DE-9IM

Dimensionally Extended nine-Intersection Model
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, R 2 ), in geometry, point-set topology, geospatial topology, and fields related to computer spatial analysis.wikipedia
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Spatial relation

spatial relationsis withinspatial relationships
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, R 2 ), in geometry, point-set topology, geospatial topology, and fields related to computer spatial analysis.
The DE-9IM model expresses important space relations which are invariant to rotation, translation and scaling transformations.

Spatial database

geodatabasespatial indexspatial
It has been used as a basis for standards of queries and assertions in geographic information systems (GIS) and spatial databases.

Spatial analysis

spatial statisticsspatial autocorrelationgeospatial analysis
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, R 2 ), in geometry, point-set topology, geospatial topology, and fields related to computer spatial analysis.

PostGIS

Most spatial databases, such as PostGIS, implements the DE-9IM model by the standard functions:,,, etc. The function outputs the standard OGC's DE-9IM string code.

Simple Features

Simple Feature AccessSFSISO 19125
The Simple Feature Access (ISO 19125) standard, in the chapter 7.2.8, "SQL routines on type Geometry", recommends as supported routines the SQL/MM Spatial (ISO 13249-3 Part 3: Spatial) ST_Dimension, ST_GeometryType, ST_IsEmpty, ST_IsSimple, ST_Boundary for all Geometry Types.
The specification defines DE-9IM spatial predicates and several spatial operators that can be used to generate new geometries from existing geometries.

Topology

topologicaltopologicallytopologist
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, R 2 ), in geometry, point-set topology, geospatial topology, and fields related to computer spatial analysis.

Interpretation (logic)

interpretationintended interpretationinterpretations
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, R 2 ), in geometry, point-set topology, geospatial topology, and fields related to computer spatial analysis.

Specification (technical standard)

specificationspecificationstechnical specifications
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, R 2 ), in geometry, point-set topology, geospatial topology, and fields related to computer spatial analysis.

2D geometric model

2D2-D2D geometric
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, R 2 ), in geometry, point-set topology, geospatial topology, and fields related to computer spatial analysis.

Geometry

geometricgeometricalgeometries
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, R 2 ), in geometry, point-set topology, geospatial topology, and fields related to computer spatial analysis.

General topology

point-set topologypoint set topologytopology
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, R 2 ), in geometry, point-set topology, geospatial topology, and fields related to computer spatial analysis.

Geospatial topology

topologicalconnectiveTopology
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, R 2 ), in geometry, point-set topology, geospatial topology, and fields related to computer spatial analysis.

Rotation (mathematics)

rotationrotationsrotate
The spatial relations expressed by the model are invariant to rotation, translation and scaling transformations.

Translation (geometry)

translationtranslationstranslational
The spatial relations expressed by the model are invariant to rotation, translation and scaling transformations.

Scaling (geometry)

scalingscaleuniform scaling
The spatial relations expressed by the model are invariant to rotation, translation and scaling transformations.

Information retrieval

queryretrievalqueries
It has been used as a basis for standards of queries and assertions in geographic information systems (GIS) and spatial databases.

First-order logic

predicate logicfirst-orderpredicate calculus
It has been used as a basis for standards of queries and assertions in geographic information systems (GIS) and spatial databases.

Geographic information system

GISgeographic information systemsgeographical information system
It has been used as a basis for standards of queries and assertions in geographic information systems (GIS) and spatial databases.

Matrix (mathematics)

matrixmatricesmatrix theory
The DE-9IM model is based on a 3×3 intersection matrix with the form:

Dimension

dimensionsdimensionalone-dimensional
where is the dimension of the intersection of the interior (I), boundary (B), and exterior (E) of geometries a and b.

Intersection (set theory)

intersectionintersectionsset intersection
where is the dimension of the intersection of the interior (I), boundary (B), and exterior (E) of geometries a and b.

Manifold

manifoldsboundarymanifold with boundary
where is the dimension of the intersection of the interior (I), boundary (B), and exterior (E) of geometries a and b.