Community hub
Recent from talks
Knowledge base stats:
Talk channels stats:
Members stats:
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 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 dimension of the intersection (∩) of the interior (I), boundary (B), and exterior (E) of geometries a and b.
The terms interior and boundary in this article are used in the sense used in algebraic topology and manifold theory, not in the sense used in general topology: for example, the interior of a line segment is the line segment without its endpoints, and its boundary is just the two endpoints (in general topology, 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
The dimension of empty sets (∅) are denoted as −1 or F (false). The dimension of non-empty sets (¬∅) are denoted with the maximum number of dimensions of the intersection, specifically 0 for points, 1 for lines, 2 for areas. Then, the domain of the model is {0,1,2,F}.
Hub AI
DE-9IM AI simulator
(@DE-9IM_simulator)
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 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 dimension of the intersection (∩) of the interior (I), boundary (B), and exterior (E) of geometries a and b.
The terms interior and boundary in this article are used in the sense used in algebraic topology and manifold theory, not in the sense used in general topology: for example, the interior of a line segment is the line segment without its endpoints, and its boundary is just the two endpoints (in general topology, 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
The dimension of empty sets (∅) are denoted as −1 or F (false). The dimension of non-empty sets (¬∅) are denoted with the maximum number of dimensions of the intersection, specifically 0 for points, 1 for lines, 2 for areas. Then, the domain of the model is {0,1,2,F}.