Transversals to line segments in three-dimensional space

2 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We completely describe the structure of the connected components of transversals to a collection of $n$ line segments in $\mathbb{R}^3$. Generically, the set of transversal to four segments consist of zero or two lines. We catalog the non-generic cases and show that $n\geq 3$ arbitrary line segments in $\mathbb{R}^3$ admit at most $n$ connected components of line transversals, and that this bound can be achieved in certain configurations when the segments are coplanar, or they all lie on a hyperboloid of one sheet. This implies a tight upper bound of $n$ on the number of geometric permutations of line segments in $\mathbb{R}^3$.
Type de document :
Article dans une revue
Discrete and Computational Geometry, Springer Verlag, 2005, 34 (3), pp.381 - 390. 〈10.1007/s00454-005-1183-1〉

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https://hal.inria.fr/inria-00000384
Contributeur : Sylvain Lazard <>
Soumis le : lundi 3 octobre 2005 - 19:05:10
Dernière modification le : jeudi 7 février 2019 - 14:52:51
Document(s) archivé(s) le : jeudi 1 avril 2010 - 22:36:58

Citation

Hervé Brönnimann, Hazel Everett, Sylvain Lazard, Frank Sottile, Sue Whitesides. Transversals to line segments in three-dimensional space. Discrete and Computational Geometry, Springer Verlag, 2005, 34 (3), pp.381 - 390. 〈10.1007/s00454-005-1183-1〉. 〈inria-00000384〉

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