TABLE OF CONTENTS In this chapter, we cover surfaces composed of more than one patch. One B zier patch is rarely flexible enough to model a real life part. More commonly, many patches will be stitched together, either in the form of a composite B zier surface or a B-spline surface. In animation, subdivision surfaces are a popular type of composite surface. Figure 12.1 is taken from "Geri's Game", an animated short film produced by Pixar Animation Studios.
In Chapter 9, we saw how to generate complex curves which consisted of simple ingredients, i.e., cubic B zier curves. In the context of surfaces, the same approach is taken. Once we know how to combine several B zier patches to form a smooth composite surface, we can build surfaces of fairly high complexity.
Let b i, j; 0 ? i, j ? 3 be a bicubic B zier patch we'll call it the "left" patch. Let b i, j; 3 ? i ? 6; 0 ? j ? 3 be a second ("right") patch such that both share a common boundary. As is typical for piecewise defined objects, we make some assumptions regarding the domains of our patches. We assume the left patch has as its domain a rectangle [ u 0, u 1] [ v 0, v 1]. For the right patch, we assume that the domain is a rectangle [ u 1
