Computer Graphics Through OpenGL, 2nd Edition

Chapter 5

Inside Animation: The Theory of Transformations

We studied transformations and their application to animation in Chapter 4. The goal for this chapter is to understand the underlying theory. We want to look under the hood of the graphics engine and understand exactly how transformations are implemented. What we’ll encounter is the mathematics of geometric transformations.

We begin our discussion of geometric transformations in Section 5.1 in the simple surroundings of Flatland (2-dimensional space), the objective being to get concepts in place and prove results that will extend fairly easily to the real world. This program starts in Section 5.1.1, Section 5.1.2, Section 5.1.3 and Section 5.1.4 with the expression of familiar geometric ...