Recursive Voronoi Diagrams

Abstract

This paper introduces procedures involving the recursive construction of Voronoi diagrams and Delaunay tessellations. In such constructions, Voronoi and Delaunay concepts are used to tessellate an object space with respect to a given set of generators and then the construction is repeated every time with a new generator set, which comprises members selected from the previous generator set plus features of the current tessellation. Such constructions are shown to provide an integrating conceptual framework for a number of disparate procedures, as well as extending the existing functionality of the basic Voronoi and Delaunay procedures to variable spatial resolutions. Further, because they are shown to be fractal in nature, it is suggested that this characteristic can be exploited in the development of new strategies for spatial modelling.