Linear time approximation of 3D convex polytopes

Authors:
Mario A. Lopez;Shlomo Reisner
Affiliations:
Department of Mathematics and Computer Science, University of Denver, Denver, CO;Department of Mathematics and Department of Mathematics Education (Oranim), University of Haifa, Haifa, Israel
Venue:
Computational Geometry: Theory and Applications
Year:
2002

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Abstract

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.