Line transversals to disjoint balls

Ciprian Borcea 1 Xavier Goaoc 2 Sylvain Petitjean 2
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.
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https://hal.inria.fr/inria-00176198
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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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