The union of convex polyhedra in three dimensions

Abstract

We show that the number of vertices, edges, and faces of the union of k convex polyhedra in 3-space, having a total of n faces, is O(k/sup 3/+knlog/sup 2/ k). This bound is almost tight in the worst case. We also describe a rather simple randomized incremental algorithm for computing the boundary of the union in O(k/sup 3/+knlog/sup 3/ k) expected time.<>