PostGIS

ST_Crosses
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ST_Crosses

7.11.1. Topological Relationships

Name

ST_Crosses — Tests if two geometries have some, but not all, interior points in common

Synopsis

+boolean +ST_Crosses(+`geometry `+g1, geometry g2`)`;

Description

Compares two geometry objects and returns true if their intersection "spatially crosses"; that is, the geometries have some, but not all interior points in common. The intersection of the interiors of the geometries must be non-empty and must have dimension less than the maximum dimension of the two input geometries, and the intersection of the two geometries must not equal either geometry. Otherwise, it returns false. The crosses relation is symmetric and irreflexive.

In mathematical terms: [.emphasis]#ST_Crosses(A, B) ⇔ (dim( Int(A) ⋂ Int(B) ) < max( dim( Int(A) ), dim( Int(B) ) )) ∧ (A ⋂ B ≠ A) ∧ (A ⋂ B ≠ B) #

Geometries cross if their DE-9IM Intersection Matrix matches:

T*T****** for Point/Line, Point/Area, and Line/Area situations
T*****T** for Line/Point, Area/Point, and Area/Line situations
0******** for Line/Line situations
the result is false for Point/Point and Area/Area situations

The OpenGIS Simple Features Specification defines this predicate only for Point/Line, Point/Area, Line/Line, and Line/Area situations. JTS / GEOS extends the definition to apply to Line/Point, Area/Point and Area/Line situations as well. This makes the relation symmetric.

This function automatically includes a bounding box comparison that makes use of any spatial indexes that are available on the geometries.

Important

Enhanced: 3.0.0 enabled support for GEOMETRYCOLLECTION

[.inlinemediaobject] check This method implements the OGC Simple Features Implementation Specification for SQL 1.1.

s2.1.13.3

check This method implements the SQL/MM specification.

SQL-MM 3: 5.1.29

Examples

The following situations all return true.

st_crosses01

MULTIPOINT / LINESTRING

st_crosses02

MULTIPOINT / POLYGON

st_crosses03

LINESTRING / POLYGON

st_crosses04

LINESTRING / LINESTRING

Consider a situation where a user has two tables: a table of roads and a table of highways.

CREATE TABLE roads (
  id serial NOT NULL,
  geom geometry,
  CONSTRAINT roads_pkey PRIMARY KEY (road_id)
);

CREATE TABLE highways (
  id serial NOT NULL,
  the_gem geometry,
  CONSTRAINT roads_pkey PRIMARY KEY (road_id)
);

To determine a list of roads that cross a highway, use a query similiar to:

SELECT roads.id
FROM roads, highways
WHERE ST_Crosses(roads.geom, highways.geom);

PostGIS

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