An output sensitive algorithm for discrete convex hulls

Given a convex body C in the plane, its discrete hull is C-0 = ConvexHull(C boolean AND L), where L = Z x Z is the integer lattice. We present an O(\C-0\ log delta(C))-time algorithm for calculating the discrete hull of C, where \C-0\ denotes the number of vertices of C-0, and delta(C) is the diameter of C. Actually, using known combinatorial bounds, the running time of the algorithm is O(delta(C)(2/3) log delta(C)). In particular, this bound applies when C is a disk. (C) 1998 Published by Elsevier Science B.V.