I'm still on my math tangent, but I'm winding down. I finally understand spinors and multivectors well enough to implement the basics. I found a really good primer on geometric algebra which filled in a few gaps in my knowledge and cleared up some misconceptions that I had.
My plan is to finish up a basic implementation of spinors (generalizations of complex numbers / quaternions), and then replace the hard coded math library I've been using with this general one. Why? Mostly because I can. My game doesn't really require super complex math, but it may come in handy.
I've been trying to get away from some of the bad math used in computer science, not just in this game, but in all my coding projects. In addition to basing things on geometric algebra, I'm also using tau (2 pi) instead of pi. Despite the work it took to learn these concepts (and more importantly, how they change traditional theories), I can happily say that they've actually made things easier.
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