 
Summary: Farthest Line Segment Voronoi Diagrams #
F. Aurenhammer + R. L. S. Drysdale # H. Krasser §
Abstract
The farthest line segment Voronoi diagram shows
properties different from both the closestsegment
Voronoi diagram and the farthestpoint Voronoi diagram.
Surprisingly, this structure did not receive attention in
the computational geometry literature. We analyze its
combinatorial and topological properties and outline an
O(n log n) time construction algorithm that is easy to im
plement. No restrictions are placed upon the n input line
segments; they are allowed to touch or cross.
Keywords: Computational geometry; Voronoi diagram;
farthest line segment; optimal algorithm.
1 Introduction
Consider a set S of n simple geometric objects (called
sites) in the plane, for example points, line segments, or
circular arcs. The closestsite Voronoi diagram of S sub
divides the plane into regions, each region being asso
ciated with some site s i # S, and containing all points
