Topological computing of arrangements with (co)chains
Computational Geometry
2019-11-20 v1 Data Structures and Algorithms
Abstract
In many areas of applied geometric/numeric computational mathematics, including geo-mapping, computer vision, computer graphics, finite element analysis, medical imaging, geometric design, and solid modeling, one has to compute incidences, adjacencies and ordering of cells, generally using disparate and often incompatible data structures and algorithms. This paper introduces computational topology algorithms to discover the 2D/3D space partition induced by a collection of geometric objects of dimension 1D/2D, respectively. Methods and language are those of basic geometric and algebraic topology. Only sparse vectors and matrices are used to compute both spaces and maps, i.e., the chain complex, from dimension zero to three.
Cite
@article{arxiv.1911.08130,
title = {Topological computing of arrangements with (co)chains},
author = {Alberto Paoluzzi and Vadim Shapiro and Antonio DiCarlo and Francesco Furiani and Giulio Martella and Giorgio Scorzelli},
journal= {arXiv preprint arXiv:1911.08130},
year = {2019}
}
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