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 nearest- and furthest-site Voronoi diagrams of point sites in the plane. We provide near-optimal deterministic O (n (log n + log ² 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. Received January 8, 1999, and in revised form January 5, 2000, and June 12, 2000. Online publication December 4, 2000.