Simploidal Sets

Pascal Lienhardt (1) , Samuel Peltier (1)

1 XLIM-ASALI - Synthèse et analyse d'images

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.

Mots clés: Simplicial Sets; Cubical Sets; Simploidal Sets; Bézier Spaces

Domaines: Géométrie algorithmique [cs.CG]; Informatique [cs]; Synthèse d'image et réalité virtuelle [cs.GR]

Pascal Lienhardt, Samuel Peltier. Simploidal Sets. 2016. ⟨hal-01274880v1⟩