These functions determine spatial relationships between geometries.
Spatial Relationships
Topological Relationships
ST_3DIntersects
Returns TRUE if the Geometries "spatially
intersect" in 3D - only for points, linestrings, polygons, polyhedral surface (area).
boolean ST_3DIntersects
geometry
geomA
geometry
geomB
Description
Overlaps, Touches, Within all imply spatial intersection. If any of the aforementioned
returns true, then the geometries also spatially intersect.
Disjoint implies false for spatial intersection.
Changed: 3.0.0 SFCGAL backend removed, GEOS backend supports TINs.
Availability: 2.0.0
This function call will automatically include a bounding box
comparison that will make use of any indexes that are available on the
geometries.
&Z_support;
&P_support;
&T_support;
&sfcgal_enhanced;
&sqlmm_compliant; SQL-MM 3: ?
Geometry Examples
SELECT ST_3DIntersects(pt, line), ST_Intersects(pt, line)
FROM (SELECT 'POINT(0 0 2)'::geometry As pt, 'LINESTRING (0 0 1, 0 2 3)'::geometry As line) As foo;
st_3dintersects | st_intersects
-----------------+---------------
f | t
(1 row)
TIN Examples
SELECT ST_3DIntersects('TIN(((0 0 0,1 0 0,0 1 0,0 0 0)))'::geometry, 'POINT(.1 .1 0)'::geometry);
st_3dintersects
-----------------
t
See Also
ST_Contains
Returns true if and only if no points of B lie in the exterior of A, and at least one point of the interior of B lies in the interior of A.
boolean ST_Contains
geometry
geomA
geometry
geomB
Description
Geometry A contains Geometry B if and only if no points of B lie in the exterior of A, and at least one point of the interior of B lies in the interior of A.
An important subtlety of this definition is that A does not contain its boundary, but A does contain itself. Contrast that to where geometry
A does not Contain Properly itself.
Returns TRUE if geometry B is completely inside geometry A. For this function to make
sense, the source geometries must both be of the same coordinate projection,
having the same SRID. ST_Contains is the inverse of ST_Within. So ST_Contains(A,B) implies ST_Within(B,A) except in the case of
invalid geometries where the result is always false regardless or not defined.
Performed by the GEOS module
Enhanced: 2.3.0 Enhancement to PIP short-circuit extended to support MultiPoints with few points. Prior versions only supported point in polygon.
Enhanced: 3.0.0 enabled support for GEOMETRYCOLLECTION
Do not use this function with invalid geometries. You will get unexpected results.
This function call will automatically include a bounding box
comparison that will make use of any indexes that are available on
the geometries. To avoid index use, use the function
_ST_Contains.
NOTE: this is the "allowable" version that returns a
boolean, not an integer.
&sfs_compliant; s2.1.1.2 // s2.1.13.3
- same as within(geometry B, geometry A)
&sqlmm_compliant; SQL-MM 3: 5.1.31
There are certain subtleties to ST_Contains and ST_Within that are not intuitively obvious.
For details check out Subtleties of OGC Covers, Contains, Within
Examples
The ST_Contains predicate returns TRUE in all the following illustrations.
LINESTRING / MULTIPOINT
POLYGON / POINT

POLYGON / LINESTRING
POLYGON / POLYGON

The ST_Contains predicate returns FALSE in all the following illustrations.
POLYGON / MULTIPOINT
POLYGON / LINESTRING

-- A circle within a circle
SELECT ST_Contains(smallc, bigc) As smallcontainsbig,
ST_Contains(bigc,smallc) As bigcontainssmall,
ST_Contains(bigc, ST_Union(smallc, bigc)) as bigcontainsunion,
ST_Equals(bigc, ST_Union(smallc, bigc)) as bigisunion,
ST_Covers(bigc, ST_ExteriorRing(bigc)) As bigcoversexterior,
ST_Contains(bigc, ST_ExteriorRing(bigc)) As bigcontainsexterior
FROM (SELECT ST_Buffer(ST_GeomFromText('POINT(1 2)'), 10) As smallc,
ST_Buffer(ST_GeomFromText('POINT(1 2)'), 20) As bigc) As foo;
-- Result
smallcontainsbig | bigcontainssmall | bigcontainsunion | bigisunion | bigcoversexterior | bigcontainsexterior
------------------+------------------+------------------+------------+-------------------+---------------------
f | t | t | t | t | f
-- Example demonstrating difference between contains and contains properly
SELECT ST_GeometryType(geomA) As geomtype, ST_Contains(geomA,geomA) AS acontainsa, ST_ContainsProperly(geomA, geomA) AS acontainspropa,
ST_Contains(geomA, ST_Boundary(geomA)) As acontainsba, ST_ContainsProperly(geomA, ST_Boundary(geomA)) As acontainspropba
FROM (VALUES ( ST_Buffer(ST_Point(1,1), 5,1) ),
( ST_MakeLine(ST_Point(1,1), ST_Point(-1,-1) ) ),
( ST_Point(1,1) )
) As foo(geomA);
geomtype | acontainsa | acontainspropa | acontainsba | acontainspropba
--------------+------------+----------------+-------------+-----------------
ST_Polygon | t | f | f | f
ST_LineString | t | f | f | f
ST_Point | t | t | f | f
See Also
, , , , ,
ST_ContainsProperly
Returns true if B intersects the interior of A but not the boundary (or exterior). A does not contain properly itself, but does contain itself.
boolean ST_ContainsProperly
geometry
geomA
geometry
geomB
Description
Returns true if B intersects the interior of A but not the boundary (or exterior).
A does not contain properly itself, but does contain itself.
Every point of the other geometry is a point of this geometry's interior. The DE-9IM Intersection Matrix for the two geometries matches
[T**FF*FF*] used in
From JTS docs slightly reworded: The advantage to using this predicate over and is that it can be computed
efficiently, with no need to compute topology at individual points.
An example use case for this predicate is computing the intersections of a set of geometries with a large polygonal geometry. Since intersection is a fairly slow operation, it can be more efficient to use containsProperly to filter out test geometries which lie
wholly inside the area. In these cases the intersection is known a priori to be exactly the original test geometry.
Performed by the GEOS module.
Availability: 1.4.0
Enhanced: 3.0.0 enabled support for GEOMETRYCOLLECTION
Do not use this function with invalid geometries. You will get unexpected results.
This function call will automatically include a bounding box
comparison that will make use of any indexes that are available on
the geometries. To avoid index use, use the function
_ST_ContainsProperly.
Examples
--a circle within a circle
SELECT ST_ContainsProperly(smallc, bigc) As smallcontainspropbig,
ST_ContainsProperly(bigc,smallc) As bigcontainspropsmall,
ST_ContainsProperly(bigc, ST_Union(smallc, bigc)) as bigcontainspropunion,
ST_Equals(bigc, ST_Union(smallc, bigc)) as bigisunion,
ST_Covers(bigc, ST_ExteriorRing(bigc)) As bigcoversexterior,
ST_ContainsProperly(bigc, ST_ExteriorRing(bigc)) As bigcontainsexterior
FROM (SELECT ST_Buffer(ST_GeomFromText('POINT(1 2)'), 10) As smallc,
ST_Buffer(ST_GeomFromText('POINT(1 2)'), 20) As bigc) As foo;
--Result
smallcontainspropbig | bigcontainspropsmall | bigcontainspropunion | bigisunion | bigcoversexterior | bigcontainsexterior
------------------+------------------+------------------+------------+-------------------+---------------------
f | t | f | t | t | f
--example demonstrating difference between contains and contains properly
SELECT ST_GeometryType(geomA) As geomtype, ST_Contains(geomA,geomA) AS acontainsa, ST_ContainsProperly(geomA, geomA) AS acontainspropa,
ST_Contains(geomA, ST_Boundary(geomA)) As acontainsba, ST_ContainsProperly(geomA, ST_Boundary(geomA)) As acontainspropba
FROM (VALUES ( ST_Buffer(ST_Point(1,1), 5,1) ),
( ST_MakeLine(ST_Point(1,1), ST_Point(-1,-1) ) ),
( ST_Point(1,1) )
) As foo(geomA);
geomtype | acontainsa | acontainspropa | acontainsba | acontainspropba
--------------+------------+----------------+-------------+-----------------
ST_Polygon | t | f | f | f
ST_LineString | t | f | f | f
ST_Point | t | t | f | f
See Also
, , , , , , ,
ST_Covers
Returns 1 (TRUE) if no point in Geometry B is outside
Geometry A
boolean ST_Covers
geometry
geomA
geometry
geomB
boolean ST_Covers
geography
geogpolyA
geography
geogpointB
Description
Returns 1 (TRUE) if no point in Geometry/Geography B is outside
Geometry/Geography A
Enhanced: 3.0.0 enabled support for GEOMETRYCOLLECTION
Do not use this function with invalid geometries. You will get unexpected results.
This function call will automatically include a bounding box
comparison that will make use of any indexes that are available on
the geometries. To avoid index use, use the function
_ST_Covers.
Performed by the GEOS module
Enhanced: 2.4.0 Support for polygon in polygon and line in polygon added for geography type
Enhanced: 2.3.0 Enhancement to PIP short-circuit for geometry extended to support MultiPoints with few points. Prior versions only supported point in polygon.
Availability: 1.5 - support for geography was introduced.
Availability: 1.2.2
NOTE: this is the "allowable" version that returns a
boolean, not an integer.
Not an OGC standard, but Oracle has it too.
There are certain subtleties to ST_Contains and ST_Within that are not intuitively obvious.
For details check out Subtleties of OGC Covers, Contains, Within
Examples
Geometry example
--a circle covering a circle
SELECT ST_Covers(smallc,smallc) As smallinsmall,
ST_Covers(smallc, bigc) As smallcoversbig,
ST_Covers(bigc, ST_ExteriorRing(bigc)) As bigcoversexterior,
ST_Contains(bigc, ST_ExteriorRing(bigc)) As bigcontainsexterior
FROM (SELECT ST_Buffer(ST_GeomFromText('POINT(1 2)'), 10) As smallc,
ST_Buffer(ST_GeomFromText('POINT(1 2)'), 20) As bigc) As foo;
--Result
smallinsmall | smallcoversbig | bigcoversexterior | bigcontainsexterior
--------------+----------------+-------------------+---------------------
t | f | t | f
(1 row)
Geeography Example
-- a point with a 300 meter buffer compared to a point, a point and its 10 meter buffer
SELECT ST_Covers(geog_poly, geog_pt) As poly_covers_pt,
ST_Covers(ST_Buffer(geog_pt,10), geog_pt) As buff_10m_covers_cent
FROM (SELECT ST_Buffer(ST_GeogFromText('SRID=4326;POINT(-99.327 31.4821)'), 300) As geog_poly,
ST_GeogFromText('SRID=4326;POINT(-99.33 31.483)') As geog_pt ) As foo;
poly_covers_pt | buff_10m_covers_cent
----------------+------------------
f | t
See Also
, ,
ST_CoveredBy
Returns 1 (TRUE) if no point in Geometry/Geography A is outside
Geometry/Geography B
boolean ST_CoveredBy
geometry
geomA
geometry
geomB
boolean ST_CoveredBy
geography
geogA
geography
geogB
Description
Returns 1 (TRUE) if no point in Geometry/Geography A is outside
Geometry/Geography B
Enhanced: 3.0.0 enabled support for GEOMETRYCOLLECTION
Do not use this function with invalid geometries. You will get unexpected results.
Performed by the GEOS module
Availability: 1.2.2
This function call will automatically include a bounding box
comparison that will make use of any indexes that are available on
the geometries. To avoid index use, use the function
_ST_CoveredBy.
NOTE: this is the "allowable" version that returns a
boolean, not an integer.
Not an OGC standard, but Oracle has it too.
There are certain subtleties to ST_Contains and ST_Within that are not intuitively obvious.
For details check out Subtleties of OGC Covers, Contains, Within
Examples
--a circle coveredby a circle
SELECT ST_CoveredBy(smallc,smallc) As smallinsmall,
ST_CoveredBy(smallc, bigc) As smallcoveredbybig,
ST_CoveredBy(ST_ExteriorRing(bigc), bigc) As exteriorcoveredbybig,
ST_Within(ST_ExteriorRing(bigc),bigc) As exeriorwithinbig
FROM (SELECT ST_Buffer(ST_GeomFromText('POINT(1 2)'), 10) As smallc,
ST_Buffer(ST_GeomFromText('POINT(1 2)'), 20) As bigc) As foo;
--Result
smallinsmall | smallcoveredbybig | exteriorcoveredbybig | exeriorwithinbig
--------------+-------------------+----------------------+------------------
t | t | t | f
(1 row)
See Also
, , ,
ST_Crosses
Returns TRUE if the supplied geometries have some, but not all,
interior points in common.
boolean ST_Crosses
geometry g1
geometry g2
Description
ST_Crosses takes two geometry objects and
returns TRUE if their intersection "spatially cross", that is, the
geometries have some, but not all interior points in common. The
intersection of the interiors of the geometries must not be the empty
set and must have a dimensionality less than the maximum dimension
of the two input geometries. Additionally, the intersection of the two
geometries must not equal either of the source geometries. Otherwise, it
returns FALSE.
In mathematical terms, this is expressed as:
TODO: Insert appropriate MathML markup here or use a gif.
Simple HTML markup does not work well in both IE and Firefox.
The DE-9IM Intersection Matrix for the two geometries is:
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)
For any other combination of dimensions this predicate returns
false.
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.
Enhanced: 3.0.0 enabled support for GEOMETRYCOLLECTION
This function call will automatically include a bounding box
comparison that will make use of any indexes that are available on the
geometries.
&sfs_compliant; s2.1.13.3
&sqlmm_compliant; SQL-MM 3: 5.1.29
Examples
The following illustrations all return TRUE.
MULTIPOINT / LINESTRING
MULTIPOINT / POLYGON

LINESTRING / POLYGON
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,
the_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.the_geom, highways.the_geom);
ST_LineCrossingDirection
Given 2 linestrings, returns a number between -3 and 3 denoting what kind of crossing behavior. 0 is no crossing.
integer ST_LineCrossingDirection
geometry linestringA
geometry linestringB
Description
Given 2 linestrings, returns a number between -3 and 3 denoting what kind of crossing behavior. 0 is no crossing. This is only supported for LINESTRING
Definition of integer constants is as follows:
0: LINE NO CROSS
-1: LINE CROSS LEFT
1: LINE CROSS RIGHT
-2: LINE MULTICROSS END LEFT
2: LINE MULTICROSS END RIGHT
-3: LINE MULTICROSS END SAME FIRST LEFT
3: LINE MULTICROSS END SAME FIRST RIGHT
Availability: 1.4
Examples
Line 1 (green), Line 2 ball is start point,
triangle are end points. Query below.
SELECT ST_LineCrossingDirection(foo.line1, foo.line2) As l1_cross_l2 ,
ST_LineCrossingDirection(foo.line2, foo.line1) As l2_cross_l1
FROM (
SELECT
ST_GeomFromText('LINESTRING(25 169,89 114,40 70,86 43)') As line1,
ST_GeomFromText('LINESTRING(171 154,20 140,71 74,161 53)') As line2
) As foo;
l1_cross_l2 | l2_cross_l1
-------------+-------------
3 | -3
Line 1 (green), Line 2 (blue) ball is start point,
triangle are end points. Query below.
SELECT ST_LineCrossingDirection(foo.line1, foo.line2) As l1_cross_l2 ,
ST_LineCrossingDirection(foo.line2, foo.line1) As l2_cross_l1
FROM (
SELECT
ST_GeomFromText('LINESTRING(25 169,89 114,40 70,86 43)') As line1,
ST_GeomFromText('LINESTRING (171 154, 20 140, 71 74, 2.99 90.16)') As line2
) As foo;
l1_cross_l2 | l2_cross_l1
-------------+-------------
2 | -2

Line 1 (green), Line 2 (blue) ball is start point,
triangle are end points. Query below.
SELECT
ST_LineCrossingDirection(foo.line1, foo.line2) As l1_cross_l2 ,
ST_LineCrossingDirection(foo.line2, foo.line1) As l2_cross_l1
FROM (
SELECT
ST_GeomFromText('LINESTRING(25 169,89 114,40 70,86 43)') As line1,
ST_GeomFromText('LINESTRING (20 140, 71 74, 161 53)') As line2
) As foo;
l1_cross_l2 | l2_cross_l1
-------------+-------------
-1 | 1
Line 1 (green), Line 2 (blue) ball is start point,
triangle are end points. Query below.
SELECT ST_LineCrossingDirection(foo.line1, foo.line2) As l1_cross_l2 ,
ST_LineCrossingDirection(foo.line2, foo.line1) As l2_cross_l1
FROM (SELECT
ST_GeomFromText('LINESTRING(25 169,89 114,40 70,86 43)') As line1,
ST_GeomFromText('LINESTRING(2.99 90.16,71 74,20 140,171 154)') As line2
) As foo;
l1_cross_l2 | l2_cross_l1
-------------+-------------
-2 | 2

SELECT s1.gid, s2.gid, ST_LineCrossingDirection(s1.the_geom, s2.the_geom)
FROM streets s1 CROSS JOIN streets s2 ON (s1.gid != s2.gid AND s1.the_geom && s2.the_geom )
WHERE ST_CrossingDirection(s1.the_geom, s2.the_geom) > 0;
See Also
ST_Disjoint
Returns TRUE if the Geometries do not "spatially
intersect" - if they do not share any space together.
boolean ST_Disjoint
geometry
A
geometry
B
Description
Overlaps, Touches, Within all imply geometries are not spatially disjoint. If any of the aforementioned
returns true, then the geometries are not spatially disjoint.
Disjoint implies false for spatial intersection.
Enhanced: 3.0.0 enabled support for GEOMETRYCOLLECTION
Performed by the GEOS module
This function call does not use indexes
NOTE: this is the "allowable" version that returns a
boolean, not an integer.
&sfs_compliant; s2.1.1.2 //s2.1.13.3
- a.Relate(b, 'FF*FF****')
&sqlmm_compliant; SQL-MM 3: 5.1.26
Examples
SELECT ST_Disjoint('POINT(0 0)'::geometry, 'LINESTRING ( 2 0, 0 2 )'::geometry);
st_disjoint
---------------
t
(1 row)
SELECT ST_Disjoint('POINT(0 0)'::geometry, 'LINESTRING ( 0 0, 0 2 )'::geometry);
st_disjoint
---------------
f
(1 row)
See Also
ST_Equals
Returns true if the given geometries represent the same geometry. Directionality
is ignored.
boolean ST_Equals
geometry A
geometry B
Description
Returns TRUE if the given Geometries are "spatially
equal". Use this for a 'better' answer than '='.
Note by spatially equal we mean ST_Within(A,B) = true and ST_Within(B,A) = true and
also mean ordering of points can be different but
represent the same geometry structure. To verify the order of points is consistent, use
ST_OrderingEquals (it must be noted ST_OrderingEquals is a little more stringent than simply verifying order of
points are the same).
This function will return false if either geometry is invalid except in the case where they are binary equal.
Enhanced: 3.0.0 enabled support for GEOMETRYCOLLECTION
&sfs_compliant; s2.1.1.2
&sqlmm_compliant; SQL-MM 3: 5.1.24
Changed: 2.2.0 Returns true even for invalid geometries if they are binary equal
Examples
SELECT ST_Equals(ST_GeomFromText('LINESTRING(0 0, 10 10)'),
ST_GeomFromText('LINESTRING(0 0, 5 5, 10 10)'));
st_equals
-----------
t
(1 row)
SELECT ST_Equals(ST_Reverse(ST_GeomFromText('LINESTRING(0 0, 10 10)')),
ST_GeomFromText('LINESTRING(0 0, 5 5, 10 10)'));
st_equals
-----------
t
(1 row)
See Also
, , ,
ST_Intersects
Returns TRUE if the Geometries/Geography "spatially
intersect in 2D" - (share any portion of space) and FALSE if they don't (they are Disjoint).
For geography tolerance is 0.00001 meters (so any points that close are considered to intersect)
boolean ST_Intersects
geometry
geomA
geometry
geomB
boolean ST_Intersects
geography
geogA
geography
geogB
Description
If a geometry or geography shares any portion of space then they intersect.
For geography -- tolerance is 0.00001 meters (so any points that are close are considered to intersect)
ST_Overlaps, ST_Touches, ST_Within all imply spatial intersection.
If any of the aforementioned
returns true, then the geometries also spatially intersect.
Disjoint implies false for spatial intersection.
Changed: 3.0.0 SFCGAL version removed.
Enhanced: 2.5.0 Supports GEOMETRYCOLLECTION.
Enhanced: 2.3.0 Enhancement to PIP short-circuit extended to support MultiPoints with few points. Prior versions only supported point in polygon.
Performed by the GEOS module (for geometry), geography is native
Availability: 1.5 support for geography was introduced.
This function call will automatically include a bounding box
comparison that will make use of any indexes that are available on the
geometries.
For geography, this function has a distance tolerance of about 0.00001 meters and uses the sphere rather
than spheroid calculation.
NOTE: this is the "allowable" version that returns a
boolean, not an integer.
&sfs_compliant; s2.1.1.2 //s2.1.13.3
- ST_Intersects(g1, g2 ) --> Not (ST_Disjoint(g1, g2 ))
&sqlmm_compliant; SQL-MM 3: 5.1.27
&sfcgal_enhanced;
Geometry Examples
SELECT ST_Intersects('POINT(0 0)'::geometry, 'LINESTRING ( 2 0, 0 2 )'::geometry);
st_intersects
---------------
f
(1 row)
SELECT ST_Intersects('POINT(0 0)'::geometry, 'LINESTRING ( 0 0, 0 2 )'::geometry);
st_intersects
---------------
t
(1 row)
Geography Examples
SELECT ST_Intersects(
'SRID=4326;LINESTRING(-43.23456 72.4567,-43.23456 72.4568)'::geography,
'SRID=4326;POINT(-43.23456 72.4567772)'::geography
);
st_intersects
---------------
t
See Also
,
ST_OrderingEquals
Returns true if the given geometries represent the same geometry
and points are in the same directional order.
boolean ST_OrderingEquals
geometry A
geometry B
Description
ST_OrderingEquals compares two geometries and returns t (TRUE) if the
geometries are equal and the coordinates are in the same order;
otherwise it returns f (FALSE).
This function is implemented as per the ArcSDE SQL
specification rather than SQL-MM.
http://edndoc.esri.com/arcsde/9.1/sql_api/sqlapi3.htm#ST_OrderingEquals
&sqlmm_compliant; SQL-MM 3: 5.1.43
Examples
SELECT ST_OrderingEquals(ST_GeomFromText('LINESTRING(0 0, 10 10)'),
ST_GeomFromText('LINESTRING(0 0, 5 5, 10 10)'));
st_orderingequals
-----------
f
(1 row)
SELECT ST_OrderingEquals(ST_GeomFromText('LINESTRING(0 0, 10 10)'),
ST_GeomFromText('LINESTRING(0 0, 0 0, 10 10)'));
st_orderingequals
-----------
t
(1 row)
SELECT ST_OrderingEquals(ST_Reverse(ST_GeomFromText('LINESTRING(0 0, 10 10)')),
ST_GeomFromText('LINESTRING(0 0, 0 0, 10 10)'));
st_orderingequals
-----------
f
(1 row)
See Also
,
ST_Overlaps
Returns TRUE if the Geometries share space, are of the same dimension, but are not completely contained by each other.
boolean ST_Overlaps
geometry A
geometry B
Description
Returns TRUE if the Geometries "spatially
overlap". By that we mean they intersect, but one does not completely contain another.
Performed by the GEOS module
Enhanced: 3.0.0 enabled support for GEOMETRYCOLLECTION
This function call will automatically include a bounding box
comparison that will make use of any indexes that are available on
the geometries. To avoid index use, use the function
_ST_Overlaps.
NOTE: this is the "allowable" version that returns a
boolean, not an integer.
&sfs_compliant; s2.1.1.2 // s2.1.13.3
&sqlmm_compliant; SQL-MM 3: 5.1.32
Examples
The following illustrations all return TRUE.
MULTIPOINT / MULTIPOINT
LINESTRING / LINESTRING
POLYGON / POLYGON

--a point on a line is contained by the line and is of a lower dimension, and therefore does not overlap the line
nor crosses
SELECT ST_Overlaps(a,b) As a_overlap_b,
ST_Crosses(a,b) As a_crosses_b,
ST_Intersects(a, b) As a_intersects_b, ST_Contains(b,a) As b_contains_a
FROM (SELECT ST_GeomFromText('POINT(1 0.5)') As a, ST_GeomFromText('LINESTRING(1 0, 1 1, 3 5)') As b)
As foo
a_overlap_b | a_crosses_b | a_intersects_b | b_contains_a
------------+-------------+----------------+--------------
f | f | t | t
--a line that is partly contained by circle, but not fully is defined as intersecting and crossing,
-- but since of different dimension it does not overlap
SELECT ST_Overlaps(a,b) As a_overlap_b, ST_Crosses(a,b) As a_crosses_b,
ST_Intersects(a, b) As a_intersects_b,
ST_Contains(a,b) As a_contains_b
FROM (SELECT ST_Buffer(ST_GeomFromText('POINT(1 0.5)'), 3) As a, ST_GeomFromText('LINESTRING(1 0, 1 1, 3 5)') As b)
As foo;
a_overlap_b | a_crosses_b | a_intersects_b | a_contains_b
-------------+-------------+----------------+--------------
f | t | t | f
-- a 2-dimensional bent hot dog (aka buffered line string) that intersects a circle,
-- but is not fully contained by the circle is defined as overlapping since they are of the same dimension,
-- but it does not cross, because the intersection of the 2 is of the same dimension
-- as the maximum dimension of the 2
SELECT ST_Overlaps(a,b) As a_overlap_b, ST_Crosses(a,b) As a_crosses_b, ST_Intersects(a, b) As a_intersects_b,
ST_Contains(b,a) As b_contains_a,
ST_Dimension(a) As dim_a, ST_Dimension(b) as dim_b, ST_Dimension(ST_Intersection(a,b)) As dima_intersection_b
FROM (SELECT ST_Buffer(ST_GeomFromText('POINT(1 0.5)'), 3) As a,
ST_Buffer(ST_GeomFromText('LINESTRING(1 0, 1 1, 3 5)'),0.5) As b)
As foo;
a_overlap_b | a_crosses_b | a_intersects_b | b_contains_a | dim_a | dim_b | dima_intersection_b
-------------+-------------+----------------+--------------+-------+-------+---------------------
t | f | t | f | 2 | 2 | 2
See Also
, , ,
ST_PointInsideCircle
Is the point geometry inside the circle defined by center_x, center_y, radius
boolean ST_PointInsideCircle
geometry a_point
float center_x
float center_y
float radius
Description
The syntax for this functions is
ST_PointInsideCircle(<geometry>,<circle_center_x>,<circle_center_y>,<radius>).
Returns the true if the geometry is a point and is inside the
circle. Returns false otherwise.
This only works for points as the name suggests
Availability: 1.2
Changed: 2.2.0 In prior versions this used to be called ST_Point_Inside_Circle
Examples
SELECT ST_PointInsideCircle(ST_Point(1,2), 0.5, 2, 3);
st_pointinsidecircle
------------------------
t
See Also
ST_Relate
Returns true if this Geometry is spatially related to
anotherGeometry, by testing for intersections between the
Interior, Boundary and Exterior of the two geometries as specified
by the values in the intersectionMatrixPattern. If no intersectionMatrixPattern
is passed in, then returns the maximum intersectionMatrixPattern that relates the 2 geometries.
boolean ST_Relate
geometry geomA
geometry geomB
text intersectionMatrixPattern
text ST_Relate
geometry geomA
geometry geomB
text ST_Relate
geometry geomA
geometry geomB
integer BoundaryNodeRule
Description
Version 1: Takes geomA, geomB, intersectionMatrix and Returns 1 (TRUE) if this Geometry is spatially related to
anotherGeometry, by testing for intersections between the
Interior, Boundary and Exterior of the two geometries as specified
by the values in the DE-9IM matrix pattern.
This is especially useful for testing compound checks of intersection, crosses, etc in one step.
This is the "allowable" version that returns a
boolean, not an integer. This is defined in OGC spec
This DOES NOT automagically include an index call. The reason for that
is some relationships are anti e.g. Disjoint. If you are
using a relationship pattern that requires intersection, then include the &&
index call.
Version 2: Takes geomA and geomB and returns the
Version 3: same as version 2, but allows to specify a boundary node rule (1:OGC/MOD2, 2:Endpoint, 3:MultivalentEndpoint, 4:MonovalentEndpoint)
Enhanced: 3.0.0 enabled support for GEOMETRYCOLLECTION
not in OGC spec, but implied. see s2.1.13.2
&sfs_compliant; s2.1.1.2 // s2.1.13.3
&sqlmm_compliant; SQL-MM 3: 5.1.25
Performed by the GEOS module
Enhanced: 2.0.0 - added support for specifying boundary node rule.
Examples
--Find all compounds that intersect and not touch a poly (interior intersects)
SELECT l.* , b.name As poly_name
FROM polys As b
INNER JOIN compounds As l
ON (p.the_geom && b.the_geom
AND ST_Relate(l.the_geom, b.the_geom,'T********'));
SELECT ST_Relate(ST_GeometryFromText('POINT(1 2)'), ST_Buffer(ST_GeometryFromText('POINT(1 2)'),2));
st_relate
-----------
0FFFFF212
SELECT ST_Relate(ST_GeometryFromText('LINESTRING(1 2, 3 4)'), ST_GeometryFromText('LINESTRING(5 6, 7 8)'));
st_relate
-----------
FF1FF0102
SELECT ST_Relate(ST_GeometryFromText('POINT(1 2)'), ST_Buffer(ST_GeometryFromText('POINT(1 2)'),2), '0FFFFF212');
st_relate
-----------
t
SELECT ST_Relate(ST_GeometryFromText('POINT(1 2)'), ST_Buffer(ST_GeometryFromText('POINT(1 2)'),2), '*FF*FF212');
st_relate
-----------
t
See Also
, , , ,
ST_RelateMatch
Returns true if intersectionMattrixPattern1 implies intersectionMatrixPattern2
boolean ST_RelateMatch
text intersectionMatrix
text intersectionMatrixPattern
Description
Takes intersectionMatrix and intersectionMatrixPattern and Returns true if the intersectionMatrix satisfies
the intersectionMatrixPattern. For more information refer to .
Performed by the GEOS module
Availability: 2.0.0
Examples
SELECT ST_RelateMatch('101202FFF', 'TTTTTTFFF') ;
-- result --
t
--example of common intersection matrix patterns and example matrices
-- comparing relationships of involving one invalid geometry and ( a line and polygon that intersect at interior and boundary)
SELECT mat.name, pat.name, ST_RelateMatch(mat.val, pat.val) As satisfied
FROM
( VALUES ('Equality', 'T1FF1FFF1'),
('Overlaps', 'T*T***T**'),
('Within', 'T*F**F***'),
('Disjoint', 'FF*FF****') As pat(name,val)
CROSS JOIN
( VALUES ('Self intersections (invalid)', '111111111'),
('IE2_BI1_BB0_BE1_EI1_EE2', 'FF2101102'),
('IB1_IE1_BB0_BE0_EI2_EI1_EE2', 'F11F00212')
) As mat(name,val);
See Also
,
ST_Touches
Returns TRUE if the geometries have at least one point in common,
but their interiors do not intersect.
boolean ST_Touches
geometry
g1
geometry
g2
Description
Returns TRUE if the only points in common between
g1 and g2 lie in the union of the
boundaries of g1 and g2.
The ST_Touches relation applies
to all Area/Area, Line/Line, Line/Area, Point/Area and Point/Line pairs of relationships,
but not to the Point/Point pair.
In mathematical terms, this predicate is expressed as:
The allowable DE-9IM Intersection Matrices for the two geometries are:
FT*******
F**T*****
F***T****
Enhanced: 3.0.0 enabled support for GEOMETRYCOLLECTION
This function call will automatically include a bounding box
comparison that will make use of any indexes that are available on
the geometries. To avoid using an index, use _ST_Touches instead.
&sfs_compliant; s2.1.1.2 // s2.1.13.3
&sqlmm_compliant; SQL-MM 3: 5.1.28
Examples
The ST_Touches predicate returns TRUE in all the following illustrations.
POLYGON / POLYGON
POLYGON / POLYGON
POLYGON / LINESTRING

LINESTRING / LINESTRING
LINESTRING / LINESTRING
POLYGON / POINT

SELECT ST_Touches('LINESTRING(0 0, 1 1, 0 2)'::geometry, 'POINT(1 1)'::geometry);
st_touches
------------
f
(1 row)
SELECT ST_Touches('LINESTRING(0 0, 1 1, 0 2)'::geometry, 'POINT(0 2)'::geometry);
st_touches
------------
t
(1 row)
ST_Within
Returns true if the geometry A is completely inside geometry B
boolean ST_Within
geometry
A
geometry
B
Description
Returns TRUE if geometry A is completely inside geometry B. For this function to make
sense, the source geometries must both be of the same coordinate projection,
having the same SRID. It is a given that if ST_Within(A,B) is true and ST_Within(B,A) is true, then
the two geometries are considered spatially equal.
Performed by the GEOS module
Enhanced: 2.3.0 Enhancement to PIP short-circuit for geometry extended to support MultiPoints with few points. Prior versions only supported point in polygon.
Enhanced: 3.0.0 enabled support for GEOMETRYCOLLECTION
Do not use this function with invalid geometries. You will get unexpected results.
This function call will automatically include a bounding box
comparison that will make use of any indexes that are available on
the geometries. To avoid index use, use the function
_ST_Within.
NOTE: this is the "allowable" version that returns a
boolean, not an integer.
&sfs_compliant; s2.1.1.2 // s2.1.13.3
- a.Relate(b, 'T*F**F***')
&sqlmm_compliant; SQL-MM 3: 5.1.30
Examples
--a circle within a circle
SELECT ST_Within(smallc,smallc) As smallinsmall,
ST_Within(smallc, bigc) As smallinbig,
ST_Within(bigc,smallc) As biginsmall,
ST_Within(ST_Union(smallc, bigc), bigc) as unioninbig,
ST_Within(bigc, ST_Union(smallc, bigc)) as biginunion,
ST_Equals(bigc, ST_Union(smallc, bigc)) as bigisunion
FROM
(
SELECT ST_Buffer(ST_GeomFromText('POINT(50 50)'), 20) As smallc,
ST_Buffer(ST_GeomFromText('POINT(50 50)'), 40) As bigc) As foo;
--Result
smallinsmall | smallinbig | biginsmall | unioninbig | biginunion | bigisunion
--------------+------------+------------+------------+------------+------------
t | t | f | t | t | t
(1 row)
See Also
, ,
Distance Relationships
ST_3DDWithin
For 3d (z) geometry type Returns true if two geometries 3d distance is within number of units.
boolean ST_3DDWithin
geometry
g1
geometry
g2
double precision
distance_of_srid
Description
For geometry type returns true if the 3d distance between two objects is within distance_of_srid specified
projected units (spatial ref units).
&Z_support;
&P_support;
&sqlmm_compliant; SQL-MM ?
Availability: 2.0.0
Examples
-- Geometry example - units in meters (SRID: 2163 US National Atlas Equal area) (3D point and line compared 2D point and line)
-- Note: currently no vertical datum support so Z is not transformed and assumed to be same units as final.
SELECT ST_3DDWithin(
ST_Transform(ST_GeomFromEWKT('SRID=4326;POINT(-72.1235 42.3521 4)'),2163),
ST_Transform(ST_GeomFromEWKT('SRID=4326;LINESTRING(-72.1260 42.45 15, -72.123 42.1546 20)'),2163),
126.8
) As within_dist_3d,
ST_DWithin(
ST_Transform(ST_GeomFromEWKT('SRID=4326;POINT(-72.1235 42.3521 4)'),2163),
ST_Transform(ST_GeomFromEWKT('SRID=4326;LINESTRING(-72.1260 42.45 15, -72.123 42.1546 20)'),2163),
126.8
) As within_dist_2d;
within_dist_3d | within_dist_2d
----------------+----------------
f | t
See Also
, , , ,
ST_3DDFullyWithin
Returns true if all of the 3D geometries are within the specified
distance of one another.
boolean ST_3DDFullyWithin
geometry
g1
geometry
g2
double precision
distance
Description
Returns true if the 3D geometries are fully within the specified distance
of one another. The distance is specified in units defined by the
spatial reference system of the geometries. For this function to make
sense, the source geometries must both be of the same coordinate projection,
having the same SRID.
This function call will automatically include a bounding box
comparison that will make use of any indexes that are available on
the geometries.
Availability: 2.0.0
&Z_support;
&P_support;
Examples
-- This compares the difference between fully within and distance within as well
-- as the distance fully within for the 2D footprint of the line/point vs. the 3d fully within
SELECT ST_3DDFullyWithin(geom_a, geom_b, 10) as D3DFullyWithin10, ST_3DDWithin(geom_a, geom_b, 10) as D3DWithin10,
ST_DFullyWithin(geom_a, geom_b, 20) as D2DFullyWithin20,
ST_3DDFullyWithin(geom_a, geom_b, 20) as D3DFullyWithin20 from
(select ST_GeomFromEWKT('POINT(1 1 2)') as geom_a,
ST_GeomFromEWKT('LINESTRING(1 5 2, 2 7 20, 1 9 100, 14 12 3)') as geom_b) t1;
d3dfullywithin10 | d3dwithin10 | d2dfullywithin20 | d3dfullywithin20
------------------+-------------+------------------+------------------
f | t | t | f
See Also
, , ,
ST_DFullyWithin
Returns true if all of the geometries are within the specified
distance of one another
boolean ST_DFullyWithin
geometry
g1
geometry
g2
double precision
distance
Description
Returns true if the geometries is fully within the specified distance
of one another. The distance is specified in units defined by the
spatial reference system of the geometries. For this function to make
sense, the source geometries must both be of the same coordinate projection,
having the same SRID.
This function call will automatically include a bounding box
comparison that will make use of any indexes that are available on
the geometries.
Availability: 1.5.0
Examples
postgis=# SELECT ST_DFullyWithin(geom_a, geom_b, 10) as DFullyWithin10, ST_DWithin(geom_a, geom_b, 10) as DWithin10, ST_DFullyWithin(geom_a, geom_b, 20) as DFullyWithin20 from
(select ST_GeomFromText('POINT(1 1)') as geom_a,ST_GeomFromText('LINESTRING(1 5, 2 7, 1 9, 14 12)') as geom_b) t1;
-----------------
DFullyWithin10 | DWithin10 | DFullyWithin20 |
---------------+----------+---------------+
f | t | t |
See Also
,
ST_DWithin
Returns true if the geometries are within the specified
distance of one another. For geometry units are in those of spatial reference and for geography units are in meters and measurement is
defaulted to use_spheroid=true (measure around spheroid), for faster check, use_spheroid=false to measure along sphere.
boolean ST_DWithin
geometry
g1
geometry
g2
double precision
distance_of_srid
boolean ST_DWithin
geography
gg1
geography
gg2
double precision
distance_meters
boolean
use_spheroid
Description
Returns true if the geometries are within the specified distance
of one another.
For geometry: The distance is specified in units defined by the
spatial reference system of the geometries. For this function to make
sense, the source geometries must both be of the same coordinate projection,
having the same SRID.
For geography units are in meters and measurement is
defaulted to use_spheroid=true, for faster check, use_spheroid=false to measure along sphere.
This function call will automatically include a bounding box
comparison that will make use of any indexes that are available on
the geometries.
Prior to 1.3, ST_Expand was commonly used in conjunction with && and ST_Distance to
achieve the same effect and in pre-1.3.4 this function was basically short-hand for that construct.
From 1.3.4, ST_DWithin uses a more short-circuit distance function which should make it more efficient
than prior versions for larger buffer regions.
Use ST_3DDWithin if you have 3D geometries.
&sfs_compliant;
Availability: 1.5.0 support for geography was introduced
Enhanced: 2.1.0 improved speed for geography. See Making Geography faster for details.
Enhanced: 2.1.0 support for curved geometries was introduced.
Examples
-- Find the nearest hospital to each school
-- that is within 3000 units of the school.
-- We do an ST_DWithin search to utilize indexes to limit our search list
-- that the non-indexable ST_Distance needs to process
-- If the units of the spatial reference is meters then units would be meters
SELECT DISTINCT ON (s.gid) s.gid, s.school_name, s.geom, h.hospital_name
FROM schools s
LEFT JOIN hospitals h ON ST_DWithin(s.the_geom, h.geom, 3000)
ORDER BY s.gid, ST_Distance(s.geom, h.geom);
-- The schools with no close hospitals
-- Find all schools with no hospital within 3000 units
-- away from the school. Units is in units of spatial ref (e.g. meters, feet, degrees)
SELECT s.gid, s.school_name
FROM schools s
LEFT JOIN hospitals h ON ST_DWithin(s.geom, h.geom, 3000)
WHERE h.gid IS NULL;
-- Find broadcasting towers that receiver with limited range can receive.
-- Data is geometry in Spherical Mercator (SRID=3857), ranges are approximate.
-- Create geometry index that will check proximity limit of user to tower
CREATE INDEX ON broadcasting_towers using gist (geom);
-- Create geometry index that will check proximity limit of tower to user
CREATE INDEX ON broadcasting_towers using gist (ST_Expand(geom, sending_range));
-- Query towers that 4-kilometer receiver in Minsk Hackerspace can get
-- Note: two conditions, because shorter LEAST(b.sending_range, 4000) will not use index.
SELECT b.tower_id, b.geom
FROM broadcasting_towers b
WHERE ST_DWithin(b.geom, 'SRID=3857;POINT(3072163.4 7159374.1)', 4000)
AND ST_DWithin(b.geom, 'SRID=3857;POINT(3072163.4 7159374.1)', b.sending_range);
See Also
, ,