Ray Tracing from the Ground Up

Chapter 20

Affine Transformations

Objectives

By the end of this chapter, you should:

• understand what affine transformations are;
• understand how to represent transformations with matrices;
• know why we use 4 × 4 matrices for 3D transformations;
• know how to compose a sequence of transformations;
• understand how to define and represent inverse transformations.

Transformations are an essential tool for ray tracing: we use them to alter the size, shape, orientation, and location of geometric objects. Without them, it would not be practical to ray trace objects such as non-axis-aligned rectangular boxes or arbitrary cylinders, cones, and tori. We ...