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*** |