Synonyms
Cell complex; CW complex; Polyhedron
Definition
A simplicial complex is a topological space constructed by gluing together dimensional simplices (points, line segments, triangles, tetrahedrons, etc.).
A simplicial complex K is a set of simplices k, which satisfies the two conditions:
- 1.
Any face of a simplex in K is also in K
- 2.
The intersection of any two simplices in K is a face of both simplices (or empty)
Historical Background
Raster (field) or vector (object) are the two dominant conceptualizations of space. Applications focusing on object with 2 or 3 dimensional geometry structure the storage of geometry as points, lines, surfaces, and volumes and the relations between them; a classical survey paper discussed the possible approaches mostly from the perspective of Computer Aided Design (CAD) where individual physical objects are constructed [1].
The representation of geographic information, e.g., maps, introduces consistency constraints between the objects; consider the...
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Frank, A.U. (2018). Simplicial Complex. In: Liu, L., Özsu, M.T. (eds) Encyclopedia of Database Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8265-9_345
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DOI: https://doi.org/10.1007/978-1-4614-8265-9_345
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