InforLorV4, Hal, Corpus, bibRecord, 004B64

The Number of Lines Tangent to Arbitrary Convex Polyhedra in 3D

Identifieur interne : 004B64 ( Hal/Corpus ); précédent : 004B63; suivant : 004B65

The Number of Lines Tangent to Arbitrary Convex Polyhedra in 3D

Auteurs : Hervé Brönnimann ; Olivier Devillers ; Vida Dujmovic ; Hazel Everett ; Marc Glisse ; Xavier Goaoc ; Sylvain Lazard ; Hyeon-Suk Na ; Sue Whitesides

Source :

RBID : Hal:inria-00103995

Abstract

We prove that the lines tangent to four possibly intersecting polytopes in $R3$ with $n$ edges in total form $\Theta(n^2)$ connected components. In the generic case, each connected component is a single line, but our result still holds for arbitrary degenerate scenes. This improves the previously known $O(n^3\log n)$ bound by Agarwal~\cite{A94}. More generally, we show that a set of $k$ polytopes with a total of $n$ edges admits, in the worse case, $\Theta(n^2k^2)$ connected components of lines tangent to any four of these polytopes.

Url:

https://hal.inria.fr/inria-00103995

DOI: 10.1145/997817.997827

Links to Exploration step

Hal:inria-00103995

Le document en format XML

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<front><div type="abstract" xml:lang="en">We prove that the lines tangent to four possibly intersecting polytopes in $R3$ with $n$ edges in total form $\Theta(n^2)$ connected components. In the generic case, each connected component is a single line, but our result still holds for arbitrary degenerate scenes. This improves the previously known $O(n^3\log n)$ bound by Agarwal~\cite{A94}. More generally, we show that a set of $k$ polytopes with a total of $n$ edges admits, in the worse case, $\Theta(n^2k^2)$ connected components of lines tangent to any four of these polytopes.</div>
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<abstract xml:lang="en">We prove that the lines tangent to four possibly intersecting polytopes in $R3$ with $n$ edges in total form $\Theta(n^2)$ connected components. In the generic case, each connected component is a single line, but our result still holds for arbitrary degenerate scenes. This improves the previously known $O(n^3\log n)$ bound by Agarwal~\cite{A94}. More generally, we show that a set of $k$ polytopes with a total of $n$ edges admits, in the worse case, $\Theta(n^2k^2)$ connected components of lines tangent to any four of these polytopes.</abstract>
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The Number of Lines Tangent to Arbitrary Convex Polyhedra in 3D

The Number of Lines Tangent to Arbitrary Convex Polyhedra in 3D

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