Chapter 2: Preliminary Math

OVERVIEW

I'm very well acquainted too with matters mathematical, I understand equations, both the simple and quadratical. About binomial theorem I'm teeming with a lot of news—With many cheerful facts about the square of the hypotenuse.

--Gilbert and Sullivan, The Pirates of Penzance

Well, there's no getting around it. If you want to really understand shader programming and be able to program some wicked shaders, you have to have a firm understanding of the basic math required for 3D graphics and how it ties together. Understanding the math is a prerequisite for setting up shaders. If you're a programmer, you really should have a good grasp on the mathematics involved in taking a vertex from a file and getting it rendered as pixels on the screen. If you're an artist, you might be able to slide on some of the math, but to fully use a shading language requires knowing what data is coming through in a particular coordinate system and knowing how to change it as needed. Expertise lies in knowing how to shift data from one range to another, how to maintain as much precision as possible, and how to spoof the system to do what you want it to do.

If you've already programmed your own 3D rendering engine, have written a tri-stripping routine, know what a projection matrix is, and understand the usefulness of negative color values, then you can probably skip this section. However, if you feel that a quick and painless refresher on the basics of useful 3D math, terminology, and the mathematics of color would be useful, read on!