SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Visibility maps of segments and triangles in 3D
Computational Geometry: Theory and Applications
Predicates for line transversals to lines and line segments in three-dimensional space
Proceedings of the twenty-fourth annual symposium on Computational geometry
Line transversals of convex polyhedra in R3
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
On the degree of standard geometric predicates for line transversals in 3D
Computational Geometry: Theory and Applications
On the complexity of umbra and penumbra
Computational Geometry: Theory and Applications
On the complexity of sets of free lines and line segments among balls in three dimensions
Proceedings of the twenty-sixth annual symposium on Computational geometry
On the computation of 3D visibility skeletons
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Line Transversals of Convex Polyhedra in $\mathbb{R}^3$
SIAM Journal on Computing
Line Localization from Single Catadioptric Images
International Journal of Computer Vision
Lines through segments in 3d space
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
| Hi-index | 0.00 |
We completely describe the structure of the connected components of transversals to a collection of n line segments in ℝ3. 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 ℝ3 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 ℝ3.