Finding stabbing lines in 3-space

Discrete & Computational Geometry, Aug 1992

A line intersecting all polyhedra in a setℬ is called a “stabber” for the setℬ. This paper addresses some combinatorial and algorithmic questions about the setℒ(ℬ) of all lines stabbingℬ. We prove that the combinatorial complexity ofℒ(ℬ) has an$$O(n^3 2^{c\sqrt {\log n} } )$$ upper bound, wheren is the total number of facets inℬ, andc is a suitable constant. This bound is almost tight. Within the same time bound it is possible to determine if a stabbing line exists and to find one.

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M. Pellegrini, P. W. Shor. Finding stabbing lines in 3-space, Discrete & Computational Geometry, 1992, 191-208, DOI: 10.1007/BF02293043