Encyclopedia of Database Systems

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

Dimension-Extended Topological Relationships

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

Definition

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...

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Recommended Reading

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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