Linear time approximation of 3D convex polytopes

Mario A. Lopez; Shlomo Reisner

doi:10.1016/S0925-7721(02)00100-1

Linear time approximation of 3D convex polytopes

Mario A. Lopez, Shlomo Reisner

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	291-301
Number of pages	11
Journal	Computational Geometry: Theory and Applications
Volume	23
Issue number	3
DOIs	https://doi.org/10.1016/S0925-7721(02)00100-1
State	Published - 2002

Bibliographical note

Funding 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

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10.1016/S0925-7721(02)00100-1

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title = "Linear time approximation of 3D convex polytopes",

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.",

author = "Lopez, {Mario A.} and Shlomo Reisner",

note = "Funding 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.",

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PY - 2002

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N2 - 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.

AB - 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.

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ER -

Linear time approximation of 3D convex polytopes

Abstract

Bibliographical note

ASJC Scopus subject areas

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