The arctangent is one of the more interesting trigonometry functions – and by “interesting” I of course mean a bitch to get right. I've been meaning to write something about the various methods of calculating it for a while now and finally got round to it recently.
I, ah, uhm, may have gotten a little carried away with it though ... but that's okay,! At least now I while one to recommend.
“Matrices from a geometry perspective” is now out. Vector and matrix math is used heavily in computer graphics because it involved geometry and coordinate transformations. While this is widely known, I've seen many people struggle with the basic concepts of how it's supposed to work. this is especially true in the GBA/NDS community, where erroneous information about the affine matrix is still found in many demos and even library code even today. And that just kills me, because the fundamentals are really quite simple to grasp once you look at it from the right direction(1)
I've wanted to write something on the subject for quite some time. Yeah, there were a few sections in Tonc that covered it, but not in the amount of detail I wanted it. A recent email (thanks Ian) finally spurred me to write something down.
In the document, I describe what points, vectors and coordinates really are in geometrical terms. This may seem obvious, but it's always good to go over the basics again because overlooking those is often the reason for misunderstandings. Then it describes how coordinate transformations work and how matrices fit into the subject.
I've tried to keep the hardcore math to a minimum in order to keep it understandable. I'd really like to get some feedback on this to know if it is comprehensible to people who don't already know how all this stuff works. If there are other items that anyone feels I should add, I'll consider that as well.
I should probably also note that many parts of it have already been rewritten three times already, so if sentences don't make sense, let me know so I can fix it.
linky: Matrices from a geometry perspective.