> This could change in the future to be more general purpose. For example, > hardware-based computations using quaternions and octonions. As far as I am > aware, it isn't done today for purely mathematical reasons; no one knows > how. And as far as I'm aware, such a mathematical breakthrough would be > huge, but not something graphics vendors would pursue/fund, since it is > "basic research" that can't be patented and so all graphics processors would > get the same speedup. [1]
Incidentally, this research has been going on for at least 10 years already and has made significant progress in terms of compiler tools and software systems that can be used for real-time systems. In Guadalajara, there's a robotics group led by Eduardo Bayro-Corrochano[1] that makes amazing machines that perform their computations in an intrinsically spatial manner using geometric (Clifford) algebra. One of the issues with this algebra is that the dimensionality of the computational space grows combinatorially. The standard 3D conformal model (5D Minkowski space) is a 32 dimensional multi-vector. Fortunately, there's some really good software that optimizes away the many redundancies and zero-ops called Gaigen[2], which can handle up to 12D Clifford Algebras. Geometric algebra subsumes quaternions and adds a lot more interesting structures and operations. I don't think it requires basic research since it's just linear algebra and easily maps to GPU hardware. Plus the research has already been done. The software already exists for use if you want it. I'm really not sure what interest the manufacturers would have in it though since their more specific applications than the general case of GA lends itself to more optimization. Also, there's an entire world of mathematics that would have to be taught to everyone since you aren't going to find courses in CS departments on this stuff except in a handful of labs around the world (Netherlands, Saudia Arabia, Mexico, Cambridge (in physics department) ...) Here are some papers about GA and hardware: using FPGAs: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.159.1691&rep=rep1&type=pdf conformal collision detection on GPUs: http://eduardoroa.3dsquash.com/portafolioeduv2/document/publications/SIACG_article.pdf and there are others implementing generic GA ops in graphics hardware that I wasn't able to find as quickly. [1] http://www.gdl.cinvestav.mx/edb/ [2] http://staff.science.uva.nl/~fontijne/g25.html _______________________________________________ fonc mailing list [email protected] http://vpri.org/mailman/listinfo/fonc
