Pinning a Line by Balls or Ovaloids in $R^3$

Xavier Goaoc 1 Stefan Koenig 2 Sylvain Petitjean 1
1 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We show that if a line L is an isolated line transversal to a finite family F of (possibly intersecting) balls in R^3 and no two balls are externally tangent on L, then there is a subfamily G ⊆ F of size at most 12 such that L is an isolated line transversal to G. We generalize this result to families of semialgebraic ovaloids.
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Submitted on : Thursday, September 16, 2010 - 12:17:33 PM
Last modification on : Thursday, January 11, 2018 - 6:20:14 AM

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Xavier Goaoc, Stefan Koenig, Sylvain Petitjean. Pinning a Line by Balls or Ovaloids in $R^3$. Discrete and Computational Geometry, Springer Verlag, 2011, 45 (2), pp.303-320. ⟨10.1007/s00454-010-9297-5⟩. ⟨inria-00518033⟩

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