English

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}
}
R2 v1 2026-06-21T14:37:11.926Z