Ray Tracing from the Ground Up

Chapter 2

Some Essential Mathematics

Image courtesy of Lisa Lönroth

Objectives

By the end of this chapter you should:

• be familiar with some of the mathematics you need for ray tracing;
• understand the difference between vectors, points, and normals;
• understand how to construct an orthonormal frame.

Ray tracing uses a lot of mathematics, from elementary coordinate geometry to multi-dimensional calculus. Fortunately, there are excellent books on all of these topics (see the Further Reading section). I’ll present here the mathematical notation used in this book and a number of mathematical topics from a ray-tracing perspective. For example, I’ll ...