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
2 TUM - Technische Universität Munchen - Technical University Munich - Université Technique de Munich

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.

Domaines: Géométrie algorithmique [cs.CG]

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