Subdivisions of n-dimensional spaces and n-dimensional generalized maps
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Graphics Gems III
Functional composition algorithms via blossoming
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Morse Homology Descriptor for Shape Characterization
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On the cohomology of 3D digital images
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
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DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
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ESOP'12 Proceedings of the 21st European conference on Programming Languages and Systems
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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 Bezier simplicial patches are well suited for the embedding of simploidal sets.