Simploidals sets: Definitions, Operations and Comparison with Simplicial Sets

Abstract : The combinatorial structure of simploidal sets generalizes both simplicial complexes and cubical complexes. More precisely, cells of simploidal sets are cartesian product of simplices. This structure can be useful for geometric modeling (e.g. for handling hybrid meshes) or image analysis (e.g. for computing topological properties of parts of n-dimensional images). In this paper, definitions and basic constructions are detailed. The homology of simploidal sets is defined and it is shown to be equivalent to the classical homology. It is also shown that products of Bézier simplicial patches are well suited for the embedding of simploidal sets.
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Discrete Applied Mathematics, Elsevier, 2009, 157, pp.542--557. <10.1016/j.dam.2008.05.032>
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https://hal.archives-ouvertes.fr/hal-00366069
Contributeur : Samuel Peltier <>
Soumis le : jeudi 5 mars 2009 - 16:12:58
Dernière modification le : mardi 22 mars 2016 - 01:05:13

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Samuel Peltier, Laurent Fuchs, Pascal Lienhardt. Simploidals sets: Definitions, Operations and Comparison with Simplicial Sets. Discrete Applied Mathematics, Elsevier, 2009, 157, pp.542--557. <10.1016/j.dam.2008.05.032>. <hal-00366069>

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