Encyclopedia of Database Systems

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

Dimension-Extended Topological Relationships

  • Eliseo ClementiniEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-8265-9_132


This definition includes a group of models for topological relationships that have in common the use of two topological invariants – the set intersection empty/nonempty content and the dimension – for distinguishing various relationships between spatial objects. These models had a strong impact in database technology and the standardization process.

Historical Background

Early descriptions of topological relationships (e.g., [1]) did not have enough formal basis to support a spatial query language, which needs formal definitions in order to specify exact algorithms to assess relationships. The importance of defining a sound and complete set of topological relationships was recognized in [2]. The first formal models were all based on point-set topology. In [3], the authors originally described the 4-intersection model (4IM) for classifying topological relationships between one-dimensional intervals. In [4], the authors adopted the same method for classifying topological...

This is a preview of subscription content, log in to check access.

Recommended Reading

  1. 1.
    Freeman J. The modelling of spatial relations. Comput Graph Image Process. 1975;4(2):156–71.CrossRefGoogle Scholar
  2. 2.
    Smith T, Park K. Algebraic approach to spatial reasoning. Int J Geogr Inf Syst. 1992;6(3):177–92.CrossRefGoogle Scholar
  3. 3.
    Pullar DV, Egenhofer MJ. Toward the definition and use of topological relations among spatial objects. In: Proceedings of the Third International Symposium on Spatial Data Handling; 1988. p. 225–42.Google Scholar
  4. 4.
    Egenhofer MJ, Franzosa RD. Point-set topological spatial relations. Int J Geogr Inf Syst. 1991;5(2):161–74.CrossRefGoogle Scholar
  5. 5.
    Egenhofer MJ, Herring JR. Categorizing binary topological relationships between regions, lines, and points in geographic databases. Orono: Department of Surveying Engineering, University of Maine; 1991.Google Scholar
  6. 6.
    Clementini E, Di Felice P, van Oosterom P. A small set of formal topological relationships suitable for end-user interaction. In: Proceedings of the 3rd International Symposium on Advances in Spatial Databases; 1993. p. 277–95.CrossRefGoogle Scholar
  7. 7.
    Clementini E, Di Felice P. A comparison of methods for representing topological relationships. Inf Sci. 1995;3(3):149–78.Google Scholar
  8. 8.
    Clementini E, Di Felice P, Califano G. Composite regions in topological queries. Inf Syst. 1995;20(7):579–94.CrossRefGoogle Scholar
  9. 9.
    Clementini E, Di Felice P. A model for representing topological relationships between complex geometric features in spatial databases. Inf Sci. 1996;90(1–4):121–36.CrossRefMathSciNetzbMATHGoogle Scholar
  10. 10.
    Egenhofer MJ, Clementini E, Di Felice P. Topological relations between regions with holes. Int J Geogr Inf Syst. 1994;8(2):129–42.CrossRefGoogle Scholar
  11. 11.
    Herring JR. The mathematical modeling of spatial and non-spatial information in geographic information systems. In: Mark D, Frank A, editors. Cognitive and linguistic aspects of geographic space. Kluwer: Dordrecht; 1991. p. 313–50.CrossRefGoogle Scholar
  12. 12.
    Clementini E, Di Felice P. Topological invariants for lines. IEEE Trans Knowl Data Eng. 1998;10(1):38–54.CrossRefGoogle Scholar
  13. 13.
    Clementini E, Di Felice P. Spatial operators. ACM SIGMOD Rec. 2000;29(3):31–8.CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.University of L’AguilaL’AguilaItaly

Section editors and affiliations

  • Ralf Hartmut Güting
    • 1
  1. 1.Fakultät für Mathematik und InformatikFernuniversität HagenHagenGermany