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.
|Full text:||(AM) Accepted Manuscript|
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|Publisher Web site:||https://doi.org/10.1016/j.cag.2012.02.016|
|Publisher 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/|
|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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