Simploidal Sets

Abstract : Simplicial sets and cubical sets are combinatorial structures studied since a long time in Algebraic Topology, and they are used for many applications in Computational Topology, Geometric Modeling, CAD, Computer Graphics, etc. Simploidal sets are defined in this paper in order to homogenize and generalize simplicial and cubical sets. Basic operations are also defined here, which extend basic simplicial and cubical operations (cone, identification, cartesian product). In order to associate shapes with structures, structural relations between simploidal sets and Bézier spaces are provided. It is then possible to (simultaneously) handle through a single formalism: simplices, cubes, and more generally cells corresponding to products of simplices, with a very low additional cost, regarding space (data structure), time (construction or computation operations) or software development.
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Contributeur : Pascal Lienhardt <>
Soumis le : mardi 16 février 2016 - 12:57:22
Dernière modification le : vendredi 19 février 2016 - 01:06:57
Document(s) archivé(s) le : mardi 17 mai 2016 - 17:22:03


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  • HAL Id : hal-01274880, version 1



Pascal Lienhardt, Samuel Peltier. Simploidal Sets. 2016. 〈hal-01274880〉



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