On lines avoiding unit balls in three dimensions

Let B be a set of n unit balls in R3 . We show that the combinatorial complexity of the space of lines in R3 that avoid all the balls of B is O(n3+ε ), for any ε > 0. This result has connections to problems in visibility, ray shooting, motion planning and geometric optimization.

• Type: Conference
• Year: 2004
• Where: COMPGEOM
• Authors: Pankaj K. Agarwal, Boris Aronov, Vladlen Koltun, Micha Sharir
• Keywords: Combinatorial Complexity, COMPGEOM 2004, Motion Planning, Unit Balls