The divider set of explicit parametric geometry

Abstract

In this paper we describe a novel concept for classification of complex parametric geometry based on the concept of the Divider Set. The Divider Set is an alternative concept to maximal disks, Voronoi sets and cut loci. The Divider Set is based on a formal definition relating to topology and differential geometry. In this paper firstly we discuss the formal definition of the Divider Set for complex 3-dimensional geometry. This is then followed by the introduction of a computationally feasible algorithm for computing the Divider Set for geometry which can be defined in explicit parametric form. Thus, an explicit solution form taking advantage of the special form of the parametric geometry is presented. We also show how the Divider Set can be computed for various complex parametric geometry by means of illustrating our concept through a number of examples