Computational Topology for Regular Closed Sets
Abstract
The Boolean algebra of regular closed sets is prominent in topology, particularly as a dual for the Stone-Cech compactification. This algebra is also central for the theory of geometric computation, as a representation for combinatorial operations on geometric sets. However, the issue of computational approximation introduces unresolved subtleties that do not occur within "pure" topology. One major effort towards reconciling this mathematical theory with computational practice is our ongoing I-TANGO project. The acronym I-TANGO is an abbreviation for "Intersections - Topology, Accuracy and Numerics for Geometric Objects". The long-range goals and initial progress of the I-TANGO team in development of computational topology are presented.
Cite
@article{arxiv.math/0402446,
title = {Computational Topology for Regular Closed Sets},
author = {The I-TANGO project and : and T. J. Peters and J. Bisceglio and D. R. Ferguson and C. M. Hoffmann and T. Maekawa and N. M. Patrikalakis and T. Sakkalis and N. F. Stewart},
journal= {arXiv preprint arXiv:math/0402446},
year = {2012}
}
Comments
12 pages, 4 figures