Discrete & Computational Geometry

, Volume 39, Issue 1–3, pp 158–173 | Cite as

Line Transversals to Disjoint Balls

Article

Abstract

We prove that the set of directions of lines intersecting three disjoint balls in ℝ3 in a given order is a strictly convex subset of \(\mathbb {S}^{2}\) . We then generalize this result to n disjoint balls in ℝd. 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.

Keywords

Transversal Geometric permutation Convexity 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Ciprian Borcea
    • 1
  • Xavier Goaoc
    • 2
  • Sylvain Petitjean
    • 3
  1. 1.Rider UniversityLawrencevilleUSA
  2. 2.LORIA–INRIA LorraineNancyFrance
  3. 3.LORIA–CNRSNancyFrance

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