Approximation of Generalized Voronoi Diagrams by Ordinary Voronoi Diagrams

Abstract

A numerically robust algorithm for the ordinary Voronoi diagrams is applied to the approximation of various types of generalized Voronoi diagrams. The generalized Voronoi diagrams treated here include Voronoi diagrams for figures, additively weighted Voronoi diagrams, Voronoi diagrams in a river, Voronoi diagrams in a Riemannian plane, and Voronoi diagrams with respect to collision-avoiding shortest paths. The construction of these generalized Voronoi diagrams is reduced to the construction of the ordinary Voronoi diagrams. The methods proposed here can save much time which is otherwise necessary for writing a computer program for each type of generalized Voronoi diagram.