Line problems in nonlinear computational geometry

Details Line problems in nonlinear computational geometry Line problems in nonlinear computational geometry

2006-10-12

arxiv.org/abs/math/0610407v2

Mathematics

Metric Geometry

22 pages, 13 color figures

Scientific paper

We first review some topics in the classical computational geometry of lines, in particular the O(n^{3+\epsilon}) 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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