Lines avoiding unit balls in three dimensions

Pankaj K. Agarwal*, Boris Aronov, Vladlen Koltun, Micha Sharir

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)231-250
Number of pages20
JournalDiscrete and Computational Geometry
Issue number2
StatePublished - Aug 2005


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