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Journal articles
Transversals to line segments in three-dimensional space
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 $\mathbb{R}^3$.
Cited literature [23 references]
https://hal.inria.fr/inria-00000384
Contributor : Sylvain Lazard Connect in order to contact the contributor
Submitted on : Monday, October 3, 2005 - 7:05:10 PM
Last modification on : Thursday, January 20, 2022 - 4:16:33 PM
Long-term archiving on: : Thursday, April 1, 2010 - 10:36:58 PM
Contributor : Sylvain Lazard Connect in order to contact the contributor
Submitted on : Monday, October 3, 2005 - 7:05:10 PM
Last modification on : Thursday, January 20, 2022 - 4:16:33 PM
Long-term archiving on: : Thursday, April 1, 2010 - 10:36:58 PM