Lines and Free Line Segments Tangent to Arbitrary Three-Dimensional Convex Polyhedra

@article{Brnnimann2007LinesAF,
  title={Lines and Free Line Segments Tangent to Arbitrary Three-Dimensional Convex Polyhedra},
  author={Herv{\'e} Br{\"o}nnimann and Olivier Devillers and Vida Dujmovic and Hazel Everett and Marc Glisse and Xavier Goaoc and Sylvain Lazard and Hyeon-Suk Na and Sue Whitesides},
  journal={SIAM J. Comput.},
  year={2007},
  volume={37},
  pages={522-551}
}
Motivated by visibility problems in three dimensions, we inve stigate the complexity and construction of the set of tangent lines in a scene of three-dimensional pol yhedra. We prove that the set of lines tangent to four possibly intersecting convex polyhedra in R3 with a total ofn edges consists of Θ(n2) connected components in the worst case. In the generic case, each connected component is a single line, but our result still holds for arbitrarily degenerate scenes. More generally, we show… CONTINUE READING