Transversals to Line Segments in Three-Dimensional Space Academic Article uri icon

abstract

  • We completely describe the structure of the connected components of transversals to a collection of n line segments in 3. 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 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 3. 2005 Springer Science+Business Media, Inc.

published proceedings

  • Discrete & Computational Geometry

author list (cited authors)

  • Brnnimann, H., Everett, H., Lazard, S., Sottile, F., & Whitesides, S.

citation count

  • 18

complete list of authors

  • Brönnimann, H||Everett, H||Lazard, S||Sottile, F||Whitesides, S

publication date

  • September 2005