Farthest-polygon Voronoi diagrams

Abstract

Given a family of k disjoint connected polygonal sites in general position and of total complexity n, we consider the farthest-site Voronoi diagram of these sites, where the distance to a site is the distance to a closest point on it. We show that the complexity of this diagram is O(n), and give an O(n log(3) n) time algorithm to compute it. We also prove a number of structural properties of this diagram. In particular, a Voronoi region may consist of k - 1 connected components, but if one component is bounded, then it is equal to the entire region. (C) 2010 Elsevier B.V. All rights reserved.