified so that quantization more accurately matches the higher resolution curve edges. There was more (doing better antialiasing, problems with matching V vs. S vs. other letters' curves), but overall it was pretty convincing, useful, and enjoyably non-intuitive.

What's the future hold for GPUs? I came upon this little technical report, by Bill Mark and Donald Fussell, mentioned by someone or other at SIGGRAPH: http://www.cs.utexas.edu/users/billmark/papers/rendering2010-TR/. The wheel of reincarnation turns again, with the authors saying that scene management should move back to the GPU (something that used to be done around the early 80's but that eventually moved back to the CPU). Lots of other musings and ideas in this one, including ray tracing as a basic tool. A related tidbit: newer games are more and more becoming CPU- bound, as its difficult to keep the newer GPUs fed with things to do.

There was lots of other fun stuff, of course. The Electronic Theater was good, with relatively few dark pieces (thankfully short, no 15-minute grayscale slow-sad-clown-driving-nails-into-himself filmfests). One new guy I met this year is Jeff Han. I was impressed by the cool hardware things he's been doing. For example, the Media Mirror, New York University Media Research Lab: http://mrl.nyu.edu/~jhan/mediamirror/. Cute idea, and amazing you can do this (a) in real-time and (b) with less hardware than you might think: take a video of a person and form a photomosaic of them using the video channels available.

Since you made it this far into this rambling article, you win two free Los Angeles SIGGRAPH tips. First, the Hotel Figueroa's room rate is the same whether booked through SIGGRAPH or not, and you can book these rooms well in advance of whenever SIGGRAPH opens its official hotel booking website. Second, the outside bar on the top floor of The Standard hotel is a cool place to visit, and during Mon-Weds there's no cover (of course, things may change).

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Eric Haines / [email protected]