Title :
The union of convex polyhedra in three dimensions
Author :
Aronov, Boris ; Sharir, Micha
Author_Institution :
Dept. of Comput. Sci., Polytechnic Univ., Brooklyn, NY, USA
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(k3+knlog2 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(k3+knlog3 k) expected time
Keywords :
computational complexity; computational geometry; randomised algorithms; almost tight; edges; faces; randomized incremental algorithm; three dimensions; union of convex polyhedra; vertices; Algorithm design and analysis; Computer science; Motion planning; Research and development; Robot motion;
Conference_Titel :
Foundations of Computer Science, 1993. Proceedings., 34th Annual Symposium on
Conference_Location :
Palo Alto, CA
Print_ISBN :
0-8186-4370-6
DOI :
10.1109/SFCS.1993.366835
