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right 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. == Matrix model == The DE-9IM model is based on a 3×3 intersection matrix with the form: where ''dim'' is the maximum number of dimensions of the intersection (∩) of the interior (I), boundary (B), and exterior (E) of geometries ''a'' and ''b''. Note that in this article the words ''interior'' and ''boundary'' are used in the sense used in algebraic topology and manifold theory, not in the sense used in general topology: e. g. by the interior of a line segment we mean the line segment without its endpoints and by its boundary, the two endpoints (in the general topology sense, the interior of a line segment in the plane is empty and the line segment is its own boundary). In the notation of topological space operators, the matrix elements can be expressed also as : ''I''(''a'')=''a''o ''B''(''a'')=∂''a'' ''E''(''a'')=''a''''e'' The dimension of empty sets (∅) are denoted as −1 or (false). The dimension of non-empty sets (¬∅) are denoted with the maximum number of dimensions of the intersection, specifically for points, for lines, for areas. Then, the domain of the model is . A simplified version of ''dim''(''x'') values are obtained mapping the values to (true), so using the boolean domain . The matrix, denoted with operators, can be expressed as Both matrix forms, with dimensional and boolean domains, can be serialized as "''DE-9IM string codes''", which represent them in a single-line string pattern. Since 1999 the ''string codes'' have a standard〔The "OpenGIS Simple Features Specification For SQL", (Revision 1.1 ), was released at May 5, 1999. It was the first international standard to establish the format conventions for ''DE-9IM string codes'', and the names of the "Named Spatial Relationship predicates based on the DE-9IM" (see section with this title).〕 format. For output checking or pattern analysis, a matrix value (or a string code) 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 (free values or "don't-care positions"). Then, the mask's domain is , or for the boolean form. The simpler models ''4-Intersection'' and ''9-Intersection'' were proposed before ''DE-9IM'' for expressing ''spatial relations''〔M. J. Egenhofer, J. Sharma, and D. Mark (1993) "(A Critical Comparison of the 4-Intersection and 9-Intersection Models for Spatial Relations: Formal Analysis )", In: (Auto-Carto XI ).〕 (and originated the terms ''4IM'' and ''9IM''). They can be used instead of the ''DE-9IM'' to optimize computation when input conditions satisfy specific constraints. 抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「DE-9IM」の詳細全文を読む スポンサード リンク
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