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Efficient construction of the Čech complex.

Dantchev, Stefan and Ivrissimtzis, Ioannis (2012) 'Efficient construction of the Čech complex.', Computers & graphics., 36 (6). pp. 708-713.


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.

Item Type:Article
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Publisher statement:© 2012 This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Date accepted:29 February 2012
Date deposited:17 June 2019
Date of first online publication:09 March 2012
Date first made open access:No date available

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