DE-9IM

About DE-9IM in brief

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 and spatial databases. The model is based on a 3×3 intersection matrix with the form: dim is the dimension of the intersection of the interior, boundary, and exterior of geometries a and b. The simpler models 4-Intersection and 9-intersection were proposed before DE-9IM for expressing spatial relations. They can be used to optimize computation when input conditions satisfy specific constraints. For output checking or pattern analysis, a matrix value can be checked by a “mask”: a desired output value with optional asterisk symbols as wildcards — that is, “*” indicating output positions that the designer does not care about. In the notation of topological space operators, the matrix elements can be expressed also as The dimension of empty sets are denoted as −1 or F.

The dimension of non-empty sets is denoted with the maximum number of dimensions of the intersections, specifically 0 for points, 1 for lines, 2 for areas. Since 1999 the string codes have a standard format. The DE- 9IM string code is ‘212212’, the compact representation of the compact representations of II-I, II-II and II-III-II. The English language contains about 10 schemes, such as “intersects”, “touches” and “equals”. When testing two geometry against a scheme, the result is a spatial predicate named by the scheme. The matrix, denoted by operators, can be named as The elements of the matrix can be serialized as shown below: Both matrix forms, with dimensional and boolean domains, are serialized in a single-line string pattern. Then, the domain of the model is {0,1,2,F}.