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...
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsRecommended Reading
Freeman J. The modelling of spatial relations. Comput Graph Image Process. 1975;4(2):156–71.
Smith T, Park K. Algebraic approach to spatial reasoning. Int J Geogr Inf Syst. 1992;6(3):177–92.
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.
Egenhofer MJ, Franzosa RD. Point-set topological spatial relations. Int J Geogr Inf Syst. 1991;5(2):161–74.
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.
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.
Clementini E, Di Felice P. A comparison of methods for representing topological relationships. Inf Sci. 1995;3(3):149–78.
Clementini E, Di Felice P, Califano G. Composite regions in topological queries. Inf Syst. 1995;20(7):579–94.
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.
Egenhofer MJ, Clementini E, Di Felice P. Topological relations between regions with holes. Int J Geogr Inf Syst. 1994;8(2):129–42.
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.
Clementini E, Di Felice P. Topological invariants for lines. IEEE Trans Knowl Data Eng. 1998;10(1):38–54.
Clementini E, Di Felice P. Spatial operators. ACM SIGMOD Rec. 2000;29(3):31–8.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Section Editor information
Rights and permissions
Copyright information
© 2018 Springer Science+Business Media, LLC, part of Springer Nature
About this entry
Cite this entry
Clementini, E. (2018). Dimension-Extended Topological Relationships. 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_132
Download citation
DOI: https://doi.org/10.1007/978-1-4614-8265-9_132
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-8266-6
Online ISBN: 978-1-4614-8265-9
eBook Packages: Computer ScienceReference Module Computer Science and Engineering