DE-9IM
The Dimensionally Extended nine-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. Since the spatial relations expressed by the model are topological they 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. For English speakers, there are about 10 schemes (relations) that have a name that reflects their semantics (e.g. "Intersects", "Touches", "Equals", and others.) When testing two geometries against a scheme, the result of this test is a spatial predicate named by the scheme.
The model was developed by Clementini and others based on the seminal works of Egenhofer and others. It has been used as a basis for standards of queries and assertions in geographic information systems (GIS) and spatial databases.
The DE-9IM model is based on a 3×3 intersection matrix with the form:
where is the maximum number of dimensions of the intersection (∩) of the interior (I), boundary (B), and exterior (E) of geometries a and b.
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