radical new solution that breaks the current lighting and shadowing restrictions currently faced by major game developers. Geomerics' solution is a replacement for 'spherical harmonics', giving the same efficient compression of a lighting environment but now coupled with their geometric algebra and wavelet technologies. Their system handles dynamically changing lighting environments, moving objects and changing viewing angles. The technology not only handles diffuse lighting and soft shadows but also allows for dynamic specular effects to be integrated into the same pipeline giving rise to realistic glossy effects unobtainable from existing spherical harmonic implementations. Geomerics' CTO, Jules Davis, said 'I am delighted with how this technology has progressed. It's extremely fast and GPU friendly, and has a great impact on in-game realism'. Geomerics will be giving a glimpse of some of their technology at the forthcoming GDC in San Jose from 22-24th March. Lighting and shadowing are key elements in the rendering of realistic-looking next generation games. A well known currently used approach - spherical harmonic pre-computed radiance transfer (PRT) lighting - has the advantage of dealing with much of the computational complexity associated with realistic shadowing in a pre-compute step so that, at run-time, only a handful of simple operations are performed allowing an efficient GPU-based implementation. However, a fundamental restriction with spherical harmonic PRT is that it is impossible to handle light effects that change with the viewing angle such as specular highlights and it struggles to cope with highly dynamic lighting environments. Geomerics has utilized the power of 'geometric algebra' to provide exciting and innovative solutions to geometric problems in real-time. This technology is poised to transform computer graphics in gaming, providing a major step-change improvement over the current state-of-the-art in terms of speed, achievable effects, and ease of programming. more screens here: http://news.teamxbox.com/xbox/10508/Geomer...logy-at-GDC-06/

I wasn't really impressed by that image at first, since the lighting is per-vertex. A much nicer, per-pixel version can be found in the same gallery: http://media.teamxbox.com/events/gallery/30/1142874594.jpg

While I'd love to read more about the technique, I don't see it as much of an advancement. If you want specular reflections, a blurred cube map modulated by some factor is a very good approximation. If you use a mipmapped cube map and select the LOD dynamically, you'd get even better results. The biggest problem with spherical harmonics is local rotation, which is handled well by LDPRT and zonal harmonics. I wonder how this company operates? Must be tough finding a way to let game developers use their technology without giving away their IP, especially for pixel and vertex shaders as opposed to DLL's or something.

Geometric Algebra was invented by some mathematician whose name I forget about 20-30 years ago b/c he was unsatisfied with standard notation for differential geometry and differential forms. Its based very much on clifford algebras and complex analysis. There is a bit of a debate in the math community exactly how much of this is just repackaging the same thing in abridged and new notation, and there are known problems with the whole enterprise (it really is not *general* like the usual treatment). On the other hand there is some computational benefit in say 2 -3 dimensions, in some sense b/c he takes known solutions to certain problems and plugs them back into hsi eqns which ultimately reduces some redundancy. The problem with all wavelet compression algorithms is complexity, the amount of logic needed to make it work is enormous and not efficient use of die space, so that problem will have to be addressed.

Fred - if you have the time, could you expand on what you mean by saying it's not "general like the usual approach" (I was trying to decide if I should pick up a book on the subject since it looked kind of interesting)?

For the curious This is an email from the (public) gd-algorithms list (which is public, so I think posting it here is ok) written by one of the companies' employees:

AFAIK it is public (well, afterall, there's no password on the web archives) and I'm sure the community (developers, IHVs etc) doesn't mind people reading

"Fred - if you have the time, could you expand on what you mean by saying it's not "general like the usual approach" (I was trying to decide if I should pick up a book on the subject since it looked kind of interesting)?" Yea this gets technical really fast, and its been awhile since i've looked into Hestenes GA and I forget many of the details (its a pretty huge body of literature). I had asked a few mathematicians about this one time and it was explained to me. Unfortunately you won't find much 'skeptical' literature on the subject or pieces of translation b/c its largely carried out in vacuo by many of its practicioners. Anyway the first problem is they tend to overhype their claims. If you read some of their intro material you will see they are basically doing the same computation as standard differential forms, say with regards to Maxwells equations. Yes, we all know differential forms beats tensor analysis some of the time. Now they do win out over standard approaches once in awhile when they implement some bits of complex analysis (they call this rotors or somesuch). Its sorta built into their notation, so in the same way differential forms win out over tensor analysis, problems with a great deal of symmetry can save some steps (sometimes). The second problem is they in some way restrict to the factorizable part of what we generally call clifford algebras, and use that exlusively. Some people don't like this, b/c as pure mathematicians its a good idea to be as general as possible. Of course, with regards to physical apps, it might be relevant and useful for problem solving. You probably should ask a differential geometer what he/she thinks (someone from outside the GA field who has some experience with this), they will explain it better.