@article{3581,
  abstract     = {A number of rendering algorithms in computer graphics sort three-dimensional objects by depth and assume that there is no cycle that makes the sorting impossible. One way to resolve the problem caused by cycles is to cut the objects into smaller pieces. In this paper we address the problem of estimating how many such cuts arc always sufficient. We also consider a few related algorithmic and combinatorial geometry problems. For example, we demonstrate that n lines in space can be sorted in randomized expected time O(n4’st’), provided that they define no cycle. We also prove an 0(n7’4) upper bound on the number of points in space so that there are n lines with the property that for each point there are at least three noncoplanar lines that contain it. },
  author       = {Chazelle, Bernard and Edelsbrunner, Herbert and Guibas, Leonidas and Pollack, Richard and Seidel, Raimund and Sharir, Micha and Snoeyink, Jack},
  issn         = {0925-7721},
  journal      = {Computational Geometry: Theory and Applications},
  number       = {6},
  pages        = {305 -- 323},
  publisher    = {Elsevier},
  title        = {{Counting and cutting cycles of lines and rods in space}},
  doi          = {10.1016/0925-7721(92)90009-H},
  volume       = {1},
  year         = {1992},
}