On the Farthest-Neighbor Voronoi Diagram of Segments in Three Dimensions

Abstract

We consider the farthest-neighbor Voronoi diagram of a set of line segments in three dimensions. To understand the structure of the diagram, we define the “farthest hull” of the segments and investigate it by its representation in a Gaussian map. We then provide lower and upper bounds on the worst-case complexities of the farthest hull and of the Voronoi diagram.