These functions determine spatial relationships between geometries.

# Spatial Relationships

## Topological Relationships

ST_3DIntersects

Returns true if two 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.

&index_aware;

Changed: 3.0.0 SFCGAL backend removed, GEOS backend supports TINs.

Availability: 2.0.0

&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_Intersects

ST_Contains

Returns true if no points of B lie in the exterior of A, and A and B have at least one interior point in common.

          boolean ST_Contains

          geometry
          geomA

          geometry
          geomB

#### Description

Returns TRUE if geometry B is completely inside geometry A. A contains 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.

A subtlety of the definition is that a geometry does not contain its boundary. This implies that polygons and lines do not contain lines and points lying in their boundary. For further details see Subtleties of OGC Covers, Contains, Within. (The ST_Covers predicate provides a more inclusive relationship.) However, a geometry does contain itself. (In contrast, in the ST_ContainsProperly predicate a geometry does not properly contain itself.)

ST_Contains is the inverse of ST_Within. So, `ST_Contains(A,B) = ST_Within(B,A)`.

&index_aware; To avoid index use, use the function `_ST_Contains`.

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.

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

#### 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_Boundary, ST_ContainsProperly, ST_Covers, ST_CoveredBy, ST_Equals, ST_Within

ST_ContainsProperly

Returns true if B intersects the interior of A but not the boundary or exterior.

          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 properly contain 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 ST_Relate

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.

&index_aware; To avoid index use, use the function `_ST_ContainsProperly`.

The advantage of this predicate over ST_Contains and ST_Intersects is that it can be computed more efficiently, with no need to compute topology at individual points.

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.

#### 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_GeometryType, ST_Boundary, ST_Contains, ST_Covers, ST_CoveredBy, ST_Equals, ST_Relate, ST_Within

ST_CoveredBy

Returns true if no point in A is outside B

          boolean ST_CoveredBy

          geometry
          geomA

          geometry
          geomB

          boolean ST_CoveredBy

          geography
          geogA

          geography
          geogB

#### Description

Returns `true` if no point in Geometry/Geography A lies outside Geometry/Geography B. Equivalently, tests if every point of geometry A is inside (i.e. intersects the interior or boundary of) geometry B.

&index_aware; To avoid index use, use the function `_ST_CoveredBy`.

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

NOTE: this is the "allowable" version that returns a boolean, not an integer.

Not an OGC standard, but Oracle has it too.

#### 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_Contains, ST_Covers, ST_ExteriorRing, ST_Within

ST_Covers

Returns true if no point in B is outside A

          boolean ST_Covers

          geometry
          geomA

          geometry
          geomB

          boolean ST_Covers

          geography
          geogpolyA

          geography
          geogpointB

#### Description

Returns `true` if no point in Geometry/Geography B is outside Geometry/Geography A. Equivalently, tests if every point of geometry B is inside (i.e. intersects the interior or boundary of) geometry A.

&index_aware; To avoid index use, use the function `_ST_Covers`.

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

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.

#### 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_Contains, ST_CoveredBy, ST_Within

ST_Crosses

Returns true if two 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:

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.

&index_aware;

Enhanced: 3.0.0 enabled support for `GEOMETRYCOLLECTION`

&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,
      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);

ST_LineCrossingDirection

Returns a number indicating the crossing behavior of two LineStrings.

          integer ST_LineCrossingDirection
          geometry  linestringA
          geometry  linestringB

#### Description

Given 2 linestrings, returns an integer between -3 and 3 indicating what kind of crossing behavior exists between them. 0 indicates no crossing. This is only supported for `LINESTRING`s.

The crossing number has the following meaning:

- 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.geom, s2.geom)
      FROM streets s1 CROSS JOIN streets s2 ON (s1.gid != s2.gid AND s1.geom && s2.geom )
    WHERE ST_CrossingDirection(s1.geom, s2.geom) > 0;

#### See Also

ST_Crosses

ST_Disjoint

Returns true if two geometries do not intersect (they have no point in common).

              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_Intersects

ST_Equals

Returns true if two geometries include the same set of points.

          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).

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_IsValid, ST_OrderingEquals, ST_Reverse, ST_Within

ST_Intersects

Returns true if two geometries intersect (they have at least one point in common).

              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.

&index_aware;

Changed: 3.0.0 SFCGAL version removed and native support for 2D TINS added.

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.

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

&curve_support;

&T_support;

#### 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)

    -- Look up in table. Make sure table has a GiST index on geometry column for faster lookup.
    SELECT id, name FROM cities WHERE ST_Intersects(geom, 'SRID=4326;POLYGON((28 53,27.707 52.293,27 52,26.293 52.293,26 53,26.293 53.707,27 54,27.707 53.707,28 53))');
     id | name
    ----+-------
      2 | Minsk
    (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

geometry_overlaps, ST_3DIntersects, ST_Disjoint

ST_OrderingEquals

Returns true if two geometries represent the same geometry and have points 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

geometry_overlaps, ST_Equals, ST_Reverse

ST_Overlaps

Returns true if two geometries intersect and have 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.

&index_aware; To avoid index use, use the function `_ST_Overlaps`.

Performed by the GEOS module

Enhanced: 3.0.0 enabled support for `GEOMETRYCOLLECTION`

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_Contains, ST_Crosses, ST_Dimension, ST_Intersects

ST_Relate

Tests if two geometries have a topological relationship matching an Intersection Matrix pattern, or computes their Intersection Matrix

            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

These functions allow testing and evaluating the spatial (topological) relationship between two geometries, as defined by the Dimensionally Extended 9-Intersection Model (DE-9IM).

The DE-9IM is specified as a 9-element matrix indicating the dimension of the intersections between the Interior, Boundary and Exterior of two geometries. It is represented by a 9-character text string using the symbols 'F', '0', '1', '2' (e.g. `'FF1FF0102'`).

A specific kind of spatial relationships is evaluated by comparing the intersection matrix to an intersection matrix pattern. A pattern can include the additional symbols 'T' and '*'. Common spatial relationships are provided by the named functions ST_Contains, ST_ContainsProperly, ST_Covers, ST_CoveredBy, ST_Crosses, ST_Disjoint, ST_Equals, ST_Intersects, ST_Overlaps, ST_Touches, and ST_Within. Using an explicit pattern allows testing multiple conditions of intersects, crosses, etc in one step. It also allows testing spatial relationships which do not have a named spatial relationship function. For example, the relationship "Interior-Intersects" has the DE-9IM pattern `T********`, which is not evaluated by any named predicate.

For more information refer to eval_spatial_rel.

Variant 1: Tests if two geometries are spatially related according to the given `intersectionMatrixPattern`.

Unlike most of the named spatial relationship predicates, this does NOT automatically include an index call. The reason is that some relationships are true for geometries which do NOT intersect (e.g. Disjoint). If you are using a relationship pattern that requires intersection, then include the && index call.

It is better to use a named relationship function if available, since they automatically use a spatial index where one exists. Also, they may implement performance optimizations which are not available with full relate evalation.

Variant 2: Returns the DE-9IM matrix string for the spatial relationship between the two input geometries. The matrix string can be tested for matching a DE-9IM pattern using ST_RelateMatch.

Variant 3: Like variant 2, but allows specifying a Boundary Node Rule. A boundary node rule allows finer control over whether geometry boundary points are considered to lie in the DE-9IM Interior or Boundary. The `boundaryNodeRule` code is: 1: OGC/MOD2, 2: Endpoint, 3: MultivalentEndpoint, 4: MonovalentEndpoint.

This function is not in the OGC spec, but is 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.

Enhanced: 3.0.0 enabled support for `GEOMETRYCOLLECTION`

#### Examples

Using the boolean-valued function to test spatial relationships.

    SELECT ST_Relate('POINT(1 2)', ST_Buffer( 'POINT(1 2)', 2), '0FFFFF212');
    st_relate
    -----------
    t

    SELECT ST_Relate(POINT(1 2)', ST_Buffer( 'POINT(1 2)', 2), '*FF*FF212');
    st_relate
    -----------
    t

Testing a custom spatial relationship pattern as a query condition, with `&&` to enable using a spatial index.

    -- Find compounds that properly intersect (not just touch) a poly (Interior Intersects)

    SELECT c.* , p.name As poly_name
        FROM polys AS p
        INNER JOIN compounds As c
              ON c.geom && p.geom
                 AND ST_Relate(p.geom, c.geom,'T********');

Computing the intersection matrix for spatial relationships.

    SELECT ST_Relate( 'POINT(1 2)',
                      ST_Buffer( 'POINT(1 2)', 2));
    st_relate
    -----------
    0FFFFF212

    SELECT ST_Relate( 'LINESTRING(1 2, 3 4)',
                      'LINESTRING(5 6, 7 8)' );
    st_relate
    -----------
    FF1FF0102

#### See Also

eval_spatial_rel, ST_RelateMatch, ST_Contains, ST_ContainsProperly, ST_Covers, ST_CoveredBy, ST_Crosses, ST_Disjoint, ST_Equals, ST_Intersects, ST_Overlaps, ST_Touches, ST_Within

ST_RelateMatch

Tests if a DE-9IM Intersection Matrix matches an Intersection Matrix pattern

          boolean ST_RelateMatch
          text  intersectionMatrix
          text  intersectionMatrixPattern

#### Description

Tests if a Dimensionally Extended 9-Intersection Model (DE-9IM) `intersectionMatrix` value satisfies an `intersectionMatrixPattern`. Intersection matrix values can be computed by ST_Relate.

For more information refer to eval_spatial_rel.

Performed by the GEOS module

Availability: 2.0.0

#### Examples

    SELECT ST_RelateMatch('101202FFF', 'TTTTTTFFF') ;
    -- result --
    t

Patterns for common spatial relationships matched against intersection matrix values, for a line in various positions relative to a polygon

    SELECT pat.name AS relationship, pat.val AS pattern,
           mat.name AS position, mat.val AS matrix,
           ST_RelateMatch(mat.val, pat.val) AS match
        FROM (VALUES ( 'Equality', 'T1FF1FFF1' ),
                     ( 'Overlaps', 'T*T***T**' ),
                     ( 'Within',   'T*F**F***' ),
                     ( 'Disjoint', 'FF*FF****' )) AS pat(name,val)
        CROSS JOIN
            (VALUES  ('non-intersecting', 'FF1FF0212'),
                     ('overlapping',      '1010F0212'),
                     ('inside',           '1FF0FF212')) AS mat(name,val);

     relationship |  pattern  |     position     |  matrix   | match
    --------------+-----------+------------------+-----------+-------
     Equality     | T1FF1FFF1 | non-intersecting | FF1FF0212 | f
     Equality     | T1FF1FFF1 | overlapping      | 1010F0212 | f
     Equality     | T1FF1FFF1 | inside           | 1FF0FF212 | f
     Overlaps     | T*T***T** | non-intersecting | FF1FF0212 | f
     Overlaps     | T*T***T** | overlapping      | 1010F0212 | t
     Overlaps     | T*T***T** | inside           | 1FF0FF212 | f
     Within       | T*F**F*** | non-intersecting | FF1FF0212 | f
     Within       | T*F**F*** | overlapping      | 1010F0212 | f
     Within       | T*F**F*** | inside           | 1FF0FF212 | t
     Disjoint     | FF*FF**** | non-intersecting | FF1FF0212 | t
     Disjoint     | FF*FF**** | overlapping      | 1010F0212 | f
     Disjoint     | FF*FF**** | inside           | 1FF0FF212 | f

#### See Also

eval_spatial_rel, ST_Relate

ST_Touches

Returns true if two geometries have at least one point in common, but their interiors do not intersect.

          boolean ST_Touches

          geometry
          A

          geometry
          B

#### Description

Returns `TRUE` if A and B intersect, but their interiors do not intersect. Equivalently, A and B have at least one point in common, and the common points lie in the intersection of their boundaries. For Point/Point inputs the relationship is always `FALSE`, since points do not have a boundary.

In mathematical terms, this relationship is expressed as:

This relationship holds if the DE-9IM Intersection Matrix for the two geometries matches one of:

- `FT*******`

- `F**T*****`

- `F***T****`

&index_aware; To avoid using an index, use `_ST_Touches` instead.

Enhanced: 3.0.0 enabled support for `GEOMETRYCOLLECTION`

&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 no points of A lie in the exterior of B, and A and B have at least one interior point in common.

          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.

A subtlety of this definition is that the boundary of a geometry is not within the geometry. This means that lines and points lying in the boundary of a polygon or line are not within the geometry. For further details see Subtleties of OGC Covers, Contains, Within. (The ST_CoveredBy predicate provides a more inclusive relationship).

ST_Within is the inverse of ST_Contains. So, `ST_Within(A,B) = ST_Contains(B,A)`.

&index_aware; To avoid index use, use the function `_ST_Within`.

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.

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

ST_Contains, ST_CoveredBy, ST_Equals, ST_IsValid

## Distance Relationships

ST_3DDWithin

Returns true if two 3D geometries are within a given 3D distance

          boolean ST_3DDWithin

          geometry
          g1

          geometry
          g2

          double precision
          distance_of_srid

#### Description

Returns true if the 3D distance between two geometry values is no larger than distance `distance_of_srid`. 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 be in the same coordinate system (have the same SRID).

&index_aware;

&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, ST_DWithin, ST_DFullyWithin, ST_3DDistance, ST_Distance, ST_3DMaxDistance, ST_Transform

ST_3DDFullyWithin

Returns true if two 3D geometries are entirely within a given 3D distance

          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.

&index_aware;

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_3DDWithin, ST_DWithin, ST_DFullyWithin, ST_3DMaxDistance

ST_DFullyWithin

Returns true if two geometries are entirely within a given distance

          boolean ST_DFullyWithin

          geometry
          g1

          geometry
          g2

          double precision
          distance

#### Description

Returns true if the geometries are entirely 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.

&index_aware;

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_MaxDistance, ST_DWithin, ST_3DDWithin, ST_3DDFullyWithin

ST_DWithin

Returns true if two geometries are within a given distance

            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 = true

#### Description

Returns true if the geometries are within a given distance

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 be in the same coordinate system (have the same SRID).

For `geography`: units are in meters and distance measurement defaults to `use_spheroid`=true. For faster evaluation use `use_spheroid`=false to measure on the sphere.

Use ST_3DDWithin for 3D geometries.

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

Prior to 1.3, ST_Expand was commonly used in conjunction with && and ST_Distance to test for distance, and in pre-1.3.4 this function used that logic. From 1.3.4, ST_DWithin uses a faster short-circuit distance function.

#### 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.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

ST_Distance, ST_3DDWithin

ST_PointInsideCircle

Tests if a point geometry is inside a circle defined by a center and radius.

          boolean ST_PointInsideCircle
          geometry  a_point
          float  center_x
          float  center_y
          float  radius

#### Description

Returns true if the geometry is a point and is inside the circle with center `center_x`,`center_y` and radius `radius`.

Does not use spatial indexes. Use ST_DWithin instead.

Availability: 1.2

Changed: 2.2.0 In prior versions this was called ST_Point_Inside_Circle

#### Examples

    SELECT ST_PointInsideCircle(ST_Point(1,2), 0.5, 2, 3);
     st_pointinsidecircle
    ------------------------
     t

#### See Also

ST_DWithin