inria-00000384, version 1
Transversals to line segments in three-dimensional space
Hervé Brönnimann 1Hazel Everett
2Sylvain Lazard 2Frank Sottile 3Sue Whitesides 4
Discrete & Computational Geometry 34, 3 (2005) 381 - 390
Résumé : 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 $\mathbb{R}^3$.
- 1 : Department of Computer and Information Science
- Polytechnic University of New York
- 2 : VEGAS (INRIA Lorraine - LORIA)
- INRIA – CNRS : UMR7503 – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine
- 3 : Department of Mathematics
- Texas A&M University
- 4 : School of Computer Science [Quebec] (SOCS)
- McGill University
- Domaine : Informatique/Géométrie algorithmique
- Commentaire : http://www.springerlink.com/
- inria-00000384, version 1
- http://hal.inria.fr/inria-00000384
- oai:hal.inria.fr:inria-00000384
- Contributeur : Sylvain Lazard
- Soumis le : Lundi 3 Octobre 2005, 19:05:10
- Dernière modification le : Mardi 4 Juillet 2006, 16:30:49
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