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I'm working through Geometric Algebra for Computer Science, and the subject does give a clearer of picture of things like quaternions and complex numbers.

I can definitely see how GA could be useful, but I'm interested in hearing from people with practical experience either doing real-time or asset pipeline stuff with GA.

Are there are any gotcha's to watch out for when implementing a GA system?

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2 Answers 2

I read a few papers and documents on GA. It's pretty fun stuff, and presents interesting generalizations for various geometric mathematical structures. I was particularly interested in it, because I wanted to see how they treated Pluecker coordinates. My general feeling, is that if one can wrap ones head around it, it can provide an excellent alternate way of visualizing geometric operations, that this can lead to new insights, however, a lot of the time I feel like I am jumping through hoops to fit fairly simple concepts into the GA framework. In terms of practicality, I think you will find that that doing something in GA generally has a simpler (but less generalizable) dual in another branch of mathematics, that will also require much fewer computational operations.

I wouldn't call myself an expert on the topic, but I don't know of any case where it specifically has proved to be useful - it seems that you have most of the essential tool kit if you understand complex numbers, projective geometry, quaternions, pluecker coordinates and duality well.

It's not really related to the post, but if you are interested in the mathematical, but practical side of geometry, books like Edelsbrunner's Combinatorial Geometry, Preparata and Shamos's Computational Geometry, and various other computational geometry books, would be interesting.

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This company appears to be experts in the field of GA, finding pracical uses for it, including as an alternative to spherical harmonics in a lighting system:

http://www.geomerics.com/technology.htm

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