InforLorV4, Hal, Curation, bibRecord, 002F23

Lines tangent to four triangles in three-dimensional space

Identifieur interne : 002F23 ( Hal/Curation ); précédent : 002F22; suivant : 002F24

Lines tangent to four triangles in three-dimensional space

Auteurs : Hervé Brönnimann [États-Unis] ; Olivier Devillers [France] ; Sylvain Lazard [France] ; Frank Sottile [États-Unis]

Source :

Discrete and Computational Geometry [ 0179-5376 ] ; 2007.

RBID : Hal:inria-00000598

Abstract

We investigate the lines tangent to four triangles in $\mathbb{R}^3$. By a construction, there can be as many as 62 tangents. We show that there are at most 162 connected components of tangents, and at most 156 if the triangles are disjoint. In addition, if the triangles are in (algebraic) general position, then the number of tangents is finite and it is always even.

Url:

https://hal.inria.fr/inria-00000598

DOI: 10.1007/s00454-006-1278-3

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<front><div type="abstract" xml:lang="en">We investigate the lines tangent to four triangles in $\mathbb{R}^3$. By a construction, there can be as many as 62 tangents. We show that there are at most 162 connected components of tangents, and at most 156 if the triangles are disjoint. In addition, if the triangles are in (algebraic) general position, then the number of tangents is finite and it is always even.</div>
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<sourceDesc><biblStruct><analytic><title xml:lang="en">Lines tangent to four triangles in three-dimensional space</title>
<author role="aut"><persName><forename type="first">Hervé</forename>
<surname>Brönnimann</surname>
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<author role="aut"><persName><forename type="first">Olivier</forename>
<surname>Devillers</surname>
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<email>Olivier.Devillers@inria.fr</email>
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<author role="aut"><persName><forename type="first">Sylvain</forename>
<surname>Lazard</surname>
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<email>sylvain.lazard@inria.fr</email>
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<author role="aut"><persName><forename type="first">Frank</forename>
<surname>Sottile</surname>
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<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">37</biblScope>
<biblScope unit="issue">3</biblScope>
<biblScope unit="pp">369-380</biblScope>
<date type="datePub">2007</date>
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<idno type="doi">10.1007/s00454-006-1278-3</idno>
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<abstract xml:lang="en">We investigate the lines tangent to four triangles in $\mathbb{R}^3$. By a construction, there can be as many as 62 tangents. We show that there are at most 162 connected components of tangents, and at most 156 if the triangles are disjoint. In addition, if the triangles are in (algebraic) general position, then the number of tangents is finite and it is always even.</abstract>
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Lines tangent to four triangles in three-dimensional space

Lines tangent to four triangles in three-dimensional space

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