InforLorV4, Hal, Corpus, bibRecord, 003B89

Pinning a Line by Balls or Ovaloids in $R^3$

Identifieur interne : 003B89 ( Hal/Corpus ); précédent : 003B88; suivant : 003B90

Pinning a Line by Balls or Ovaloids in $R^3$

Auteurs : Xavier Goaoc ; Stefan Koenig ; Sylvain Petitjean

Source :

Discrete and Computational Geometry [ 0179-5376 ] ; 2011.

RBID : Hal:inria-00518033

Abstract

We show that if a line L is an isolated line transversal to a finite family F of (possibly intersecting) balls in R^3 and no two balls are externally tangent on L, then there is a subfamily G ⊆ F of size at most 12 such that L is an isolated line transversal to G. We generalize this result to families of semialgebraic ovaloids.

Url:

https://hal.inria.fr/inria-00518033

DOI: 10.1007/s00454-010-9297-5

Links to Exploration step

Hal:inria-00518033

Le document en format XML

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<front><div type="abstract" xml:lang="en">We show that if a line L is an isolated line transversal to a finite family F of (possibly intersecting) balls in R^3 and no two balls are externally tangent on L, then there is a subfamily G ⊆ F of size at most 12 such that L is an isolated line transversal to G. We generalize this result to families of semialgebraic ovaloids.</div>
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<sourceDesc><biblStruct><analytic><title xml:lang="en">Pinning a Line by Balls or Ovaloids in $R^3$</title>
<author role="aut"><persName><forename type="first">Xavier</forename>
<surname>Goaoc</surname>
</persName>
<email>goaoc@loria.fr</email>
<idno type="halAuthorId">58709</idno>
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<author role="aut"><persName><forename type="first">Stefan</forename>
<surname>Koenig</surname>
</persName>
<idno type="halAuthorId">526679</idno>
<affiliation ref="#struct-121672"></affiliation>
</author>
<author role="aut"><persName><forename type="first">Sylvain</forename>
<surname>Petitjean</surname>
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<idno type="halAuthorId">60838</idno>
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<monogr><idno type="halJournalId" status="VALID">12620</idno>
<idno type="issn">0179-5376</idno>
<idno type="eissn">1432-0444</idno>
<title level="j">Discrete and Computational Geometry</title>
<imprint><publisher>Springer Verlag</publisher>
<biblScope unit="volume">45</biblScope>
<biblScope unit="issue">2</biblScope>
<biblScope unit="pp">303-320</biblScope>
<date type="datePub">2011</date>
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<abstract xml:lang="en">We show that if a line L is an isolated line transversal to a finite family F of (possibly intersecting) balls in R^3 and no two balls are externally tangent on L, then there is a subfamily G ⊆ F of size at most 12 such that L is an isolated line transversal to G. We generalize this result to families of semialgebraic ovaloids.</abstract>
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Pinning a Line by Balls or Ovaloids in $R^3$

Pinning a Line by Balls or Ovaloids in $R^3$

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