Lines Avoiding Unit Balls in Three Dimensions

Authors:
Pankaj K. Agarwal;Boris Aronov;Vladlen Koltun;Micha Sharir
Affiliations:
Department of Computer Science, Duke University, Durham, NC 27708-0129, USA;Department of Computer Science, Duke University, Durham, NC 27708-0129, USA;Department of Computer Science, Duke University, Durham, NC 27708-0129, USA;School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel and Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
Venue:
Discrete & Computational Geometry
Year:
2005

Citing 0
Cited 2

On the complexity of sets of free lines and line segments among balls in three dimensions

Proceedings of the twenty-sixth annual symposium on Computational geometry
Lines avoiding balls in three dimensions revisited

Proceedings of the twenty-sixth annual symposium on Computational geometry

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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(n3+ε), for any ε 0. This result has connections to problems in visibility, ray shooting, motion planning, and geometric optimization.