On lines avoiding unit balls in three dimensions

Authors:
Pankaj K. Agarwal;Boris Aronov;Vladlen Koltun;Micha Sharir
Affiliations:
Duke University, Durham, NC;Polytechnic University, Brooklyn, NY;University of California, Berkeley, CA;Tel Aviv University, Tel Aviv, Israel and New York University, New York, NY
Venue:
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Year:
2004

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Abstract

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(n 3+e), for any ε0. This result has connections toproblems in visibility, ray shooting, motion planning andgeometric optimization.