Transversals to Line Segments in Three-Dimensional Space Academic Article

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.

authors

• Sottile, Frank

published proceedings

• Discrete & Computational Geometry

author list (cited authors)

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

citation count

• 19

complete list of authors

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

publication date

• September 2005

publisher

• Springer Nature  Publisher

published in

• Discrete and Computational Geometry: an international journal of mathematics and computer science  Journal

keywords

• 49 Mathematical Sciences
• 4904 Pure Mathematics

Digital Object Identifier (DOI)

• 10.1007/s00454-005-1183-1

start page

• 381

end page

• 390

volume

• 34

issue

• 3

URL

• http://dx.doi.org/10.1007/s00454-005-1183-1