The union of convex polyhedra in three dimensions

Authors:
B. Aronov;M. Sharir
Affiliations:
Dept. of Comput. Sci., Polytechnic Univ., Brooklyn, NY, USA;-
Venue:
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Year:
1993

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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.