Fast and Robust Smallest Enclosing Balls
ESA '99 Proceedings of the 7th Annual European Symposium on Algorithms
Topological persistence and simplification
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Discrete & Computational Geometry
Reconstruction using witness complexes
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Computer-Aided Design
Technical Section: Fast construction of the Vietoris-Rips complex
Computers and Graphics
Quasi-worlds and quasi-operators on quasi-triangulations
Computer-Aided Design
Three-dimensional beta-shapes and beta-complexes via quasi-triangulation
Computer-Aided Design
Querying simplexes in quasi-triangulation
Computer-Aided Design
Topological estimation using witness complexes
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
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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 Cech complex of P for a given value @e 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 @e can handle inputs with tens of thousands of points. We also present an algorithm for the construction of all possible Cech complices on P.