A Convex Hull Algorithm for Discs, and Applications

Rappaport D., A convex hull algorithm for discs, and applications, Computational Geometry: Theory and Applications 1 (1992) 171-187. We show that the convex hull of a set of discs can be determined in @(n log n) time. The algorithm is straightforward and simple to implement. We then show that the convex hull can be used to efficiently solve various problems for a set of discs. This includes O(n log n) algorithms for computing the diameter and the minimum spanning circle, computing the furthest site Voronoi diagram, computing the stabbing region, and establishing the region of intersection of the discs.