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18 March, 2008

Four dimensions and more.

Are you doing you maths right? Are you tired of three dimensions? Linear Algebra is too way easy? Well, Geometric Algebra is more spicy. Jaap Suter tutorial is a great read. Geometric Algebra is a unification of mhm almost everything, vectors, lines, planes, quaternion, complex numbers, the awful plucker stuff, to any dimension.

It's nice to be able of reasoning in arbitrary dimensions. Now what we need is a killer application. Latest game programming gems (6) has an interesting article about using projective algebra to do enhance robustness of geometrical algorithms. But there aren't many other examples of uses of that extra coordinate we all get from memory alignment anyway. It's a shame, cool things could be done...


Remigiusz said...

You mean the article "Using Projective Space to Improve Precision of Geometric Computations" by Krzysztof Kluczek from GPG 7? I wanted to get that guy to Milestone ;)

DEADC0DE said...

Yep, that's surely a good article. I don't really thing it has much of practical application right now but at least it's exploring an interesting direction.
Actually it made me think a lot, expecially on how we could use the w coordinate to do something like "HDR" vectors, for example they could be useful for PSP matrices (that have that awful 24bit float truncation)