DE-9IM

The Dimensionally Extended 9-Intersection Model (DE-9IM) is a topological model and a standard used to describe the spatial relations of two regions (two geometries in two-dimensions, R2), in geometry, point-set topology, geospatial topology, and fields related to computer spatial analysis. The spatial relations expressed by the model are invariant to rotation, translation and scaling transformations.

The matrix provides an approach for classifying geometry relations. Roughly speaking, with a true/false matrix domain, there are 512 possible 2D topologic relations, that can be grouped into binary classification schemes. The English language contains about 10 schemes (relations), such as "intersects", "touches" and "equals". When testing two geometries against a scheme, the result is a spatial predicate named by the scheme.

The model was developed by Clementini and others[1][2] based on the seminal works of Egenhofer and others.[3][4] It has been used as a basis for standards of queries and assertions in geographic information systems (GIS) and spatial databases.

  1. ^ Clementini, Eliseo; Di Felice, Paolino; van Oosterom, Peter (1993). "A small set of formal topological relationships suitable for end-user interaction". In Abel, David; Ooi, Beng Chin (eds.). Advances in Spatial Databases: Third International Symposium, SSD '93 Singapore, June 23–25, 1993 Proceedings. Lecture Notes in Computer Science. Vol. 692/1993. Springer. pp. 277–295. doi:10.1007/3-540-56869-7_16. ISBN 978-3-540-56869-8.
  2. ^ Clementini, Eliseo; Sharma, Jayant; Egenhofer, Max J. (1994). "Modelling topological spatial relations: Strategies for query processing". Computers & Graphics. 18 (6): 815–822. doi:10.1016/0097-8493(94)90007-8.
  3. ^ Egenhofer, M.J.; Franzosa, R.D. (1991). "Point-set topological spatial relations". Int. J. GIS. 5 (2): 161–174. doi:10.1080/02693799108927841.
  4. ^ Egenhofer, M.J.; Herring, J.R. (1990). "A Mathematical Framework for the Definition of Topological Relationships" (PDF). Proceedings of the 4th International Symposium on Spatial Data Handling. Archived from the original (PDF) on 2010-06-14.