# Line transversals to disjoint balls

2 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We prove that the set of directions of lines intersecting three disjoint balls in $\mathbb{R}^3$ in a given order is a strictly convex subset of $\mathbb{S}^2$. We then generalize this result to $n$ disjoint balls in $\mathbb{R}^d$. As a consequence, we can improve upon several old and new results on line transversals to disjoint balls in arbitrary dimension, such as bounds on the number of connected components and Helly-type theorems.
Document type :
Journal articles

Cited literature [20 references]

https://hal.inria.fr/inria-00176198
Contributor : Xavier Goaoc <>
Submitted on : Tuesday, October 2, 2007 - 6:41:17 PM
Last modification on : Thursday, January 11, 2018 - 6:20:14 AM
Long-term archiving on : Thursday, September 27, 2012 - 12:36:02 PM

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### Citation

Ciprian Borcea, Xavier Goaoc, Sylvain Petitjean. Line transversals to disjoint balls. Discrete and Computational Geometry, Springer Verlag, 2008, 39 (1-3), pp.158--173. ⟨10.1007/s00454-007-9016-z⟩. ⟨inria-00176198⟩

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