Name
ST_Crosses — Tests if a Geometry A crosses a Geometry B, returns True if so.
Synopsis
boolean ST_Crosses(bytea GeomA, bytea GeomB);
Description
Returns true if Geometry A crosses a Geometry B.
The crosses predicate has the following equivalent definitions:
The geometries have some but not all interior points in common.
In mathematical terms:
Equation 9.0.
a.Crosses(b) «-» (dim(I(a) ∩ I(b)) < max(dim(I(a)), dim(I(b)))) Ʌ (a ∩ b ≠a ) Ʌ (a ∩ b ≠b)The DE-9IM Intersection Matrix for the two geometries is:
T*T****** (for P/L, P/A, and L/A situations)
T*****T** (for L/P, L/A, and A/L situations)
0******** (for L/L situations)
For any other combination of dimensions this predicate returns false.
The SFS defined this predicate only for P/L, P/A, L/L, and L/A situations. JTS extends the definition to apply to L/P, A/P and A/L situations as well. This makes the relation symmetric.
![[Note]](images/note.png) | |
The term P is used to refer to 0 dimensional geometries (Points and MultiPoints), L is used to refer to one-dimensional geometries (LineStrings and MultiLineStrings) and A is used to refer to two-dimensional geometries (Polygons and MultiPolygons). |
Coordinate Dimensions
| 2D | 3D | M |
|---|---|---|
 | | |
Spatial Standards Support
| OGC SFS for SQL. 1.1 (1999) | OGC SFS for SQL. 1.1.0 (2005) | OGC SFS for SQL. 1.2.0 (2006) | SQL-MM Part 3 |
|---|---|---|---|
| 2.1.1.2 , 2.1.13.3 | 7.2.19.1 | 7.2.8.1 | 5.1.29 |
Examples
--P/L
SELECT ST_Crosses(MPoint,Line) as CrossesPL,ST_Crosses(Line,MPoint) as CrossesLP,ST_Relate(MPoint,Line) from
(SELECT ST_GeomFromText('LINESTRING (10 15, 10 27, 20 20, 25 30)') as Line,
ST_GeomFromText('MULTIPOINT (10 30, 15 20, 10 20, 20 25, 17 23)') as MPoint) as foo;
crossespl | crosseslp | st_relate
-----------+-----------+-----------
t | t | 0F0FFF102
--P/A
SELECT ST_Crosses(MPoint,Poly) as CrossesPA,ST_Crosses(Poly,MPoint) as CrossesAP,ST_Relate(MPoint,Poly) from
(SELECT ST_GeomFromText('POLYGON ((10 30, 5 10, 30 20, 30 30, 20 40, 10 30))') as Poly,
ST_GeomFromText('MULTIPOINT (5 30, 15 20)') as MPoint) as foo;
crossespa | crossesap | st_relate
-----------+-----------+-----------
t | t | 0F0FFF212
--L/A
SELECT ST_Crosses(Line,Poly) as CrossesLA,ST_Crosses(Poly,Line) as CrossesAL,ST_Relate(Line,Poly) from
(SELECT ST_GeomFromText('POLYGON ((10 30, 5 10, 30 20, 30 30, 20 40, 10 30))') as Poly,
ST_GeomFromText('LINESTRING (0 20, 15 25, 20 30, 35 25, 35 25)') as Line) as foo;
crossesla | crossesal | st_relate
-----------+-----------+-----------
t | t | 101FF0212
--L/L
SELECT ST_Crosses(LA,LB) as CrossesLL,ST_Crosses(LB,LA) as CrossesLL2,ST_Relate(LA,LB)
from (SELECT ST_GeomFromText('LINESTRING (0 20, 15 25, 20 30, 35 25)') as LA,
ST_GeomFromText('LINESTRING (10 35, 5 25, 15 20, 15 10)') as LB) as foo;
crossesll | crossesll2 | st_relate
-----------+------------+-----------
t | t | 0F1FF0102
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