Stefan Dantchev
Efficient construction of the Čech complex
Dantchev, Stefan; Ivrissimtzis, Ioannis
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.
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 |
Public URL | https://durham-repository.worktribe.com/output/1299490 |
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Copyright Statement
© 2012 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
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