InforLorV4, Main, Exploration, bibRecord, 006166

Transversals to Line Segments in Three-Dimensional Space

Identifieur interne : 006166 ( Main/Exploration ); précédent : 006165; suivant : 006167

Transversals to Line Segments in Three-Dimensional Space

Auteurs : H. Brönnimann [États-Unis] ; H. Everett [France] ; S. Lazard [France] ; F. Sottile [États-Unis] ; S. Whitesides [Canada]

Source :

Discrete & Computational Geometry [ 0179-5376 ] ; 2005-09-01.

RBID : ISTEX:983587829D53AE680ED515FE6DCBA0804C0F04C5

Abstract

Abstract: We completely describe the structure of the connected components of transversals to a collection of n line segments in ℝ3. Generically, the set of transversals to four segments consists of zero or two lines. We catalog the non-generic cases and show that n≥ 3 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.

Url:

DOI: 10.1007/s00454-005-1183-1

Affiliations:

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Transversals to Line Segments in Three-Dimensional Space

Transversals to Line Segments in Three-Dimensional Space

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