In geometric modeling, we combine simple shapes to construct complex models. The techniques we use must produce valid models. For example, a completed model must be dimensionally homogeneous. If it is a three-dimensional solid, it must have no dangling edges or surfaces. Model connectivity and homogeneity are topological properties, so consideration of topology is also an important part of the modeling process (Mortenson 1995, 1999).

This chapter discusses two important approaches to representing complex models: one approach uses an implicit construction technique called constructive solid geometry, or CSG, and the other uses an explicit boundary-based technique called boundary representation, or b-rep. The CSG scheme defines complex solids as Boolean combinations of simpler solids. The complete representation is sometimes referred to as a CSG tree, because it uses a binary tree whose terminal nodes are simple solids and whose nonterminal nodes are so-called regularized Boolean combining operations. The data structure of a b-rep is a graph associating the curves and surfaces that comprise the boundary of a solid.

In the early chapters, we discussed the basic elements of a geometric model: The parametric and implicit curves, surfaces, and solids. We then discussed the geometric properties and transformations of these elements. In the previous chapter, we discussed how to generate simple solid shapes using instances of parameterized shapes, sweeps, and deformations. All of these form the foundation on which we build the complex models that are the subject of this chapter. Here we will discuss graph-based models, Boolean models,...