Dimension-Extended Topological Relationships
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.
Early descriptions of topological relationships (e.g., ) 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 . The first formal models were all based on point-set topology. In , the authors originally described the 4-intersection model (4IM) for classifying topological relationships between one-dimensional intervals. In , the authors adopted the same method for classifying topological...
- 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
- 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
- 7.Clementini E, Di Felice P. A comparison of methods for representing topological relationships. Inf Sci. 1995;3(3):149–78.Google Scholar