Voronoi Diagrams for Convex Polygon-Offset Distance Functions

In this paper we develop the concept of a convex polygon-offset distance function. Using offset as a notion of distance, we show how to compute the corresponding nearestand furthest-site Voronoi diagrams of point sites in the plane. We provide nearoptimal deterministic O(n(log n + log m) + m)-time algorithms, where n is the number of points and m is the complexity of the underlying polygon, for computing compact representations of both diagrams.