An efficient algorithm for determining the extreme vertices of a moving 3D convex polyhedron with respect to a plane

We present an efficient algorithm for finding the sequence of extreme vertices of a moving convex polyhedron P with respect to a fixed plane H. Using the spherical extreme vertex diagram due to the point-plane duality, we are able to find such a sequence in O(log n + ∑sj=1 mj) time, where s is the number of extreme vertices in the sequence, and mj, 1 ≤ j ≤ s, is the number of edges of the spherical region Svj corresponding to an extreme vertex vj in the sequence.