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Abstract: We develop algorithms for the approximation of a convex polytope in R 3 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-di erence. The running time is linear in the number of vertices or facets, under mild constraints. 1 Introduction In this paper we develop algorithms for the approximation of convex polytopes in R... (Update)
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BibTeX entry: (Update)
@misc{ lopez-linear,
author = "Mario A. Lopez and Shlomo Reisner",
title = "Linear Time Approximation of 3D Convex Polytopes",
url = "citeseer.ist.psu.edu/lopez01linear.html" }
Citations (may not include all citations):37 Algorithms for polytope covering and approximation - Clarkson - 1993
24 Derandomizing an output-sensitive convex hull algorithm in t.. (context) - Chazelle, Matou - 1995
22 Optimal output-sensitive convex hull algorithms in two and t.. - Chan - 1996
17 Aspects of approximation of convex bodies (context) - Gruber - 1993
11 Almost optimal set covers in nite VC-dimensions (context) - Br, Goodrich - 1995
2 Constructing a polytope to approximate a convex body (context) - Gordon, Meyer et al. - 1995
2 Convex hulls of nite sets of points in two and three dimensi.. (context) - Preparata, Hong - 1977
2 Approximation by convex polytopes (context) - Gruber - 1994
2 Lagerung von Punkten auf der Kugel (context) - Habicht, van der Waerden - 1951
1 Dropping a vertex or a facet from a convex polytope (context) - Reisner, Sch et al.
1 Algorithms for polyhedral approximation of multidimensional .. (context) - Lopez, Reisner - 1999
1 Ecient approximation of convex polygons (context) - Lopez, Reisner
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