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Some Discrete Properties of the Space of Line Transversals to Disjoint Balls

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Abstract

Attempts to generalize Helly's theorem to sets of lines intersecting convex sets led to a series of results relating the geometry of a family of sets in R^d to the structure of the space of lines intersecting all of its members. We review recent progress in the special case of disjoint Euclidean balls in R^d, more precisely the inter-related notions of cone of directions, geometric permutations and Helly-type theorems, and discuss some algorithmic applications.
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inria-00335946 , version 1 (12-11-2009)

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Xavier Goaoc. Some Discrete Properties of the Space of Line Transversals to Disjoint Balls. I. Emiris, F. Sottile and T. Theobald. Non-linear Computational Geometry, 151, Springer New York, pp.51-84, 2008, The IMA Volumes in Mathematics and its Applications, 978-1-4419-0998-5 (Print) 978-1-4419-0999-2 (Online). ⟨10.1007/978-1-4419-0999-2_3⟩. ⟨inria-00335946⟩
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