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

Conference paper
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 151)

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 ℝd 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 ℝd, more precisely the inter-related notions of cone of directions, geometric permutations and Helly-type theorems, and discuss some algorithmic applications.

Keywords

Geometric transversal Helly’s theorem line sphere geometric permutation cone of directions 

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© Springer-Verlag New York 2009

Authors and Affiliations

  1. 1.Loria – INRIA Nancy Grand-Est.NancyFrance

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