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Journal Articles Discrete and Computational Geometry Year : 2008

## Line transversals to disjoint balls

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Ciprian Borcea
• Function : Author
Xavier Goaoc
Sylvain Petitjean
• Function : Author
• PersonId : 755697
• IdRef : 172437156

#### 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.

### Dates and versions

inria-00176198 , version 1 (02-10-2007)

### Identifiers

• HAL Id : inria-00176198 , version 1
• DOI :

### Cite

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

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