Hughes/Computer Graphics, 3/E

Chapter 24. Implicit Representations of Shape

24.1. Introduction

We introduced implicit functions in Chapters 7 and 14 as a means for defining shapes. Implicitly defined shapes, like the circle defined by x² + y² = 1, or the sphere defined by x²+y²+z² = 1, or far more general shapes defined by equations of the form F(P) = c for some complicated function F, serve several roles in graphics. First, for a wide class of functions, computing ray-surface intersections with such shapes is fairly easy. Second, it’s sometimes convenient to represent surfaces like “the boundary between water and air” in a simulation implicitly, because it’s very easy to change the topology of an implicitly defined surface (by changing either F or c), while it’s generally ...