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On Lines Avoiding Unit Balls in Three Dimensions # Pankaj K. Agarwal + Boris Aronov # Vladlen Koltun Micha Sharir
 

Summary: On Lines Avoiding Unit Balls in Three Dimensions #
Pankaj K. Agarwal + Boris Aronov # Vladlen Koltun § Micha Sharir ¶
December 10, 2003
Abstract
Let B be a set of n unit balls in R 3 . We show that the combinatorial complexity of the space of lines in R 3 that
miss all the balls of B is O(n 3+e ), for any e > 0. This result has connections to problems in visibility, ray shooting,
motion planning, and geometric optimization.
# Work on this paper has been supported by a joint grant from the U.S.--Israel Binational Science Foundation. Work by Pankaj Agarwal was also
supported by NSF under grants CCR­00­86013 EIA­98­70724, EIA­99­72879, EIA­01­31905, and CCR­02­04118. Work by Boris Aronov was
also supported by NSF Grants CCR­99­72568 and ITR CCR­00­81964. Work by Vladlen Koltun was also supported by NSF Grant CCR­01­21555.
Work by Micha Sharir was also supported by NSF Grants CCR­97­32101 and CCR­00­98246, by a grant from the Israeli Academy of Sciences for
a Center of Excellence in Geometric Computing at Tel Aviv University, and by the Hermann Minkowski--MINERVA Center for Geometry at Tel
Aviv University.
+ Department of Computer Science, Duke University, Durham, NC 27708­0129, USA; pankaj@cs.duke.edu.
# Department of Computer and Information Science, Polytechnic University, Brooklyn, NY 11201­3840, USA; aronov@cis.poly.edu.
§ Computer Science Division, University of California, Berkeley, CA 94720­1776, USA; vladlen@cs.berkeley.edu.
¶ 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; michas@post.tau.ac.il.

1 Introduction

  

Source: Aronov, Boris - Department of Computer Science and Engineering, Polytechnic Institute of New York University

 

Collections: Computer Technologies and Information Sciences