Let me quote a co-author of Quake:<p>'At this point in the book, I was originally going to present a BSP-based renderer, to complement the BSP compiler I presented in the previous chapter. What changed my plans was the considerable amount of mail about 3-D math that I’ve gotten in recent months. In every case, the writer has bemoaned his/her lack of expertise with 3-D math, and has asked what books about 3-D math I’d recommend, and how else he/she could learn more.<p>That’s a commendable attitude, but the truth is, there’s not all that much to 3-D math, at least not when it comes to the sort of polygon-based, realtime 3-D that’s done on PCs. You really need only two basic math tools beyond simple arithmetic: dot products and cross products, and really mostly just the former. My friend Chris Hecker points out that this is an oversimplification; he notes that lots more math-related stuff, like BSP trees, graphs, discrete math for edge stepping, and affine and perspective texture mappings, goes into a production-quality game. While that’s surely true, dot and cross products, together with matrix math and perspective projection, constitute the bulk of what most people are asking about when they inquire about “3-D math,” and, as we’ll see, are key tools for a lot of useful 3-D operations.'<p>(Michael Abrash, "Graphics Programming Black Book Special Edition")