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Line problems in nonlinear computational geometry

Frank Sottile·Thorsten Theobald
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Abstract

We first review some topics in the classical computational geometry of lines, in particular the O(n^{3+ε}) bounds for the combinatorial complexity of the set of lines in R^3 interacting with $n$ objects of fixed description complexity. The main part of this survey is recent work on a core algebraic problem--studying the lines tangent to k spheres that also meet 4-k fixed lines. We give an example of four disjoint spheres with 12 common real tangents.

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Frank Sottile, Thorsten Theobald. 2007-04-17. Line problems in nonlinear computational geometry. https://arxiv.org/abs/math/0610407

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