*"Light Makes Right"*

June 26, 1997

Volume 10, Number 2

Compiled by

All contents are copyright (c) 1996, 1997, 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 and the Mother of all Ray Tracing Pages.

- SIGGRAPH Roundtable
- Introduction
- New People: Marcos Fajardo Orellana
- Ray Tracing Roundup
- Illuminated by Black Light, by Dan Wexler
- What's Wrong with Monte-Carlo Methods? by Nguyen D.C. (JuHu), Pete Shirley, Stephen Westin, and Eric Veach
- More on Rendering Bugs, by Eric Haines
- The Curse of the Monkey's Paw, by Eric Haines
- Global Illumination "Bible"? by Ian Ashdown
- Megahedron
- Detecting Points on the Edge of a Polygon, by Eric Haines
- Rendering Unflat Polygons, by Eric Haines
- Free Polygon Tessellators, by Eric Haines
- Octree Neighbor Finding, by Andrew Glassner, Francois Sillion, and Paul Heckbert
- Author Sues Publisher, by Ralph Grabowski
- European Graphics Tour, by Nelson Max
- Fast Shadow Testing Bibliography, by Slawomir Kilanowski

Time: Thursday, 6:30 pm to 7:45 pm (room opens at 6) Place: Hotel InterContinental, Cocker Room

As usual, the location is near the Thursday evening papers reception which follows. The roundtable is simply a gathering for people interested in rendering and ray tracing and who'd like to talk about what they've been doing and meet other like-minded souls. It's extremely informal: the agenda is that we introduce ourselves, then break up and chat.

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Graphically speaking, I've been working a little bit with Java and VRML. I went to the VRML '97 symposium back in February, which was pretty fun. The most memorable event was the Monday night demo dinner. Each demo was limited to five minutes, which was strictly enforced by the use of a countdown and nerf guns in the hands of front-row audience members. A brilliant feedback system was also implemented by the organizers, in which the audience could immediately register their feelings about anything done during the demo. Each person at dinner was provided with two toys: if you liked something you heard, you would squeeze your squeaky toy; if you disliked something you'd turn over your moo-cow can toy.

I helped with the VRML Illumination working group at the conference, and one thing that came out of this meeting was the need for a sample "perfect" implementation of the VRML illumination model. Happily, there's a nice way to do this: Java. This program seemed like it should have been easy: make a GUI accepting the various variables, hit a "compute" button, compute an image. The two big roadblocks for me were figuring out how to get the GUI elements to stay put on the screen and to get the compilers to work. I won't get into the particulars, but the hardest part for me was getting the various pieces of text and input boxes to not realign themselves in some obscure fashion. Also, I found that if certain routines in my code had more than, say, 40 lines of code, they would not compile (Sun's compiler gave false errors, Microsoft's just gave an internal compiler error and quit). Anyway, the promise of Java is great, it seems like a pleasant language, but before doing another project I'll probably wait another year or two until the tools become more visual and more stable. If you want to see my application, check it out at http://www.acm.org/tog/resources/applets/vrml/pellucid.html.

The cool thing about Java is that the GUI (once you get it going) is indeed portable, a huge advantage over C++. This feature makes it possible to actually write tutorials about computer graphics concepts and be able to easily distribute them and for educators to share them. Being able to actually play with BSP trees, or vary illumination models, or see the relationships between matrices and operations is great stuff. Such applets can build up an intuition of how variables affect results and how algorithms work. I have begun to gather Java applets used to teach about computer graphics, go to http://www.acm.org/tog/resources/applets/overview.html to see the collection. If you know of related applet URLs or can provide more Java code, please do let me know!

One of the more entertaining and enlightening books I've read this year has been Scott McCloud's "Understanding Comics". It was recommended by the folks at Thinkfish (www.thinkfish.com), who do real-time non-photorealistic rendering, this book discusses many different facets of comics. Visual styles, portrayal of time, and a zillion other topics are covered. Oh, and it's all done entirely in comic form. Good one!

On this issue: I've still got a backlog of about 200K+ bytes of material to wade through, and some of it I need to edit (and some I need to just plain understand). This issue has a theme of global illumination methods; the next looks to be more about ray tracing efficiency (yet again) and various tricks and hacks.

____

Contest news: Josh Hays was the first to correctly identify the packages in RTNv9n1. The question was what are the real names for !FalseSpace, 3D-Atelier, LightSwell, RayReverie, and AutoPUNK. The answers: truespace, 3d studio, lightwave, raydream, and autocad.

Stephen Westin was the first to identify the two uses of the acronym "STL" in the field of computer graphics (RTNv10n1): (1) Stereolithography (actually the triangle-based geometry file format for 3D Systems' Stereolithography (r) devices), (2) Standard Template Library (for C++). Jens Kilian came in a close second.

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We've got a small computer graphics research group here at Malaga University, Spain, and I've been playing for some time with analytic atmospheric scattering effects (I mean, avoiding sampling along rays, using simplified scattering models that have a direct integral solution). In particular, we've devised a nice solution for Warn spotlights within homogeneous fog.

You can see some test images in: http://www.geocities.com/TimesSquare/2143

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Efficiency Scheme Pointers

I've been browsing all the Ray Tracing Newses more than I ever have in the past, since I'm spending a few weeks in a graduate course I'm currently teaching going over spatial data structures to speed up ray tracing. In a sense, we're just putting together the pieces from all the papers that have been written over the years. Your RTN collections are a nice complement to the (often too formal and biased) presentations of journal and conference papers.

In any case, I've found it helpful to collect together a list of the most relevant RTN articles into my own HTML file and organize them by topic, instead of chronologically: http://www.cs.cmu.edu/~ph/rtn_index.html

- Paul Heckbert (ph@CS.CMU.EDU)

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An encyclopedia-like collection of articles from comp.graphics.* on a wide variety of topics is available at: http://research.microsoft.com/~hollasch/cgnotes/

- Steve Hollasch (stevehol@MICROSOFT.com)

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On my homepage I have added links to graphics journals and conferences with home pages: http://www.cs.utah.edu/~shirley/

I have a list of advanced graphics course pages:

http://www.cs.utah.edu/~shirley/courses.html

If you teach some sort of advanced graphics course (e.g. a seminar on rendering) and want to be listed send me mail.

- Pete Shirley (shirley@cs.utah.edu)

________

BMRT 2.3.5 is ready! Lots of bug fixes and subtle enhancements are there, but the big news is that this version has support for true displacements. It's expensive, and less flexible than PRMan, but it basically works. Give it a try. Look in the manual for more details.

Other highlights of 2.3.5 include: fixes to some subtle handedness problems of 1-sided primitives; fixes to vertex variable interpolation; working trim curve sense attribute; improved derivative calculations for some subtle cases; support for RiReadArchive instead of ##Include; and HTML documentation. The full list of fixes and enhancements can be found in the "Changes" file that comes with the distribution.

The WWW site for BMRT is http://www.seas.gwu.edu/student/gritz/bmrt.html

- Larry Gritz (lg@pixar.com)

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3DS/NFF Online Raytracer!

I just installed an online-raytracer for 3DS/NFF scenes at:

http://tissot.rz.tu-ilmenau.de:8000/cgi-bin/gxtrace.cgi

It's a PVM'ed version of the GX/GENERIC raytracer, running on 10 SGI R5000

- JuHu (Nguyen Duc Cuong) (juhu@rz.tu-ilmenau.de)

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There is a wonderful *annotated* global illumination bibliography that has been put together by Travlex Yeap. You can access it at: http://www.scs.leeds.ac.uk/mscytsy/md/abs-mnu.htm

- Ian Ashdown (iashdown@ledalite.com)

____

Ian's 1031 bibliography have been converted to a 2 frames hyperlink format for easy reference... http://www.scs.leeds.ac.uk/mscytsy/md/abs-ian0.htm

for direct access.

- Tralvex Yeap (mscytsy@scs.leeds.ac.uk)

________

SIGGRAPH Articles

Many of the articles in the SIGGRAPH '96 Proceedings were available on the web before the conference. If you don't have this Proceedings, the web site is still around, at: http://www.cs.utah.edu/~ppsloan/siggraph96.html

SIGGRAPH '97 articles are also starting to appear on-line. One paper about ray tracing is "Rendering Complex Scenes with Memory-Coherent Ray Tracing" by Matt Pharr, Craig Kolb, and Pat Hanrahan, at: http://www-graphics.stanford.edu/papers/coherentrt/

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Cool Relight Trick

At Foundation imaging we used the primary and secondary specular colors, combined with the edge-falloff, to make really cool view-dependent iridescence! Set one broad specular to be full strength in direct view and 0 strength at the edge, and the other specular to be opposite. It's fun.

- Steve Worley (steve@worley.com)

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RT Evolution

For info about RTEvol (RayTraced Evolution), a free package for procedural modelling, using Lindenmeyer-grammars and interpreted C-like macros/function, look at this URL: http://www.rz.tu-ilmenau.de/~juhu/GX/RTEvol/

Primarily I use this package to test some raytracing-acceleration techniques, but now it expands to a fully programmable system. It is an ideal tool for quickly generation of test-scenes.

- JuHu (Nguyen Duc Cuong) (juhu@rz.tu-ilmenau.de)

________

Free Daily Spectrum Subscription

Email subscriptions to Daily Spectrum are now free of charge to members of the interactive media/online development industry. If you do not currently receive Daily Spectrum by email, and would like to, fill out the following form and send it by email to duberman@dnai.com

Please forward copies of this message to associates who you think would like to subscribe to Daily Spectrum.

Your name: email address: Organization name: Your title:

Please note: You must fill out the above form in its entirety to receive a free subscription to Daily Spectrum.

- David Duberman (duberman@dnai.com)

[I like the Daily Spectrum, I even laid out money for a subscription when it first went commercial. Other good computer graphics related ezines include "The WAVE" (http://www.fourthwave.com/wave/), "The Tessellation Times" (http://www.3dartist.com/tess/tessmain.htm), and "upFront" (http://users.uniserve.com/~ralphg/) -EAH]

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Java raytracer @ http://web.mit.edu/lbw/www/laser/html/raytrace.html

I believe it is the first real raytracer written in Java; Gamelan (www.gamelan.com) only lists one other and it is not very powerful.

- Morgan McGuire (morganm@mit.edu)

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The paper "Ray-Tracing with Affine Transforms" is available at: http://www.olympus.net/biz/7seas/contain.html

________

I was recently pointed to the web page:

http://www.erim.org/on-line-docs/GUIDE/guide.frm.html

which has a discussion of several BRDF models. It has several small errors, but also some very good information.

________

A postscript version of the paper:

Automatic Termination Criteria for Ray Tracing Hierarchies (from Graphics Interface '91)

is available from my web page: http://www.cs.uncc.edu/~krs/publ.html

I also have a postscript file of my thesis.

- K.R.Subramanian (krs@zappa.cs.uncc.edu)

________

ART (Advanced Rendering Technology) - has developed a dedicated ray-tracing chip claiming 80,000,000 intersections a second. Also, they will have a box with 64 of these chips on it: http://www.art.co.uk

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Snapshots of Silly Space v2.00 are now on-line at: http://inside.net/silicon_softworks

Silly Space v2.00 supports:

- Real-time 3D click and drag, mindless user interface. - Multiple Cameras and multiple views with split panes, zooming, wireframe, field shape/size indicators. - Real-time 3D transparent blob modeling. - Multiple field shapes (not just spheres) with scaling in all directions of *individual field shapes*. - Adjustable space tessellation. - File loading and saving. - It's OpenGL based now so it's really reliable.

Silly Space, it's "Artsy Space."

- Kyle Lussier (lussier@cis.ufl.edu)

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Iv2Ray - Inventor (VRML 1.0) to Rayshade Translator

The beta executable of iv2ray for Irix 5.3 is now available from Cow House Productions web page at http://www.cowhouse.com/Home/Iv2Ray/IvToRay.html. Iv2ray is an OpenInventor to Rayshade translator. It converts Inventor 2.0 format files (VRML 1.0) to the input language of the Rayshade ray-tracer.

Cow House is offering this program free of charge. If you need the source code, drop me an e-mail at laser@cowhouse.com - I will consider giving it out if you give me a good reason.

If you do download and use this tool, please drop me an e-mail and let me know what you think. And absolutely, let me know if find any bugs.

- Mark Lasersohn (laser@cowhouse.com)

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There is a comparison between Lightscape, Specter and Radiance at: http://rmp.kiam1.rssi.ru/articles/pals/.

There is also a paper "Comparison of two Methods of Global Illumination Analysis" devoted to comparison of Deterministic and Monte Carlo algorithms of global illumination analysis: http://rmp.kiam1.rssi.ru/articles/cmgia/

- Andrei Khodulev (abkhod@gin.keldysh.ru)

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If you want to see some other examples of how close Radiance can come to reality (I always do), check out the following web page: http://sap.mit.edu/projects/studioimages.html

This is work done independently by Philip Thompson and Jack DeValpine at MIT.

- Greg Ward (greg@hobbes.lbl.gov)

[If you are seriously interested in the topic, you might contact Greg or Andrei; there was an involved debate about the testing conditions used for the images. -EAH]

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The large (6500 ref) computational geometry bibliography is at: http://www.cs.duke.edu/~jeffe/compgeom/biblios.html

- Paul Heckbert (ph@CS.CMU.EDU)

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Free Textures!

You can find free textures on my site : http://www.mnet.fr/axem

- CORREIA Emmanuel (axem@mnet.fr)

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I've created an index to mesh generation info on the world wide web. This might be of interest to radiosity researchers: http://www.cs.cmu.edu/~ph/mesh.html

- Paul Heckbert (ph@CS.CMU.EDU)

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Here's a haptic web site: http://haptic.mech.nwu.edu/

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My Ph.D Thesis is available on the WWW:

http://www.cs.kuleuven.ac.be/cwis/research/graphics/CGRG.PUBLICATIONS/PHDPHD/

The files are available as gzipped postscript. If you have any problems in downloading the text, please do not hesitate to contact me.

Title: Mathematical Frameworks and Monte Carlo Algorithms for Global Illumination in Computer Graphics

- Philip Dutre (Philip.Dutre@cs.kuleuven.ac.be)

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Try rendering through the Web (project I supervised summer of '96): http://www.cse.ucsc.edu/~jastory/volrender.html

Links to Bill Lorensen's neat vol. renderer web interfaces there too.

- Craig Wittenbrink (craig@verity.hpl.hp.com)

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One of our animators was trying to simulate a shadow using a projection light. He created a texture that was white where he wanted light, and black where he wanted shadow. Then he used a special material shader we have called a 'shadow-only' shader that renders the inverse shadow (ie. white/gray wherever there are shadows and black everywhere else). As you might guess, the "shadows" from the projection light did not show up in the image generated by the shadow-only shader.

When I explained the situation to him I caught myself saying:

"Well, those points are not in shadow. They are illuminated with black light."

He looked at me with a completely blank expression, so I went on:

"If you were in a completely closed room without a light, would the room be completely shadowed, or not illuminated?"

The boundary between science and philosophy is a blurry one.

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I often ask myself: Monte-Carlo ray-tracing, is this the way to do global illumination in the future? After reading a lot of papers about Monte Carlo methods, I still get confused with their terminologies. I can't see any advantage of these methods over traditional methods (radiosity), except the fact that meshing is not needed, and that you can do reference-images for RMS-benchmarking (!)

[Pete's reply quotes JuHu's text, so the rest of his note is included there]

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Pete Shirley (shirley@facility.cs.utah.edu) replies:

There is a lot of confusion on this because we all over-hype our methods in papers (me included) and as reviewers and authors we are sloppy about making people carefully characterize their methods.

Here - I will make up four scenes:

1. Lambertian Cornell box 2. Lambertian Cornell box w/smooth metal box 3. Lambertian Cornell box w/glass sphere instead of short block 4. Semi-matte (direction diffuse) Cornell box 5. Semi-matte (direction diffuse) Cornell box with "real object (10^6 patches)

1. Traditional world-space FE (finite elements, i.e. meshed polygons) will work easily and we can do a walkthrough. RADIANCE will also work easily, but will not in practice allow a walkthrough - the view-independent info is there, but it is not easily accessible. MCPT (Monte Carlo path tracing) will take all day, but will give an unbiased image (so what?).

2. Now radiosity has problems. We can add a virtual world, or use particle-tracing based radiosity with a density estimation post-process, but then doing the walkthrough is a problem. RADIANCE does fine for a given viewpoint, and we can re-use the irradiance map. MCPT will have LOTS of noise on the ceiling unless very good importance sampling is used.

3. Uh-oh - particle tracing based radiosity works. RADIANCE and MCPT will have a very noisy caustic under the ball (although RADIANCE will not have this problem for the important glass case - windows!).

4. Ouch. Sillion-style FE works, as does Jensen's photon map. MCPT is so dumb, it doesn't realize that this case is harder than Lambertian. RADIANCE will not work because it caches irradiance, so it will degenerate to MCPT (really, you can treat secondary bounces as Lambertian - I believe this is a good move in almost all scenes, but it is hard to quantitatively justify).

5. Ouch^2. FE runs out of memory FAST. MCPT works no worse than 4. Jensen's photon map also works, but will be storage-intensive if the object is not very smooth. Radiance will perform as in 4.

In summary, pure MCPT has only two advantages - it is so dumb that it doesn't get hit by big scenes, and it is easy to implement. If you want an interactive walkthrough, then you are currently limited to radiosity (I use that term for all world space irradiance calculating alg's), and that limits you to a relatively small scene (100k initial polygons will kill almost all radiosity implementations).

JuHu writes:

> For me, the most important feature of a rendering method is not its

> physical-correctness, but its efficiency and visual-aesthetic-possibilty.

> With MC-rendering, I must spend lot of works to develop specific sampling

> schemes and reasonable 'good' estimators. Even w/ that, I still get useless

> images (too noisy!), or I must increase the sampling rate and wait forever...

> It is not always true that most people find noises less observable than

> aliasing (i.e. white pixels in a dark-corner versus aliased dark-lines).

I agree with the above, and I think the solution is hybrid methods - add bias! (This is blasphemy in MC circles :^) ). I do want to keep the good parts of MC methods - they are damned robust and are possible to implement correctly - my MC code does not bomb on weird untweaked inputs - tell me with a straight face that is true of most non-MC implementations. However, you are right that the results are too noisy!!! We can keep these benefits and reduce noise if we add bias the right way (not that I know what that right way is).

JuHu writes:

> Especially for the direct lighting computation, MC-methods are definitely

> *NOT* the way to go. Most regions of an image are not in shadow, so why

> should we cast so many shadow-rays to the light-source? In fact, we don't

> need to cast any

> shadow-rays, if the visibilities are known a priori ( w/ shaftculling) and

> the radiance coming from the light can be easily computed (analytically).

> Only for the case where complex shadowing occurs would MC-sampling be

> helpful. Also for this case, the soft-shadows generated w/ them can be much

> better without increasing the sampling rate (We simple smooth the

> shadow-regions, visual-aesthetic, not physical-correct!).

I welcome you to implement shaft-culling on scene 5 above. Slower than MC, and will usually core-dump even with a year of implementation I'll bet. Now shaft culling on simplified geometries (which it sounds like you might be suggesting) sounds like a very good idea. Only use MC when needed - yes, definitely smart.

Overall, this has got me to again reflect on the state of our field. It is VERY hard to get a rendering paper into SIGGRAPH, even with good reviews. It is easy to get toys based on low-hanging fruit into SIGGRAPH. Clearly we are doing something very wrong (you could rightly argue SIGGRAPH is doing something wrong, but that won't change anything - we have to figure out where our share of the blame is). I think this is partially because most graphics people think TOY STORY graphics is good enough. I, however, want virtual reality that looks REAL and is predictive - I don't want a virtual cartoon world. We are very far from getting things to look real, and from understanding our algorithms' behaviors. No working program gives useful error estimates. We have totally inadequate local reflection models. Most algorithms are memory hogs and don't parallelize. Most algorithms do a very poor job with dielectrics (water, glass). I think we need to make our own "grand challenge" models, and publicize that they can't currently be done (e.g. a human at a desk illuminated through a skylight), so that our field won't dry up and blow away.

____

Nguyen D.C. (JuHu) replies:

> I welcome you to implement shaft-culling on scene 5 above. Slower

> than MC, and will usually core-dump even with a year

> of implementation I'll bet.

I've actually implemented shaft-culling for complex-scenes in GX/GENERIC. Not really shaft-culling, but a combined version of Arvo's hyperoctree and Haines's light-buffer. It's definitely faster than pure MC, because the cost for collision-test between a beam and a bbox is quite the same between a ray and a bbox.

____

Stephen Westin (swestin@ford.com) writes:

Why do folks bother at all with Monte Carlo methods for global illumination? Complexity.

Think of the problem of computing the irradiance at a given point. Do you want to go around the whole environment, calculating the irradiance from every object, regardless of occlusion or distance from the point? Or do you want to probe the environment, spending similar effort for every incident direction? This is the basic choice between mesh-based methods and Monte Carlo calculations. For simple environments, the mesh-based methods are excellent; they give no noise artifacts, and computation is tractable. For extremely complex environments, mesh-based algorithms tend to get inefficient.

Actually, the mesh-based world and Monte Carlo are working toward each other. Hierarchical meshing is basically a way to make a mesh-based algorithm behave more like Monte Carlo, spending effort for irradiance contributions rather than for geometric complexity. And any well-designed Monte Carlo calculation uses deterministic methods wherever practical, and attempts to take advantage of spatial coherence. The ultimate global illumination method will probably be a hybrid of Monte Carlo and mesh-based methods.

____

From: Eric Veach (ericv@cs.stanford.edu)

One of the big advantages of MC algorithms is that they let you model the scene you actually want to use. Sure, radiosity algorithms can be efficient - if we limit ourselves to diffuse surfaces, with maybe a few mirrors or whatever that are handled in a ray-tracing pass. But flat polygons and diffuse reflectors do not go very far in modeling the real world, and finite-element algorithms don't seem to be practical for much more than this (Memory usage blows up for complex scenes, or when there are lots of glossy surfaces).

This is an important issue in graphics, since often the biggest source of error is the scene model itself. What good is an accurate solution to the wrong scene model? At least MC algorithms start with the desired input. Even if you aren't interested in physically correct results, diffuse surfaces lead to that wonderful "computer graphics look" we all know and love.

It's no wonder that radiosity algorithms tend to be faster, since they are solving a much simpler problem: the solution is only a two-dimensional function rather than a four-dimensional one. To me, the amazing thing is that radiosity algorithms need to be so *complicated* to be efficient. By the time you implement discontinuity meshing, hierarchical basis functions, clustering, shaft culling, etc., how many lines of code are we talking about? And can you actually trust it not to core-dump, and to compute a reasonable result in a reasonable amount of time?

And let's not kid ourselves that an algorithm is "general" just because it can handle a few mirrors or glossy surfaces. The real test of generality is how an algorithm performs when there are *no* diffuse surfaces, since that's how it is in the real world.

Another reason to use MC algorithms is scene complexity. Finite element algorithms work with explicit representations of the scene and its properties. They are strongly affected by the size and complexity of the scene representation. On the other hand, Monte Carlo algorithms are based on sampling, which means that the scene model is accessed through a small set of queries (e.g. what is the first surface point intersected by this ray?) This hides the scene complexity behind a layer of abstraction, and can mean that rendering times are only loosely coupled to the scene representation (e.g. it may affect the time required to cast a ray). In effect, Monte Carlo algorithms can sample the scene to determine the information they actually need, while deterministic algorithms examine every detail, whether it is relevant or not.

That's not to say that MC algorithms need to sample *everything*. It's perfectly reasonable to embed deterministic calculations within a Monte Carlo framework, especially for low-dimensional integration problems (e.g. direct lighting from a small number of uniform, diffuse, polygonal luminaires). Sometimes this introduces bias, but often this is okay, especially when we can bound the errors or at least characterize them.

Ideally, rendering algorithms should not depend on the details of the scene representation, but only on the underlying mathematical model. For example, a square area light source can be simulated fairly well with a ten by ten array of point sources, but many rendering algorithms would have a much worse performance in the second case. Similarly, if we replace the square light source by two fluorescent bulbs covered by a diffusely transmitting panel, why should it make a huge difference to our algorithms? The same comments apply to geometric complexity: if we represent an indoor plant as a thousand polygons or a million Bezier patches, how much should the rendering time go up?

I can't say that MC algorithms have achieved this level of isolation from the scene representation, but at least it seems that the opportunity is there. There has been a lot of emphasis on rendering algorithms that exploit special properties of the input scene, e.g. that lighting is direct rather than through a diffusing panel or bouncing off the ceiling. It would be nice to see more work on algorithms whose performance does not go down the tubes when these conditions are not met, i.e. algorithms that are more *robust*. It seems that this should be possible without resorting to the level of "dumbness" found in MCPT (as Pete Shirley put it).

I guess the last major issue for MC algorithms is the correctness of the results. Here it is important to distinguish between unbiased, biased, and consistent estimators. Intuitively, an unbiased estimator computes the right answer, on average. A biased estimator computes the wrong answer, on average. A consistent estimator also computes the wrong answer, on average, but the error can be made arbitrarily small by increasing the number of samples. Most of the "biased" algorithms in graphics are in fact consistent, otherwise we wouldn't have any confidence at all in their results.

The main advantage of unbiased algorithms is that they make it far easier to estimate the error in a solution. For unbiased algorithms, this error can be estimated by the sample variance, since any error is guaranteed to show up as random variation among the samples. Thus, if an unbiased image is not noisy, we can be reasonably sure that it is correct. For scene of realistic complexity, this seems to be the only practical way to generate correct images.

For algorithms which are merely consistent, however, we must also bound the bias. In general this is difficult to do; we cannot estimate bias by simply drawing a few more samples. Bias shows up as results that are not noisy, but in fact are incorrect. In graphics algorithms, this error is often noticeable visually, in the form of discontinuities, excessive blurring, or surface shading that just looks wrong.

Other things being equal, it is clear that we should prefer an unbiased algorithm. If these algorithms were also robust and efficient, then why would we want to use anything else? However, conventional wisdom says that unbiased methods are "too expensive", and that we can achieve an acceptable image in less time by making approximations.

But where is the research to support this claim? There has been a huge amount of effort on approximate methods in graphics, while there has been hardly any work on unbiased algorithms. Some people seem to think that "unbiased" is a synonym for "pure Monte Carlo path tracing". Until we have thoroughly explored this type of algorithm, we can hardly make judgements on their capabilities. I would like to see more results on what can and cannot be achieved by unbiased methods, so that we can make better decisions on these issues.

(Can you tell that I'm writing a thesis? :-)

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- The surface acne problem [in which a ray originating from a surface intersects the surface itself - a bad thing] can be fixed by being careful about keeping the surface orientation information around and ignoring intersections that are definitely acne. Top of p. 47 of "An Introduction to Ray Tracing" discusses this solution, and it's my favorite - I wish I had explained it more thoroughly there.

For a polygon, when you know the ray is originating on it, you simply never test the ray against the polygon, since there's no way such an originating ray can hit it. For a sphere, you determine which sort of ray it is, i.e. whether it is passing into or out of the sphere. If out of, then you can never hit the sphere; if into, then only accept the larger of the two roots as an acceptable intersection point (the closer intersection will be at the origin). This is foolproof.

For closed [i.e. manifold, where there is a definite inside and outside]higher order surfaces you also don't need an epsilon. For example, imagine you have some arbitrarily high order closed surface, terribly warped, and you have a ray originating on its surface. Say one side of the patch is red and the other side blue. Now, the ray originates and travels away from one side or the other, which can be determined at the start of its journey. Say we start with the ray leaving from the red side. Now we get a list of intersections for that ray. What we want is only the intersections in which we hit the red side; blue side intersections are not what the ray needs. Even if the ray is a shadow feeler for transmitting rays (where you're filtering by all it hits, say) or a ray cast for solids properties computations, you can wait until you get to the first positive red intersection on the ray and then deal with all intersections from here on in.

Spline patches or other surfaces that are not manifold (closed) need more care, and this is where an epsilon starts to come back into play, since you could view the blue side of a surface from the red side. The nice thing is that you do not need to use an epsilon for the red intersections, so very close, valid intersection points are not discarded for being within epsilon. Anyway, my main point is that for a large number of classes of primitives you can fully solve the problem without using epsilon at all.

[For what it's worth, I think I invented the "acne" term - some claim to fame! I used it in the 1987 ray tracing course at SIGGRAPH - my only laugh-getter in an otherwise dull talk.]

- The terminator problem [in which, due to interpolation of the normal across a flat polygon, a reflected ray actually reflects into the surface instead of away from it] I solve in a similar fashion: I never let reflective rays actually reflect through the surface. By forcing the reflection to stay on the same side (rotating it in the reflection plane until it is), it is not a problem. Of course, the reflection itself will not quite be right, but it will be a lot better than some sudden blackness due to intersection (i.e. due to the ray reflecting into the surface and hitting inside the object). This approach doesn't work for shadows, though...

- Naive texture interpolation: good points, and it's even worse in the limiting cases of say the tip of a cone or pole of a sphere: here the quads are still quads, but two of the vertices are in the same location (but with different (u,v)'s and normals). Replacing with two triangles is absolutely horrible.

Which leads into the next article...

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Here's the case: you have a cone (or section of a cone; the singularity at the tip is not the problem, it just exacerbates it. Having one end of the cone have a radius much smaller than the other is the real problem) and a texture you want on the cone. Say the texture image says VRML, and you want it to naturally go around the cone in a typical (u,v) [or (s,t) or whatever you like to use] fashion, with the cone's tip pointing upwards. This is the default mapping of a texture on a cone in VRML, in fact.

What you typically do is to tessellate the cone into a set of triangles, right? However, at the tip of each of these triangles you really need two vertices - each of these two vertices have the same x,y,z location (the apex) but a different (u,v) pair [e.g. if you tessellate into 10 triangles, you really need 10 quads, with the first quad having two apex points with (u,v) of (0,1) and (0.1,1), second quad (0.1,1) and (0.2,1), etc]. If you just make triangles and not quads and just arbitrarily pick one of the two (u,v)'s to store at the apex, you'll lose half of the texture because each triangle will only cover half of its section in the texture map. So anyway you make quads. Using a reasonable software renderer that handles polygons as is, these quads will render fine. However, if you're using hardware and that hardware renders triangles (or software renders only triangles, for that matter), you're in trouble: the hardware will "split" the quads you sent to it into two triangles. But because two of the quad's vertices are in the same location, one of these two triangles will have zero area (coincident vertices) and so will have no effect on the rendering; that triangle's part of the texture map disappears. An underlying assumption of most hardware accelerators is that a convex polygon can be perfectly replaced by a fan of triangles, but this turns out to be false.

I don't think most people have really realized that it has a serious effect on hardware acceleration schemes. I personally found this problem surprising - I always thought triangles really were enough for rendering any textured surface. Of course, you could always subdividing the cone with horizontal cuts and so make quads with area for both triangles (Ken Turkowski's idea; Woo et al. also present this idea in their article) but there's still a problem at the tip. You could also warp the texture map itself so that the "missing" triangles no longer have any texture information and the rest of the texture is pushed into the visible textured areas. Neither of these is a good solution for VRML, where polygon counts are to be kept low and the level of tessellation is not under the user's control.

This problem is actually more general than just the somewhat pathological cone tip problem. It happens any place where a texture mapping has some singularity. For example, at the poles of a tessellated sphere you get the same sort of problem. The famous teapot has the same problem at the center of the handle when texture mapped and when triangles are used. It is not that noticeable because these triangles are pretty small, but it is there.

Also, this problem is not limited to texture mapping. Normals at the tip of the cone have the same interpolation problems. The visual artifact is that the shading is not smooth near the tip of the cone. In fact, some surface-based modelers which use triangles as their underlying primitives will not allow the creation of a cone with a tip for a similar reason: since each vertex has only one normal stored with it, if a tip gets created then the proper set of normals cannot be used. Such modelers address the problem by trimming off a tiny bit of the tip so that a set of vertices is generated, each storing a reasonable normal. Note that this solution does not fully eradicate the discontinuities - the extra points generate extremely thin triangles (almost zero area). In practice, such shading discontinuities due to normals not matching along an edge between two triangles are not that noticeable (the effect is strongest at the tip, which covers little area) and can be addressed by simply tessellating the cone into more triangles.

Note that this problem occurs only when using triangles and keeping information like normals and texture coordinates at the vertices. Using quads solves the problem, and other rendering techniques can also solve the problem. For example, if instead of using texture coordinates to do texture mapping on the cone you instead accessed the inverse mapping function for the cone [i.e. you take the point on the approximated cone that you want to texture and compute from it the exact (u,v) coordinate on the cone] you would get the right answer. This is often what photo-realistic renderers will do, but is usually not practical for real-time performance.

The gist is that triangles are not always enough. Quads turning into triangles is the limiting case, but as Woo et al [http://ada.computer.org:80/pubs/cg&a/articles/g50021.pdf] show, texturing problems occur whenever a non-rectangular quad is tessellated into two triangles.

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>I'm surveying a cross section of research publications in global illumination

>and have come across a few candidates for what I'd consider to be "the bible"

>for this field (in the same sense that the Foley & Van Dam book is for CG in

>general). I'd like to hear your opinions on the matter. I've skimmed through

>the past archived communications for globillum in case this was already

>discussed, but it doesn't seem to have been recently. So...

In my very humble opinion, the definitive bible on global illumination has yet to be written. One good reason for this is that global illumination research is still a very active topic. There have been close to 100 global illumination papers and theses released in the past six months alone. Given that it takes 12 to 18 months to get a book written and published, any "bible" will be at least a year out of date as soon as it is released.

>Andrew S. Glassner: Principles of Digital Image Synthesis

>

>Is it well worth the US$90? How much does it cost in the UK?

>I'm considering diverting a portion of my student grant toward acquiring

>the two volume set. (Fewer beers on weekends, looks like...)

Knowing how much one publisher in particular marks up its books for the UK market, I shudder to think how much the two-volume set will cost you. You may have to give up beer for the remainder of your academic career :+)

For what it's worth, I much prefer Glassner to Foley et alia as my primary CG reference. However, I can appreciate that many undergraduate students may be intimidated by the mathematical depth of the former. Different strokes ...

>How does it compare to the less expensive alternatives:

>

>Francois X. Sillion & Claude Puech: Radiosity and Global Illumination

>

>Michael F. Cohen & John R. Wallace: Radiosity and Realistic Image Synthesis

It all depends on your needs and interests, and also on whether you are interested in (and enjoy) the mathematical details. I have all three, and I can recommend any of them.

>...any others I should know about?

I haven't had the opportunity to read this book, but you might try:

Kok, Arjan J. F. 1994. "Ray Tracing and Radiosity Algorithms for Photorealistic Image Synthesis," Delft University Press, Stevinweg 1, 2628 CN Delft, The Netherlands, ISBN 90-6275-981-5. (Also available from Coronet Books, Philadelphia.)

This was Arjan's PhD thesis at the Delft University of Technology.

There have been at least two other books written on radiosity, but neither qualify as global illumination "bibles."

Actually, the best sources of up-to-date and comprehensive information on global illumination techniques are the most recent MSc and PhD theses, many of which are available online. PhD theses in particular are great -- the poor students are required to demonstrate their in-depth knowledge of the field, which generally means a 50-page prologue to their actual research topic, and a bibliography with at least 50 references.

For a complete listing ... ah heck, you know where to find my bibliography ;+> [http://www.ledalite.com/]

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Syndesis Corporation recently released Megahedron, a 3D graphics engine controlled by a high-level interpreted language called SMPL. SMPL reportedly combines the broad functionality of C, the ease of Pascal and BASIC, and the type-safe, interpreted nature of Java.

With Megahedron, you can write interactive 3D programs containing "smart" objects designed to move and react. Your scripts can build models according to rules and procedures, instead of building models by hand. It includes a renderer for static scenes.

This precision is important for simulation, scientific visualization, virtual reality and game design. Megahedron is useful for learning about 3D programming, too. The SMPL language frees you from the chore of writing low-level graphics functions. Useful programs can be written in just a few lines of code.

Megahedron includes distributed ray-tracing, combining up to 64 computers to compute a single image, sharing computers on a local network or even across the Internet. It can ray-trace in real-time, in an interactive low-res fashion.

Megahedron has a retail price of $99. The CD-ROM includes online documentation viewable in any Web browser, more than 300 example SMPL programs, and executables for Windows 95, Windows NT Intel and Alpha, Linux and SGI IRIX. With its flexible software license, one person may run as many copies as they can.

Time-limited demos of Megahedron for each platform are available on Syndesis' Web site at http://www.threedee.com. The manual for Megahedron is online, too, along with dozens of example scripts and sample images.

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The first question to ask is, "why do you want to test the on edge condition?" One nice feature of the crossings test (where you count the number of edges between the test point and the outside world; an odd number of edges means the point is inside) is that when a single test point is checked against a mesh of polygons, at most one polygon will contain the point. That is, when a point is on an edge shared by two polygons, the crossings test is consistent (though somewhat arbitrary) in that the point will not be inside both or outside both polygons but always inside one polygon or the other. This feature is handy for, say, GIS - any point on a map split into areas will be inside one and only one area when using the crossings test. [See the next article for another use of this property]

If you truly do want to test for the "on" condition, my general advice is to test for this separately. First test each edge against the sample point and see if the sample is within your epsilon of the edge. If this test fails, then go ahead and do a normal inside-outside test. Yes, it's more expensive than trying to modify the crossings test to (attempt to) yield "on" conditions, but it's more predictable, understandable, and debuggable.

Actually, you can probably gain a bit of efficiency by using some other inside-outside test such as the barycentric or half-plane tests, in which the point is tested to see if it is inside an odd number of triangles formed by a fan from one polygon vertex. These sorts of inside-outside tests can be a little flakey on concave polygons, as if the test point is on an edge shared by neighboring triangles it must be counted as being inside only once. The advantage of using these sorts of tests is that they compute intermediate values (edge vectors, dot products, etc) which are also useful in computing the distance from an exterior edge to the test point.

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However, not all data is well-defined for some systems. For example, a complex bevel might be represented by a quadrilateral mesh and some of the quads may be warped. There are other operations which can yield unflat general polygons (I recall a beautiful polygonal model of the Statue of Liberty which looked great when z-buffered but had all sorts of terrible warped polygons when ray traced). If you do point in poly testing you can get a bug: some of these unflat polygons will cast onto one orthogonal plane, some upon another, and the warped nature of the polygons can give a result in which a ray that should have hit *some* polygon in the mesh will miss them all. This all sounds unlikely and theoretic, but it definitely does happen.

One answer is to triangulate these polygons (triangles always being flat), which costs more memory and changes the database. Also, a tessellator that works on all misshapen polygons is hard to find (I don't have one!) - the problem is that you usually need to find a direction to cast the polygon which keeps the data well-behaved and avoids having any self-intersection. However, a direct test is possible: if you cast all polygons along the direction of the ray itself when you do inside-outside testing, you guarantee that when a ray is directed towards the interior of the mesh it will hit (at least) one polygon in the mesh.

One little side effect of such an intersection test is that the intersection point first computed for the plane is somewhat arbitrary - since all the vertices of this unflat polygon do not lie in a plane, there is no right answer for what exact depth a point in the interior has. However, we do know the edges have a precise depth, so a good solution is to find the left and right edges (by giving the ray an arbitrary "up" direction) and interpolate a good depth from these.

Note that this method of casting along the ray is essentially the same as that used in scanline hidden surface algorithms, where a projection is used to cast the polygons onto the image plane.

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I'm the archivist for Graphics Gems; the latest Graphics Gems release is at http://www.acm.org/tog/GraphicsGems. Watch out with the Narkhede tessellator in Graphics Gems V. It probably works for polygons without holes, but it fails on single outline polygons with holes (in other words, you connect the holes to the perimeter with a pair of bridging edges).

O'Rourke does have a tessellator available online, from his (wonderful) book "Computational Geometry in C", it's at ftp://cs.smith.edu/pub/compgeom/ - I can't vouch for the robustness, I vaguely recall that it may not handle bridging edges well either.

Also check Paul Heckbert's site http://www.cs.cmu.edu/~ph/ under "My Bibliographies and Link Collections" for some links to mesh generation and simplification related material.

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I have a problem relating to finding neighbouring voxels in octrees and feel sure this must have been addressed previously.

I want to be able to find all the neighbouring (adjacent in space) voxels from a given voxel stored in an octree. It seems feasible that an operation based on traversal of the octree will allow neighbouring voxels to be discovered.

____

From: Andrew Glassner (glassner@microsoft.com)

I believe they're called "Neighbor Pointers" - that might be a good place to start looking in the index.

____

From: Francois Sillion (Francois.Sillion@imag.fr)

I have only done it with quadtrees, but I believe that you will find simple code that does precisely that in one of H. Samet's book on hierarchical data structures.

book{Samet90, author = {Hanan Samet}, title = {The Design and Analysis of Spatial Data Structures}, publisher = {Addison-Wesley}, address = {Reading, Massachusetts}, year = {1990} }

book{Samet, author = {Hanan Samet}, title = {Applications of Spatial Data Structures}, publisher = {Addison-Wesley}, address = {Reading, Massachusetts}, year = {1990} }

____

From: Paul Heckbert (ph@cs.cmu.edu)

One of the methods that Samet describes does not require neighbor pointers (although that is certainly one way to do it), but instead you ascend the tree until you can step in the direction you want, then you descend the tree, staying as close spatially to the previous point as possible, until you hit a leaf, or get to the level of the tree that you desire.

With this method, you don't need neighbor pointers, just 8 child pointers and 1 parent pointer. Samet shows, as I recall, that you go up and down 2 times, on average, i.e. that the average cost to find a neighbor is O(1). If you found neighbors by starting at the root every time, it would cost O(depth).

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A Canadian free-lance writer (not me!) this week launched a CDN$100 million law suit against ITP (International Thompson Publishing) for copyright infringement. She had sold an excerpt from her book to ITP's Globe and Mail newspaper of Toronto ON. In addition to printing the article in the newspaper, ITP placed the article in their electronic database, which is accessible by other ITP-owned companies. The author is objecting to the possibility of other newspapers reprinting her article without compensation.

One problem faced by authors is that publishers sometimes reuse their work without additional compensation. (The situation is akin to the problem software companies have of people using more than one copy of a single software license.) One AutoCAD author successfully sued after the publisher reused her book as part of a larger book without compensation.

What can authors do? First, remember that no contract is "standard," as publishers are fond of describing them. You are free to change any part you don't like, even when the publisher insists no changes are permitted. (I am amused at how quickly an iron-clad contract changes when faced by a contract with better terms from a competing publisher!) An unsigned contract is merely an offer and you have every right to present a counter offer.

Second, follow this procedure: many magazines include a clause in their "standard" writer's contract that allows them to reuse the article in any form without additional compensation to the author. I routinely cross out that section and replace it with: "First North American serial rights only." That means the publisher can only print it once ("First") in a magazine ("serial") in North America. The publisher cannot place the article on a Web site, nor reuse the article, nor use the article outside of North America. These and other situations require the publisher to negotiate another contract with the author.

The Web makes it easy for authors to enforce these legal requirements. Simply use any search engine (I prefer Alta Vista) and do a search for your name. In less than a minute, you have a list of all Web sites containing your name. In case the publisher stripped your name, you may want to search for phrases you used in your articles.

____

Ralph runs the XYZ Publishing, Ltd. and, among other things, publishes a useful free ezine called upFront, which tracks CAD related topics and VRML. Visit his site at http://users.uniserve.com/~ralphg/

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My first stop was the University of Kaiserslautern, where I visited the research laboratory of Hans Hagen. Hans arranged for a schedule of demonstrations and discussions with his graduate students, and arranged for them to take me out to lunch and dinner in town (I paid for my food, but they provided the transportation and the company, which was a nice form of hospitality.) I was impressed with Hans' personal research in the design of plastic reflector and lens shapes for car headlights, to give a desired distribution of illumination intensity on the road. I also had a long discussion with Alexander Keller, who explained to me in detail the Quasi-Monte-Carlo method he was using for global illumination, which he presented at both of the next two meetings. He gave me the longer "uncut" version of his paper, so I was able to appreciate well the fact that certain non-random sequences of test points give estimates that converge much faster than for random test points. A final memorable project was a method where potential purchasers could design and view semi-custom prefabricated homes over the Internet.

The meeting in Schloss Dagstuhl was one of a series of week-long seminars in aspects of Computer Science partially supported by the governments of Germany and the state of Saarbrucken. The topic of this seminar was rendering, and it was scheduled to just precede the Eurographics workshop the following week. The hope was that attendees from outside Europe would gain efficiency in their long distance travel plans, which was the case for me, but many Europeans could not afford more than a week away from their institutions, especially if they were teaching, so the attendance at the Eurographics Workshop was actually down from last year. A summary of the some of talks follows.

Xavier Pueyo proposed methods for generating random densities of infinite lines in space, and intersecting each line with all objects in the scene to get form factor contributions from each segment in the space between two object surfaces. He chose his lines by connecting two random points on the surface of a sphere enclosing all the objects, which in fact does give the appropriate random density of lines, although this seems non-intuitive at first. Dani Tost discussed her work on visualizing blood vessels, involving both maximum intensity projection and shading, with voxel splats.

Henrick Wann Jensen's talk on "Global Illumination using Photon Maps" generated the most excitement and discussion of the seminar, because of the impressive performance of his method, which is based on saving in a spatial data structure (a KD tree) both position and direction of all hits by photon paths traced from light sources through multiple random bounces. During viewpoint dependent rendering, these are used for the intensity at the second bounce in a local pass from the eye, by expanding a sphere about the hit point until the n closest photon hits are found in the KD tree. At the first bounce from the eye, the same distribution is used for importance sampling of the bounced rays. Finally, the initial rays from the light source are continued past their first surface intersection to create shadow maps at subsequent intersections, which are used to decide when shadow feelers are necessary to determine direct illumination. Since the incoming directions are available, non diffuse reflections can be rendered. A separate caustic map, with many more photons directed at only the shiny surfaces, is used similarly at the first bounce in rendering.

Dani Lischinski gave a preview of a Siggraph paper on "Hierarchical Image Caching for Accelerated Walkthroughs of Complex Environments." Robert Garmann talked on the computational complexity of hierarchical radiosity, and gave a careful analysis of the number of links required in a simple scene with two parallel plane patches, in which the subdivision oracle is based on the total form factor of a link. He showed that the total number of links, as the allowed error approaches zero, is of order O(N^2), where N is the number of leaf nodes in the hierarchical subdivision. This seems to contradict previous beliefs that it would be O(N log N), or even O(N).

Dieter Fellner, working with Stefan Mueller's group at Darmstadt, showed how real time rendering of radiosity scenes could be accomplished on environments with the order of a million polygons, and presented an impressive video of additions to the Frankfort airport.

Wolfgang Sturzlinger talked about using hierarchical radiosity links in the local pass (final one bounce gather to the viewpoint) by doing a Weiler-Atherton type subdivision of the unit hemisphere, using 3D coordinates of the unit vectors, in order to determine the links involved at a pixel. Mark Summinger from Erlangen University talked about decoupling the reflection and transport operators in a progressive radiosity framework for non diffuse surfaces. The shot and transported energy is saved in a data structure which is indexed by both receiving position and angle bins. The advantage is that when it is time to shoot for a patch, all the energy in an incoming angle bin can be reflected at once, which requires fewer evaluations or accesses to the BDRF.

The abstracts to these talks were handwritten into a Dagstuhl record book, and are being transcribed to be sent to the participants and saved at Dagstuhl. The proceedings of the next conference I attended, the 7th Eurographics Workshop on Rendering, at Porto, Portugal, will be published rapidly by Springer.

At Porto, (and also at Dagstuhl) I spoke on "Hierarchical Rendering of Trees from Precomputed Multi-Layer Z-Buffers". This is based on reprojecting images of trees and their subparts, prerendered from different viewpoints (image based rendering). Fabrice Neyret gave a related paper which had an impressive video of a flight over a forest, produced by ray tracing hierarchical (mip mapped) volume textures with an ellipsoidally approximated surface normal distribution at each voxel.

Fredo Durand, George Drettakis, and Claude Puech gave a speculative talk on an unimplemented method of dividing the 4D space of all lines in 3D up in to regions where the visibility along the ray is constant. To deal with rays which have multiple segments in the free volume between objects, they use and extra discrete dimension to index the segments, but the space of such segments still has only 4 real parameters for a fixed scene. They discuss the various lower dimensional manifolds of visibility change events that divide this space into regions of homogeneous visibility, and show why the resulting data structure is of size O(n^4), where n is the number of polygon edges, and can be constructed by a sort and sweep algorithm in time O(n^4 log n). This is considerably better than the aspect graph, of size O(n^6), because the aspect graph computes for each viewing direction (or viewpoint) the intersection of the 2D pencil of lines making up the image, with this subdivision of the 4D space of all lines. Eric Veach pointed out that in the case of caustic maps under water, and the case of bump mapped shading normals differing from the normals of the surfaces which intercept the light transport rays, non symmetric scattering functions (BDRFs or BDTFs) must be used, which do not satisfy reciprocity, and therefore act differently when light energy or importance are being transported, or equivalently, act differently for the two directions in bidirectional path tracing (photon paths and viewing paths).

Stephen Hardt and Seth Teller from MIT showed how the rendering pipeline and texture mapping hardware with perspective correction of a high end workstation could be cleverly used to produce accurate radiosity rendering at interactive rates by fitting the radiosity off-line (ahead of time) by quadratic triangular patches, and then using the hardware polygon renderer to deposit at each pixel the polygon ID and two barycentric coordinates in the triangle. They use the perspective correction in the texture mapper to get the barycentric coordinates accurately. With Michael Allison, I showed in Graphic Gems III how the barycentric coordinates could be stored in color fields, using only the Gouraud shading interpolation hardware, if perspective corrections are not needed. The radiosity is then computed in software as a quadratic polynomial in the two barycentric coordinates, with coefficients indexed by the polygon ID.

Jos Stam and Eric Languenou spoke about ray tracing in non-constant media (mirages). Eric Lafortune and Yves Willems extended bidirectional path tracing to the case of 3D volumes with participating media (smoke, steam, or clouds). George Dretakis and Francois Sillion spoke on incorporating discontinuity meshing into hierarchical quadtree meshes, which allows large quadtree cells on homogeneous unoccluded regions; previous discontinuity meshes based on BSP trees had unnecessarily long edges crossing into regions beyond the discontinuities that defined them.

I spent the 6 days between the Porto and Chamonix conferences on vacation in Portugal, cycling with my wife Mika from Coimbra to Alcobaca, on bicycles kindly loaned by the local conference organizer, Augusto de Sousa, because there were no bicycle rental shops in northern Portugal. The final day before the Curves and Surfaces conference began was spent travelling from Porto to Chamonix.

The topics of the Chamonix conference were less familiar to me, being weighted towards approximation theory based on functional analysis on Sobelov spaces (I still haven't figured out what these are) and wavelets. I attended because Greg Nielson invited me to give a talk at a Mini-symposium he organized an Scientific Visualization. I spoke on "Applications of Texture Mapping to Volume and Flow Visualization," giving in 25 minutes almost all the content of the version I also earlier presented at the University of Kaiserslautern in 65 minutes. In the same session, Marcus Gross gave a talk on "Finite Element Modelling and Visualization for Facial Surgery," in which the soft tissues between the bone and skin are modelled by finite elements, whose deformation is simulated as bones are cut and displaced, so that the final appearance of the face can be displayed before the operation is carried out.

There were 6 days of mostly 3 parallel sessions of 25 minute talks form 8:30 AM until 6:30 PM (with a 2 hour break for lunch, and two half hour coffee breaks) for 6 conference days, which made for a pretty grueling schedule. I attended most of the time, but admit to "playing hooky" for two mornings in order to enjoy the mountain scenery. I probably absorbed some approximation theory by osmosis, especially from an excellent Mini-symposium on non-linear and adaptive wavelet approximation, including talks by Yves Meyer on the bump algebra, by S. Mallet on Image Compression, emphasizing the quantization and coding of the wavelet or basis coefficients, and the coding of the position indices of the non-zero coefficients, as well as just which coefficients can be set to zero, and by Ron DeVore on adaptive numerical methods for partial differential equations. There was also an interesting talk by A. Pinkus on approximating by ridge functions, the set of finite linear combinations of ridges, which are "long crested waves" of one linear parameter in 2 or 3 dimensions. There were many talks on extending the ideas of wavelets from the plane to arbitrary 2-manifolds, and in particular, to the 2-sphere.

Beyond these approximation theory talks, the talks I understood best were on surface shape. There were a couple of talks on developable surfaces, which are important in manufacturing because they can be formed from sheet metal without stretching. An invited talk by Joseph Hoschek on interpolation and approximation with developable surfaces gave an example of designing the blank holder in a sheet metal forming process. This is the part of the mold which should first clamp the sheet, without stretching it, and hold it while the part of the deformation involving more severe stretching deformations takes place. Another talk by Y. L. Kergosian analyzed the folds and cusps where a developable surface can have singularities, and simulated them for the case of a bent tin can, generating impressively realistic images.

There was also a Mini-symposium on Multiresolution Methods in Computer Graphics, including the following talks. Richard Bartels talked on hierarchical splines. Peter Schroeder spoke on spherical wavelets, and showed his Siggraph '95 images. After hearing it for the nth time, I finally understood the idea behind lifting. R. Westerman described his wavelet-based volume rendering, in which the wavelets are used only for determining the appropriate adaptive sampling frequency along a ray and for reconstructing the samples, for a traditional opacity accumulation algorithm. Thus full opacity effects are possible, in contrast to faster algorithms which try to precompute the splats of each wavelet, and therefore cannot account for interwavelet opacity effects. David Salesin presented three multiresolution techniques from his past and future Siggraph papers: image editing, image querying, and multiresolution video "clip art".

____

Dieter Fellner writes that I have attributed too much to his group at Darmstadt. Here is the text of his message:

May I suggest a minor change to your report on the Dagstuhl workshop?

You write:

> Dieter Fellner, working with Stefan Mueller's group at Darmstadt,

> showed how real time rendering of radiosity scenes could be accomplished

> on environments with the order of a million polygons, and presented an

> impressive video of additions to the Frankfort airport.

Well, I don't know how the two presentations could be linked so closely. And of course, it's quite flattering for my group. But truth is, that our two groups have not cooperated in this activity.

My group has been working on a graphics architecture called MRT and as one of the more interesting applications I talked about the simulation of radio wave propagation in urban environments used in the planing of micro cells for mobile phone networks as well as on the consistent handling of approximative rendering and radiosity, both based of a clever use of a data structure derived from the winged edge data structure.

[There turns out to be a large body of literature using ray tracing for mobile phone network related planning - see IEEE's site (members only) at http://www.biblio.ieee.org/biblio/keyword_search.html and search on "ray tracing". - EAH]

As I don't want to take credit for things we haven't done and your mail reached a large number of people I would like to ask you to consider a revised version of your report.

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For those who are interested in "quick fix" of performance of a ray tracer with shadows calculated by ray casting I may honestly devise the Greg Ward's method described in "Adaptive Shadow Testing for Ray Tracing". It gave average speed-up factor varying from 1.5 - 5.0 calculated on models build of 10,000 - 40,000 polygons, with 50 - 400 lights. The differences in resultant images were not noticeable. In absolute terms (number of differing pixels and magnitude of differences) the differences were smaller than introduced by standard JPEG compression.

Andrew Woo and Pierre Poulin and Alain Fournier, "A Survey of Shadow Algorithms", IEEE Computer Graphics and Applications, Vol 10, No 6, November 1990Andrew Woo and John Amanatides, "Voxel Occlusion Testing: A Shadow Determination Accelerator for Ray Tracing", Proceedings of Graphics Interface '90, held in Halifax, Nova Scotia; 14-18 May 1990",

Andrew Pearce and David Jevans "Exploiting Shadow Coherence in Ray Tracing", Proceedings of Graphics Interface '91", held in Calgary, Alberta; 3-7 June 1991,

Frederic Asensio, "A Hierarchical Ray-Casting Algorithm for Radiosity Shadows" Third Eurographics Workshop on Rendering, 1991, Bristol, UK

H. K. Choi and C. M. Kyung Pysha: "A Shadow-Testing Acceleration Scheme for Ray Tracing" Computer-aided design, Vol 24, No 2, February 1992

A. James Stewart and Sherif Ghali, "An Output Sensitive Algorithm for the Computation of Shadow Boundaries", Canadian Conference on Computational Geometry, August 1993

Arjan J. F. Kok and Frederik W. Jansen and C. Woodward, "Efficient, Complete Radiosity Ray Tracing Using a Shadow-Coherence Method", The Visual Computer, Vol 10, 1994

A. James Stewart and Sherif Ghali, "Fast Computation of Shadow Boundaries Using Spatial Coherence and Backprojections", Proceedings of SIGGRAPH '94 (Orlando, Florida, July 24--29, 1994)

Yiorgos Chrysanthou and Mel Slater, "Shadow Volume BSP Trees for Computation of Shadows in Dynamic Scenes", 1995 Symposium on Interactive 3D Graphics,

Seth Teller and Pat Hanrahan, "Global Visibility Algorithms for Illumination Computations", Computer Graphics Proceedings, Annual Conference Series, 1993,

A.J.F. Kok and F.W. Jansen "Source Selection of the Direct Lighting Computation in Global Illumination", Proceedings Second Rendering Workshop, Barcelona, Spain, May 1991 In: Photorealistic Rendering in Computer Graphics, Springer Verlag, 75-82.

Kurt Zimmerman, Peter Shirley "A Two-Pass Realistic Image Synthesis Method for Complex Scenes" Rendering Techniques '95 (Proceedings of the Sixth Eurographics Workshop on Rendering), Springer-Verlag, New York, NY 1995, pp 284-295

George Dretakkis and Eugene Fiume, "A Fast Shadow Algorithm for Area Light Sources Using Backprojection" Proceedings of SIGGRAPH '94 (Orlando, Florida, July 24--29, 1994)

Seth J. Teller and Carlo H. Sequin, "Visibility preprocessing for interactive walkthroughs", Computer Graphics (SIGGRAPH '91 Proceedings), held in Las Vegas, Nevada; 28 July - 2 August 1991,

Ward, Gregory, "Adaptive Shadow Testing for Ray Tracing," Second EUROGRAPHICS Workshop on Rendering, Barcelona, Spain, May 1991

Shirley, Peter, "Direct Lighting Calculation by Monte Carlo Integration," Second EUROGRAPHICS Workshop on Rendering, Barcelona, Spain, May 1991

George Drettakis, Francois Sillion "Accurate Visibility and Meshing Calculations for Hierarchical Radiosity"

Seth Teller, Pat Hanrahan "Global Visibility Algorithms for Illumination Computations", Computer Graphics, SIGGRAPH '94 proceedings.

Kurt Zimmerman, Peter Shirley "A Two-Pass Realistic Image Synthesis Method for Complex Scenes", Indiana University, Technical Report No 434

Eric Haines, Donald Greenberg "The Light Buffer: A Ray Tracer Shadow Testing Accelerator", IEEE Computer Graphics and Applications, Vol. 6, No. 9, Sept. 1986

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Eric Haines / erich@acm.org