Discrete & Computational Geometry

, Volume 45, Issue 2, pp 303–320 | Cite as

Pinning a Line by Balls or Ovaloids in ℝ3

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Abstract

We show that if a line is an isolated line transversal to a finite family \(\mathcal{F}\) of (possibly intersecting) balls in ℝ3 and no two balls are externally tangent on , then there is a subfamily \(\mathcal{G}\subseteq\mathcal{F}\) of size at most 12 such that is an isolated line transversal to \(\mathcal{G}\). We generalize this result to families of semialgebraic ovaloids.

Keywords

Geometric transversals Helly-type theorems Line geometry Ovaloids 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Xavier Goaoc
    • 1
  • Stefan König
    • 2
  • Sylvain Petitjean
    • 1
  1. 1.Project-team VEGASINRIA Nancy–LORIAVandœuvreFrance
  2. 2.Zentrum MathematikTechnische Universität MünchenGarching bei MünchenGermany

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