Article Dans Une Revue Discrete and Computational Geometry Année : 2005

Transversals to line segments in three-dimensional space

Résumé

We completely describe the structure of the connected components of transversals to a collection of n line segments in R3. Generically, the set of transversal to four segments consist of zero or two lines. We catalog the non-generic cases and show that n3 arbitrary line segments in R3 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 R3.
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Dates et versions

inria-00000384 , version 1 (03-10-2005)

Identifiants

Citer

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