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Efficient construction of the Čech complex

Dantchev, Stefan; Ivrissimtzis, Ioannis

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Authors

Stefan Dantchev



Abstract

In many applications, the first step into the topological analysis of a discrete point set P sampled from a manifold is the construction of a simplicial complex with vertices on P. In this paper, we present an algorithm for the efficient computation of the Čech complex of P for a given value ε of the radius of the covering balls. Experiments show that the proposed algorithm can generally handle input sets of several thousand points, while for the topologically most interesting small values of ε can handle inputs with tens of thousands of points. We also present an algorithm for the construction of all possible Čech complices on P.

Citation

Dantchev, S., & Ivrissimtzis, I. (2012). Efficient construction of the Čech complex. Computers and Graphics, 36(6), 708-713. https://doi.org/10.1016/j.cag.2012.02.016

Journal Article Type Article
Acceptance Date Feb 29, 2012
Online Publication Date Mar 9, 2012
Publication Date Mar 9, 2012
Deposit Date Jun 17, 2019
Publicly Available Date Jun 17, 2019
Journal Computers and Graphics
Print ISSN 0097-8493
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 36
Issue 6
Pages 708-713
DOI https://doi.org/10.1016/j.cag.2012.02.016

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