Line problems in nonlinear computational geometry
Metric Geometry
2007-05-23 v2 Algebraic Geometry
Abstract
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 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.
Cite
@article{arxiv.math/0610407,
title = {Line problems in nonlinear computational geometry},
author = {Frank Sottile and Thorsten Theobald},
journal= {arXiv preprint arXiv:math/0610407},
year = {2007}
}
Comments
22 pages, 13 color figures