On Non-smooth Convex Distance Functions
Ngoc-Minh Lê · Canadian Conference on Computational Geometry · 1996
Abstract Under the Euclidean metric in 3-space, the bisectors of three points intersect in at most one connected component — namely, a line. In contrast to this, we show that, under non-smooth convex distance functions, there is no general upper bound to the number of connected components of the intersection of the bisectors of three points in 3-space. Our result is important for the further study of abstract Voronoi diagrams in 3-space, and — as a byproduct — disproves a conjecture of Schaudt and Drysdale (1992).