Line problems in nonlinear computational geometry

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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.
22 pages, 13 color figures

Keywords

Metric Geometry, Algebraic Geometry, 14N99; 14Q15; 52C45; 68U05

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/127438

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0610407
 http://arxiv.org/abs/math/0610407

Collections

arXiv