Farthest-Polygon Voronoi Diagrams
Computational Geometry
2010-12-02 v2
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.
Keywords
Cite
@article{arxiv.1001.3593,
title = {Farthest-Polygon Voronoi Diagrams},
author = {Otfried Cheong and Hazel Everett and Marc Glisse and Joachim Gudmundsson and Samuel Hornus and Sylvain Lazard and Mira Lee and Hyeon-Suk Na},
journal= {arXiv preprint arXiv:1001.3593},
year = {2010}
}