FUNDAMENTAL TECHNIQUES FOR GEOMETRIC AND SOLID MODELING'

We review traditional and novel paradigms for representing solids and interrogating them. The traditional paradigms reviewed are the bound-ary, constructive, and spatial subdivision representations. The novel rep-resentation paradigms are the B-rep index, the dimensionality paradigm, and the skeleton (medial-axis transform). The B-rep index is a polyhedral representation that integrates bound-ary and subdivision representation. We show how to construct it and explain some of the advantages this representation offers for operations such as point/solid and line/solid classification. We also discuss how it can account for the robustness problem. The dimensionality paradigm is a technique for representing exactly complex surfaces that satisfy prescribed constraints, and we discuss some of the algorithmic infrastructure available to manipulate and interrogate this surface representation. This paradigm generalizes both implicit an