86 research outputs found
Transversals to Line Segments in Three-Dimensional Space
We completely describe the structure of the connected components of transversals to a collection of n line segments in R3. We show that n \u3e 3 arbitrary line segments in R3 admit 0, 1, . . . , n or infinitely many line transversals. In the latter case, the transversals form up to n connected components
Affine configurations and pure braids
We show that the fundamental group of the space of ordered affine-equivalent
configurations of at least five points in the real plane is isomorphic to the
pure braid group modulo its centre. In the case of four points this fundamental
group is free with eleven generators.Comment: 5 pages, 1 figure, final version; to appear in Discrete &
Computational Geometry, available from the publishers at
http://www.springerlink.com/content/384516n7q24811ph
Transversals to line segments in three-dimensional space
http://www.springerlink.com/We completely describe the structure of the connected components of transversals to a collection of line segments in . Generically, the set of transversal to four segments consist of zero or two lines. We catalog the non-generic cases and show that arbitrary line segments in admit at most 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 on the number of geometric permutations of line segments in
- …