We develop algorithms for the approximation of a convex polytope in R3 by polytopes that are either contained in it or containing it, and that have fewer vertices or facets, respectively. The approximating polytopes achieve the best possible general order of precision in the sense of volume-difference. The running time is linear in the number of vertices or facets.
Bibliographical noteFunding Information:
Mario A. Lopez has been partially supported by NSF grants DMS-9626749 and DMS-0107628. Shlomo Reisner has been partially supported by NSF grants DMS-9626749 and DMS-0107628 and by NATO Collaborative Linkage Grant PST.CLG. 976356.
ASJC Scopus subject areas
- Computer Science Applications
- Geometry and Topology
- Control and Optimization
- Computational Theory and Mathematics
- Computational Mathematics