Transversals to line segments in three-dimensional space
Identifieur interne : 006079 ( Main/Exploration ); précédent : 006078; suivant : 006080Transversals to line segments in three-dimensional space
Auteurs : Hervé Brönnimann ; Hazel Everett ; Sylvain Lazard ; Frank Sottile ; Sue WhitesidesSource :
- Discrete and Computational Geometry ; 2005.
English descriptors
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.
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