Bounded-Degree Polyhedronization of Point Sets

Abstract

In 1994 Grunbaum [2] showed, given a point set S in R3, that it is always possible to construct a polyhedron whose vertices are exactly S. Such a polyhedron is called a polyhedronization of S. Agarwal et al. [1] extended this work in 2008 by showing that a polyhedronization always exists that is decomposable into a union of tetrahedra (tetrahedralizable). In the same work they introduced the notion of a serpentine polyhedronization for which the dual of its tetrahedralization is a chain. In this work we present an algorithm for constructing a serpentine polyhedronization that has vertices with bounded degree of 7, answering an open question by Agarwal et al. [1].