Voronoi Methods for 3D Medial Axis Approximation

Abstract

As shown in the previous chapter, the medial axis of an object can be approximated using a subset of the Voronoi diagram of a sample of points taken from the object surface. In this chapter we focus on the 3D case and review some theoretical results on the approximation of medial axes by Voronoi diagrams. We present algorithms for selecting the boundary point samples used to produce the Voronoi diagram and for selecting parts of the Voronoi diagram as a step in constructing more accurate medial axis representations. We also state some open questions that concern the quality of these algorithms and their dependence on the sampling density.