- DE-9IM
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In geometry, a dimensionally extended nine-intersection model (DE-9IM) is a topological model used to describe the spatial relation of two geometries in two-dimensions (R2). The representation was developed by Clementini and others[1][2] and is used as a basis for spatial predicate functions in geographic information systems (GIS) and spatial databases.
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. Empty sets (∅) are denoted as −1 or F (false). Non-empty sets (¬∅) or T (true) are denoted with the maximum number of dimensions of the intersection, specifically 0 for points, 1 for lines, 2 for areas. The domain of the model also uses * as a wildcard for any condition for dim. The matrix can be represented in a single-line string pattern.
The spatial predicate functions that can be derived from DE-9IM include:[3]
Name (synonym) Intersection matrix and code string Equals T*F**FFF*
Disjoint FF*FF****
Intersects or or or T********
*T*******
***T*****
****T****
Touches (meets) or or FT*******
F**T*****
F***T****
Crosses or or T*T******
T*****T**
0********
Within (inside) T*F**F***
Contains T*****FF*
Overlaps or T*T***T**
1*T***T**
Covers or or or T*****FF*
*T****FF*
***T**FF*
****T*FF*
CoveredBy or or or T*F**F***
*TF**F***
**FT*F***
**F*TF***
References
- ^ Clementini, Eliseo; Paolino Di Felice and Peter van Oosterom (1993). "A small set of formal topological relationships suitable for end-user interaction". In Abel, David; Ooi, Beng Chin. Advances in Spatial Databases: Third International Symposium, SSD '93 Singapore, June 23–25, 1993 Proceedings. Lecture Notes in Computer Science. 692/1993. Springer. pp. 277–295. doi:10.1007/3-540-56869-7_16.
- ^ Clementini, Eliseo; Sharma, Jayant; Egenhofer, Max J. (1994). "Modelling topological spatial relations: Strategies for query processing". Computers & Graphics 18 (6): 815–822. doi:10.1016/0097-8493(94)90007-8.
- ^ JTS: Class IntersectionMatrix, Vivid Solutions, Inc., http://www.vividsolutions.com/jts/javadoc/com/vividsolutions/jts/geom/IntersectionMatrix.html
External links
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