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# Geometric Permutations of Disjoint Unit Spheres

2 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We show that a set of $n$ disjoint unit spheres in $R^d$ admits at most two distinct geometric permutations if $n \geq 9$, and at most three if $3 \leq n \leq 8$. This result improves a Helly-type theorem on line transversals for disjoint unit spheres in $R^3$: if any subset of size $18$ of a family of such spheres admits a line transversal, then there is a line transversal for the entire family.
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Journal articles

Cited literature [14 references]

https://hal.inria.fr/inria-00000637
Contributor : Xavier Goaoc Connect in order to contact the contributor
Submitted on : Thursday, October 5, 2006 - 1:25:45 PM
Last modification on : Wednesday, February 2, 2022 - 3:51:34 PM
Long-term archiving on: : Friday, April 2, 2010 - 6:56:12 PM

### Identifiers

• HAL Id : inria-00000637, version 1

### Citation

Otfried Cheong, Xavier Goaoc, Na Hyeon-Suk. Geometric Permutations of Disjoint Unit Spheres. Computational Geometry, 2005, 30 (3), pp.253-270. ⟨inria-00000637⟩

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