Encyclopedia of Database Systems

2018 Edition
| Editors: Ling Liu, M. Tamer Özsu

Simplicial Complex

  • Andrew U. Frank
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-8265-9_345

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. 1.

    Any face of a simplex in K is also in K

     
  2. 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...
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Recommended Reading

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    Alexandrov PS. Combinatorial topology volumes 1, 2 and 3. Mineola/New York: Dover Publications, Inc.; 1960.Google Scholar
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    Thompson RJ. Towards a rigorous logic for spatial data representation. Doctoral thesis, Delft, NCG; 2007.Google Scholar
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    Sellis T, et al., editors. Spatiotemporal databases: the chorochronos approach. LNCS, vol. 2520. Berlin: Springer; 2003.Google Scholar
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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Vienna University of TechnologyViennaAustria

Section editors and affiliations

  • Ralf Hartmut Güting
    • 1
  1. 1.Computer ScienceUniversity of HagenHagenGermany