# Spatial Relationships and Measurements

ST_3DClosestPoint

Returns the 3-dimensional point on g1 that is closest to g2. This is the first point of the 3D shortest line.

    				geometry ST_3DClosestPoint

    				geometry
    				g1

    				geometry
    				g2

### Description

Returns the 3-dimensional point on g1 that is closest to g2. This is the first point of the 3D shortest line. The 3D length of the 3D shortest line is the 3D distance.

&Z_support;

&P_support;

Availability: 2.0.0

Changed: 2.2.0 - if 2 2D geometries are input, a 2D point is returned (instead of old behavior assuming 0 for missing Z). In case of 2D and 3D, Z is no longer assumed to be 0 for missing Z.

### Examples

linestring and point -- both 3d and 2d closest point
    SELECT ST_AsEWKT(ST_3DClosestPoint(line,pt)) AS cp3d_line_pt,
    		ST_AsEWKT(ST_ClosestPoint(line,pt)) As cp2d_line_pt
    	FROM (SELECT 'POINT(100 100 30)'::geometry As pt,
    			'LINESTRING (20 80 20, 98 190 1, 110 180 3, 50 75 1000)'::geometry As line
    		) As foo;

     cp3d_line_pt						|               cp2d_line_pt
    -----------------------------------------------------------+------------------------------------------
     POINT(54.6993798867619 128.935022917228 11.5475869506606) | POINT(73.0769230769231 115.384615384615)
linestring and multipoint -- both 3d and 2d closest point
    SELECT ST_AsEWKT(ST_3DClosestPoint(line,pt)) AS cp3d_line_pt,
    		ST_AsEWKT(ST_ClosestPoint(line,pt)) As cp2d_line_pt
    	FROM (SELECT 'MULTIPOINT(100 100 30, 50 74 1000)'::geometry As pt,
    			'LINESTRING (20 80 20, 98 190 1, 110 180 3, 50 75 900)'::geometry As line
    		) As foo;

                           cp3d_line_pt                        | cp2d_line_pt
    -----------------------------------------------------------+--------------
     POINT(54.6993798867619 128.935022917228 11.5475869506606) | POINT(50 75)
Multilinestring and polygon both 3d and 2d closest point
    SELECT ST_AsEWKT(ST_3DClosestPoint(poly, mline)) As cp3d,
        ST_AsEWKT(ST_ClosestPoint(poly, mline)) As cp2d
            FROM (SELECT  ST_GeomFromEWKT('POLYGON((175 150 5, 20 40 5, 35 45 5, 50 60 5, 100 100 5, 175 150 5))') As poly,
                    ST_GeomFromEWKT('MULTILINESTRING((175 155 2, 20 40 20, 50 60 -2, 125 100 1, 175 155 1),
                    (1 10 2, 5 20 1))') As mline ) As foo;
                       cp3d                    |     cp2d
    -------------------------------------------+--------------
     POINT(39.993580415989 54.1889925532825 5) | POINT(20 40)

### See Also

ST_AsEWKT, ST_ClosestPoint, ST_3DDistance, ST_3DShortestLine

ST_3DDistance

For geometry type Returns the 3-dimensional cartesian minimum distance (based on spatial ref) between two geometries in projected units.

    			float ST_3DDistance

    			geometry
    			g1

    			geometry
    			g2

### Description

For geometry type returns the 3-dimensional minimum cartesian distance between two geometries in projected units (spatial ref units).

&Z_support;

&P_support;

&sqlmm_compliant; SQL-MM ?

&sfcgal_enhanced;

Availability: 2.0.0

Changed: 2.2.0 - In case of 2D and 3D, Z is no longer assumed to be 0 for missing Z.

### 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_3DDistance(
    			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)
    		) As dist_3d,
    		ST_Distance(
    			ST_Transform(ST_GeomFromText('POINT(-72.1235 42.3521)',4326),2163),
    			ST_Transform(ST_GeomFromText('LINESTRING(-72.1260 42.45, -72.123 42.1546)', 4326),2163)
    		) As dist_2d;

         dist_3d      |     dist_2d
    ------------------+-----------------
     127.295059324629 | 126.66425605671

    -- Multilinestring and polygon both 3d and 2d distance
    -- Same example as 3D closest point example
    SELECT ST_3DDistance(poly, mline) As dist3d,
        ST_Distance(poly, mline) As dist2d
            FROM (SELECT  ST_GeomFromEWKT('POLYGON((175 150 5, 20 40 5, 35 45 5, 50 60 5, 100 100 5, 175 150 5))') As poly,
                    ST_GeomFromEWKT('MULTILINESTRING((175 155 2, 20 40 20, 50 60 -2, 125 100 1, 175 155 1),
                    (1 10 2, 5 20 1))') As mline ) As foo;
          dist3d       | dist2d
    -------------------+--------
     0.716635696066337 |      0

### See Also

ST_Distance, ST_3DClosestPoint, ST_3DDWithin, ST_3DMaxDistance, ST_3DShortestLine, ST_Transform

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_3DDistance, ST_Distance, ST_DWithin, ST_3DMaxDistance, ST_Transform

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_3DMaxDistance, ST_3DDWithin, ST_DWithin, ST_DFullyWithin

ST_3DIntersects

Returns TRUE if the Geometries "spatially intersect" in 3d - only for points, linestrings, polygons, polyhedral surface (area). With SFCGAL backend enabled also supports TINS

    					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.

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.

In order to take advantage of support for TINS, you need to enable the SFCGAL backend. This can be done at session time with: `set postgis.backend = sfcgal;` or at the database or system level. Database level can be done with `ALTER DATABASE gisdb SET postgis.backend = sfcgal;`.

&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

    set postgis.backend = sfcgal;
    SELECT ST_3DIntersects('TIN(((0 0,1 0,0 1,0 0)))'::geometry, 'POINT(.1 .1)'::geometry);
     st_3dintersects
    -----------------
     t

### See Also

ST_Intersects

ST_3DLongestLine

Returns the 3-dimensional longest line between two geometries

    			geometry ST_3DLongestLine

    			geometry
    			g1

    			geometry
    			g2

### Description

Returns the 3-dimensional longest line between two geometries. The function will only return the first longest line if more than one. The line returned will always start in g1 and end in g2. The 3D length of the line this function returns will always be the same as ST_3DMaxDistance returns for g1 and g2.

Availability: 2.0.0

Changed: 2.2.0 - if 2 2D geometries are input, a 2D point is returned (instead of old behavior assuming 0 for missing Z). In case of 2D and 3D, Z is no longer assumed to be 0 for missing Z.

&Z_support;

&P_support;

### Examples

linestring and point -- both 3d and 2d longest line
    SELECT ST_AsEWKT(ST_3DLongestLine(line,pt)) AS lol3d_line_pt,
    		ST_AsEWKT(ST_LongestLine(line,pt)) As lol2d_line_pt
    	FROM (SELECT 'POINT(100 100 30)'::geometry As pt,
    			'LINESTRING (20 80 20, 98 190 1, 110 180 3, 50 75 1000)'::geometry As line
    		) As foo;

               lol3d_line_pt           |       lol2d_line_pt
    -----------------------------------+----------------------------
     LINESTRING(50 75 1000,100 100 30) | LINESTRING(98 190,100 100)
linestring and multipoint -- both 3d and 2d longest line
    SELECT ST_AsEWKT(ST_3DLongestLine(line,pt)) AS lol3d_line_pt,
    		ST_AsEWKT(ST_LongestLine(line,pt)) As lol2d_line_pt
    	FROM (SELECT 'MULTIPOINT(100 100 30, 50 74 1000)'::geometry As pt,
    			'LINESTRING (20 80 20, 98 190 1, 110 180 3, 50 75 900)'::geometry As line
    		) As foo;

              lol3d_line_pt          |      lol2d_line_pt
    ---------------------------------+--------------------------
     LINESTRING(98 190 1,50 74 1000) | LINESTRING(98 190,50 74)
Multilinestring and polygon both 3d and 2d longest line
    SELECT ST_AsEWKT(ST_3DLongestLine(poly, mline)) As lol3d,
        ST_AsEWKT(ST_LongestLine(poly, mline)) As lol2d
            FROM (SELECT  ST_GeomFromEWKT('POLYGON((175 150 5, 20 40 5, 35 45 5, 50 60 5, 100 100 5, 175 150 5))') As poly,
                    ST_GeomFromEWKT('MULTILINESTRING((175 155 2, 20 40 20, 50 60 -2, 125 100 1, 175 155 1),
                    (1 10 2, 5 20 1))') As mline ) As foo;
                lol3d             |          lol2d
    ------------------------------+--------------------------
     LINESTRING(175 150 5,1 10 2) | LINESTRING(175 150,1 10)

### See Also

ST_3DClosestPoint, ST_3DDistance, ST_LongestLine, ST_3DShortestLine, ST_3DMaxDistance

ST_3DMaxDistance

For geometry type Returns the 3-dimensional cartesian maximum distance (based on spatial ref) between two geometries in projected units.

    			float ST_3DMaxDistance

    			geometry
    			g1

    			geometry
    			g2

### Description

For geometry type returns the 3-dimensional maximum cartesian distance between two geometries in projected units (spatial ref units).

&Z_support;

&P_support;

Availability: 2.0.0

Changed: 2.2.0 - In case of 2D and 3D, Z is no longer assumed to be 0 for missing Z.

### 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_3DMaxDistance(
    			ST_Transform(ST_GeomFromEWKT('SRID=4326;POINT(-72.1235 42.3521 10000)'),2163),
    			ST_Transform(ST_GeomFromEWKT('SRID=4326;LINESTRING(-72.1260 42.45 15, -72.123 42.1546 20)'),2163)
    		) As dist_3d,
    		ST_MaxDistance(
    			ST_Transform(ST_GeomFromEWKT('SRID=4326;POINT(-72.1235 42.3521 10000)'),2163),
    			ST_Transform(ST_GeomFromEWKT('SRID=4326;LINESTRING(-72.1260 42.45 15, -72.123 42.1546 20)'),2163)
    		) As dist_2d;

         dist_3d      |     dist_2d
    ------------------+------------------
     24383.7467488441 | 22247.8472107251

### See Also

ST_Distance, ST_3DDWithin, ST_3DMaxDistance, ST_Transform

ST_3DShortestLine

Returns the 3-dimensional shortest line between two geometries

    			geometry ST_3DShortestLine

    			geometry
    			g1

    			geometry
    			g2

### Description

Returns the 3-dimensional shortest line between two geometries. The function will only return the first shortest line if more than one, that the function finds. If g1 and g2 intersects in just one point the function will return a line with both start and end in that intersection-point. If g1 and g2 are intersecting with more than one point the function will return a line with start and end in the same point but it can be any of the intersecting points. The line returned will always start in g1 and end in g2. The 3D length of the line this function returns will always be the same as ST_3DDistance returns for g1 and g2.

Availability: 2.0.0

Changed: 2.2.0 - if 2 2D geometries are input, a 2D point is returned (instead of old behavior assuming 0 for missing Z). In case of 2D and 3D, Z is no longer assumed to be 0 for missing Z.

&Z_support;

&P_support;

### Examples

linestring and point -- both 3d and 2d shortest line
    SELECT ST_AsEWKT(ST_3DShortestLine(line,pt)) AS shl3d_line_pt,
    		ST_AsEWKT(ST_ShortestLine(line,pt)) As shl2d_line_pt
    	FROM (SELECT 'POINT(100 100 30)'::geometry As pt,
    			'LINESTRING (20 80 20, 98 190 1, 110 180 3, 50 75 1000)'::geometry As line
    		) As foo;

     shl3d_line_pt						                 |               shl2d_line_pt
    ----------------------------------------------------------------------------+------------------------------------------------------
     LINESTRING(54.6993798867619 128.935022917228 11.5475869506606,100 100 30)  | LINESTRING(73.0769230769231 115.384615384615,100 100)
linestring and multipoint -- both 3d and 2d shortest line
    SELECT ST_AsEWKT(ST_3DShortestLine(line,pt)) AS shl3d_line_pt,
    		ST_AsEWKT(ST_ShortestLine(line,pt)) As shl2d_line_pt
    	FROM (SELECT 'MULTIPOINT(100 100 30, 50 74 1000)'::geometry As pt,
    			'LINESTRING (20 80 20, 98 190 1, 110 180 3, 50 75 900)'::geometry As line
    		) As foo;

                           shl3d_line_pt                                       | shl2d_line_pt
    ---------------------------------------------------------------------------+------------------------
     LINESTRING(54.6993798867619 128.935022917228 11.5475869506606,100 100 30) | LINESTRING(50 75,50 74)
Multilinestring and polygon both 3d and 2d shortest line
    SELECT ST_AsEWKT(ST_3DShortestLine(poly, mline)) As shl3d,
        ST_AsEWKT(ST_ShortestLine(poly, mline)) As shl2d
            FROM (SELECT  ST_GeomFromEWKT('POLYGON((175 150 5, 20 40 5, 35 45 5, 50 60 5, 100 100 5, 175 150 5))') As poly,
                    ST_GeomFromEWKT('MULTILINESTRING((175 155 2, 20 40 20, 50 60 -2, 125 100 1, 175 155 1),
                    (1 10 2, 5 20 1))') As mline ) As foo;
                       shl3d                                                                           |     shl2d
    ---------------------------------------------------------------------------------------------------+------------------------
     LINESTRING(39.993580415989 54.1889925532825 5,40.4078575708294 53.6052383805529 5.03423778139177) | LINESTRING(20 40,20 40)

### See Also

ST_3DClosestPoint, ST_3DDistance, ST_LongestLine, ST_ShortestLine, ST_3DMaxDistance

ST_Area

Returns the area of the surface if it is a Polygon or MultiPolygon. For geometry, a 2D Cartesian area is determined with units specified by the SRID. For geography, area is determined on a curved surface with units in square meters.

    			  float ST_Area
    				geometry g1

    			  float ST_Area
    				geography geog
    				boolean use_spheroid=true

### Description

Returns the area of the geometry if it is a Polygon or MultiPolygon. Return the area measurement of an ST_Surface or ST_MultiSurface value. For geometry, a 2D Cartesian area is determined with units specified by the SRID. For geography, by default area is determined on a spheroid with units in square meters. To measure around the faster but less accurate sphere, use ST_Area(geog,false).

Enhanced: 2.0.0 - support for 2D polyhedral surfaces was introduced.

Enhanced: 2.2.0 - measurement on spheroid performed with GeographicLib for improved accuracy and robustness. Requires Proj >= 4.9.0 to take advantage of the new feature.

&sfs_compliant;

&sqlmm_compliant; SQL-MM 3: 8.1.2, 9.5.3

&P_support;

For polyhedral surfaces, only supports 2D polyhedral surfaces (not 2.5D). For 2.5D, may give a non-zero answer, but only for the faces that sit completely in XY plane.

&sfcgal_enhanced;

### Examples

Return area in square feet for a plot of Massachusetts land and multiply by conversion to get square meters. Note this is in square feet because EPSG:2249 is Massachusetts State Plane Feet

    SELECT ST_Area(the_geom) As sqft, ST_Area(the_geom)*POWER(0.3048,2) As sqm
    		FROM (SELECT
    		ST_GeomFromText('POLYGON((743238 2967416,743238 2967450,
    			743265 2967450,743265.625 2967416,743238 2967416))',2249) ) As foo(the_geom);
      sqft   |     sqm
    ---------+-------------
     928.625 | 86.27208552

Return area square feet and transform to Massachusetts state plane meters (EPSG:26986) to get square meters. Note this is in square feet because 2249 is Massachusetts State Plane Feet and transformed area is in square meters since EPSG:26986 is state plane Massachusetts meters

    SELECT ST_Area(the_geom) As sqft, ST_Area(ST_Transform(the_geom,26986)) As sqm
    		FROM (SELECT
    		ST_GeomFromText('POLYGON((743238 2967416,743238 2967450,
    			743265 2967450,743265.625 2967416,743238 2967416))',2249) ) As foo(the_geom);
      sqft   |       sqm
    ---------+------------------
     928.625 | 86.2724304199219

Return area square feet and square meters using geography data type. Note that we transform to our geometry to geography (before you can do that make sure your geometry is in WGS 84 long lat 4326). Geography always measures in meters. This is just for demonstration to compare. Normally your table will be stored in geography data type already.

    SELECT ST_Area(the_geog)/POWER(0.3048,2) As sqft_spheroid,  ST_Area(the_geog,false)/POWER(0.3048,2) As sqft_sphere, ST_Area(the_geog) As sqm_spheroid
    		FROM (SELECT
    		geography(
    		ST_Transform(
    			ST_GeomFromText('POLYGON((743238 2967416,743238 2967450,743265 2967450,743265.625 2967416,743238 2967416))',
    				2249
    				) ,4326
    			)
    		)
    	) As foo(the_geog);
      sqft_spheroid   |   sqft_sphere    |   sqm_spheroid
    ------------------+------------------+------------------
     928.684403538925 | 927.049336105925 | 86.2776042893529

     --if your data is in geography already
     SELECT ST_Area(the_geog)/POWER(0.3048,2) As  sqft, ST_Area(the_geog) As sqm
    	FROM somegeogtable;

### See Also

ST_GeomFromText, ST_GeographyFromText, ST_SetSRID, ST_Transform

ST_Azimuth

Returns the north-based azimuth as the angle in radians measured clockwise from the vertical on pointA to pointB.

    			  float ST_Azimuth
    			  geometry pointA
    			  geometry pointB

    			  float ST_Azimuth
    			  geography pointA
    			  geography pointB

### Description

Returns the azimuth in radians of the segment defined by the given point geometries, or NULL if the two points are coincident. The azimuth is angle is referenced from north, and is positive clockwise: North = 0; East = π/2; South = π; West = 3π/2.

For the geography type, the forward azimuth is solved as part of the inverse geodesic problem.

The azimuth is mathematical concept defined as the angle between a reference plane and a point, with angular units in radians. Units can be converted to degrees using a built-in PostgreSQL function degrees(), as shown in the example.

Availability: 1.1.0

Enhanced: 2.0.0 support for geography was introduced.

Enhanced: 2.2.0 measurement on spheroid performed with GeographicLib for improved accuracy and robustness. Requires Proj >= 4.9.0 to take advantage of the new feature.

Azimuth is especially useful in conjunction with ST_Translate for shifting an object along its perpendicular axis. See upgis_lineshift Plpgsqlfunctions PostGIS wiki section for example of this.

### Examples

Geometry Azimuth in degrees

    SELECT degrees(ST_Azimuth(ST_Point(25, 45), ST_Point(75, 100))) AS degA_B,
    	    degrees(ST_Azimuth(ST_Point(75, 100), ST_Point(25, 45))) AS degB_A;

          dega_b       |     degb_a
    ------------------+------------------
     42.2736890060937 | 222.273689006094

Green: the start Point(25,45) with its vertical. Yellow: degA_B as the path to travel (azimuth). | Green: the start Point(75,100) with its vertical. Yellow: degB_A as the path to travel (azimuth).

### See Also

ST_Point, ST_Translate, ST_Project, PostgreSQL Math Functions

ST_Angle

Returns the angle between 3 points, or between 2 vectors (4 points or 2 lines).

    			  float ST_Angle
    			  geometry point1
    			  geometry point2
    			  geometry point3
    			  geometry point4

    			  float ST_Angle
    			  geometry line1
    			  geometry line2

### Description

For 3 points, computes the angle measured clockwise of P1P2P3. If input are 2 lines, get first and last point of the lines as 4 points. For 4 points,compute the angle measured clockwise of P1P2,P3P4. Results are always positive, between 0 and 2*Pi radians. Uses azimuth of pairs or points.

ST_Angle(P1,P2,P3) = ST_Angle(P2,P1,P2,P3)

Result is in radian and can be converted to degrees using a built-in PostgreSQL function degrees(), as shown in the example.

Availability: 2.5.0

### Examples

Geometry Azimuth in degrees

    	WITH rand AS (
    		SELECT s, random() * 2 * PI() AS rad1
    			, random() * 2 * PI() AS rad2
    		FROM  generate_series(1,2,2) AS s
    	)
    	 , points AS (
    		SELECT s, rad1,rad2, ST_MakePoint(cos1+s,sin1+s) as p1, ST_MakePoint(s,s) AS p2, ST_MakePoint(cos2+s,sin2+s) as p3
    		FROM rand
    			,cos(rad1) cos1, sin(rad1) sin1
    			,cos(rad2) cos2, sin(rad2) sin2
    	)
    	SELECT s, ST_AsText(ST_SnapToGrid(ST_MakeLine(ARRAY[p1,p2,p3]),0.001)) AS line
    		, degrees(ST_Angle(p1,p2,p3)) as computed_angle
    		, round(degrees(2*PI()-rad2 -2*PI()+rad1+2*PI()))::int%360 AS reference
    		, round(degrees(2*PI()-rad2 -2*PI()+rad1+2*PI()))::int%360 AS reference
    	FROM points ;

    1 | line | computed_angle | reference
    ------------------+------------------
    1 | LINESTRING(1.511 1.86,1 1,0.896 0.005) | 155.27033848688 | 155

ST_Centroid

Returns the geometric center of a geometry.

      		  geometry ST_Centroid

      		  geometry
      		  g1

                    geography ST_Centroid

                    geography
                    g1
                    boolean
                    use_spheroid=true

### Description

Computes the geometric center of a geometry, or equivalently, the center of mass of the geometry as a `POINT`. For [`MULTI`]`POINT`s, this is computed as the arithmetic mean of the input coordinates. For [`MULTI`]`LINESTRING`s, this is computed as the weighted length of each line segment. For [`MULTI`]`POLYGON`s, "weight" is thought in terms of area. If an empty geometry is supplied, an empty `GEOMETRYCOLLECTION` is returned. If `NULL` is supplied, `NULL` is returned. If `CIRCULARSTRING` or `COMPOUNDCURVE` are supplied, they are converted to linestring wtih CurveToLine first, then same than for `LINESTRING`

New in 2.3.0 : support `CIRCULARSTRING` and `COMPOUNDCURVE` (using CurveToLine)

Availability: 2.4.0 support for geography was introduced.

The centroid is equal to the centroid of the set of component Geometries of highest dimension (since the lower-dimension geometries contribute zero "weight" to the centroid).

&sfs_compliant;

&sqlmm_compliant; SQL-MM 3: 8.1.4, 9.5.5

### Examples

In each of the following illustrations, the green dot represents the centroid of the source geometry.

Centroid of a `MULTIPOINT` | Centroid of a `LINESTRING`
Centroid of a `POLYGON` | Centroid of a `GEOMETRYCOLLECTION`

    SELECT ST_AsText(ST_Centroid('MULTIPOINT ( -1 0, -1 2, -1 3, -1 4, -1 7, 0 1, 0 3, 1 1, 2 0, 6 0, 7 8, 9 8, 10 6 )'));
    				st_astext
    ------------------------------------------
     POINT(2.30769230769231 3.30769230769231)
    (1 row)

    SELECT ST_AsText(ST_centroid(g))
    FROM  ST_GeomFromText('CIRCULARSTRING(0 2, -1 1,0 0, 0.5 0, 1 0, 2 1, 1 2, 0.5 2, 0 2)')  AS g ;
    ------------------------------------------
    POINT(0.5 1)

    SELECT ST_AsText(ST_centroid(g))
    FROM  ST_GeomFromText('COMPOUNDCURVE(CIRCULARSTRING(0 2, -1 1,0 0),(0 0, 0.5 0, 1 0),CIRCULARSTRING( 1 0, 2 1, 1 2),(1 2, 0.5 2, 0 2))' ) AS g;
    ------------------------------------------
    POINT(0.5 1)

### See Also

ST_PointOnSurface, ST_GeometricMedian

ST_ClosestPoint

Returns the 2-dimensional point on g1 that is closest to g2. This is the first point of the shortest line.

    			geometry ST_ClosestPoint

    			geometry
    			g1

    			geometry
    			g2

### Description

Returns the 2-dimensional point on g1 that is closest to g2. This is the first point of the shortest line.

If you have a 3D Geometry, you may prefer to use ST_3DClosestPoint.

Availability: 1.5.0

### Examples

Closest between point and linestring is the point itself, but closest point between a linestring and point is the point on line string that is closest.
    SELECT ST_AsText(ST_ClosestPoint(pt,line)) AS cp_pt_line,
    	ST_AsText(ST_ClosestPoint(line,pt)) As cp_line_pt
    FROM (SELECT 'POINT(100 100)'::geometry As pt,
    		'LINESTRING (20 80, 98 190, 110 180, 50 75 )'::geometry As line
    	) As foo;

       cp_pt_line   |                cp_line_pt
    ----------------+------------------------------------------
     POINT(100 100) | POINT(73.0769230769231 115.384615384615)
| closest point on polygon A to polygon B
    SELECT ST_AsText(
    		ST_ClosestPoint(
    			ST_GeomFromText('POLYGON((175 150, 20 40, 50 60, 125 100, 175 150))'),
    			ST_Buffer(ST_GeomFromText('POINT(110 170)'), 20)
    			)
    		) As ptwkt;

                      ptwkt
    ------------------------------------------
     POINT(140.752120669087 125.695053378061)

### See Also

ST_3DClosestPoint,ST_Distance, ST_LongestLine, ST_ShortestLine, ST_MaxDistance

ST_ClusterDBSCAN

Windowing function that returns integer id for the cluster each input geometry is in based on 2D implementation of Density-based spatial clustering of applications with noise (DBSCAN) algorithm.

    			integer ST_ClusterDBSCAN

    			geometry winset
    			geom

    			float8
    			eps

    			integer
    			minpoints

### Description

Returns cluster number for each input geometry, based on a 2D implementation of the Density-based spatial clustering of applications with noise (DBSCAN) algorithm. Unlike ST_ClusterKMeans, it does not require the number of clusters to be specified, but instead uses the desired distance (`eps`) and density (`minpoints`) parameters to construct each cluster.

An input geometry will be added to a cluster if it is either:

- A "core" geometry, that is within `eps` distance of at least `minpoints` input geometries (including itself) or

- A "border" geometry, that is within `eps` distance of a core geometry.

Note that border geometries may be within `eps` distance of core geometries in more than one cluster; in this case, either assignment would be correct, and the border geometry will be arbitrarily asssigned to one of the available clusters. In these cases, it is possible for a correct cluster to be generated with fewer than `minpoints` geometries. When assignment of a border geometry is ambiguous, repeated calls to ST_ClusterDBSCAN will produce identical results if an ORDER BY clause is included in the window definition, but cluster assignments may differ from other implementations of the same algorithm.

Input geometries that do not meet the criteria to join any other cluster will be assigned a cluster number of NULL.

Availability: 2.3.0 - requires GEOS

### Examples

Assigning a cluster number to each polygon within 50 meters of each other. Require at least 2 polygons per cluster

within 50 meters at least 2 per cluster. singletons have NULL for cid
    SELECT name, ST_ClusterDBSCAN(geom, eps := 50, minpoints := 2) over () AS cid
    FROM boston_polys
    WHERE name > '' AND building > ''
    	AND ST_DWithin(geom,
            ST_Transform(
                ST_GeomFromText('POINT(-71.04054 42.35141)', 4326), 26986),
               500);
                    name                 | bucket
    -------------------------------------+--------
     Manulife Tower                      |      0
     Park Lane Seaport I                 |      0
     Park Lane Seaport II                |      0
     Renaissance Boston Waterfront Hotel |      0
     Seaport Boston Hotel                |      0
     Seaport Hotel & World Trade Center  |      0
     Waterside Place                     |      0
     World Trade Center East             |      0
     100 Northern Avenue                 |      1
     100 Pier 4                          |      1
     The Institute of Contemporary Art   |      1
     101 Seaport                         |      2
     District Hall                       |      2
     One Marina Park Drive               |      2
     Twenty Two Liberty                  |      2
     Vertex                              |      2
     Vertex                              |      2
     Watermark Seaport                   |      2
     Blue Hills Bank Pavilion            |   NULL
     World Trade Center West             |   NULL
    (20 rows)

Combining parcels with the same cluster number into a single geometry. This uses named argument calling

    SELECT cid, ST_Collect(geom) AS cluster_geom, array_agg(parcel_id) AS ids_in_cluster FROM (
        SELECT parcel_id, ST_ClusterDBSCAN(geom, eps := 0.5, minpoints := 5) over () AS cid, geom
        FROM parcels) sq
    GROUP BY cid;

### See Also

ST_DWithin, ST_ClusterKMeans, ST_ClusterIntersecting, ST_ClusterWithin

ST_ClusterIntersecting

Aggregate. Returns an array with the connected components of a set of geometries

                geometry[] ST_ClusterIntersecting
                geometry set g

### Description

ST_ClusterIntersecting is an aggregate function that returns an array of GeometryCollections, where each GeometryCollection represents an interconnected set of geometries.

Availability: 2.2.0 - requires GEOS

### Examples

    WITH testdata AS
      (SELECT unnest(ARRAY['LINESTRING (0 0, 1 1)'::geometry,
    		       'LINESTRING (5 5, 4 4)'::geometry,
    		       'LINESTRING (6 6, 7 7)'::geometry,
    		       'LINESTRING (0 0, -1 -1)'::geometry,
    		       'POLYGON ((0 0, 4 0, 4 4, 0 4, 0 0))'::geometry]) AS geom)

    SELECT ST_AsText(unnest(ST_ClusterIntersecting(geom))) FROM testdata;

    --result

    st_astext
    ---------
    GEOMETRYCOLLECTION(LINESTRING(0 0,1 1),LINESTRING(5 5,4 4),LINESTRING(0 0,-1 -1),POLYGON((0 0,4 0,4 4,0 4,0 0)))
    GEOMETRYCOLLECTION(LINESTRING(6 6,7 7))

### See Also

ST_ClusterDBSCAN, ST_ClusterKMeans, ST_ClusterWithin

ST_ClusterKMeans

Windowing function that returns integer id for the cluster each input geometry is in.

    			integer ST_ClusterKMeans

    			geometry winset
    			geom

    			integer
    			number_of_clusters

### Description

Returns 2D distance based k-means cluster number for each input geometry. The distance used for clustering is the distance between the centroids of the geometries.

Availability: 2.3.0 - requires GEOS

### Examples

Generate dummy set of parcels for examples

    CREATE TABLE parcels AS
    SELECT lpad((row_number() over())::text,3,'0') As parcel_id, geom,
    ('{residential, commercial}'::text[])[1 + mod(row_number()OVER(),2)] As type
    FROM
        ST_Subdivide(ST_Buffer('LINESTRING(40 100, 98 100, 100 150, 60 90)'::geometry,
        40, 'endcap=square'),12) As geom;

Original Parcels | Parcels color-coded by cluster number (cid)
    SELECT ST_ClusterKMeans(geom, 5) OVER() AS cid, parcel_id, geom
    FROM parcels;
    -- result
     cid | parcel_id |   geom
    -----+-----------+---------------
       0 | 001       | 0103000000...
       0 | 002       | 0103000000...
       1 | 003       | 0103000000...
       0 | 004       | 0103000000...
       1 | 005       | 0103000000...
       2 | 006       | 0103000000...
       2 | 007       | 0103000000...
    (7 rows)

     -- Partitioning parcel clusters by type
    SELECT ST_ClusterKMeans(geom,3) over (PARTITION BY type) AS cid, parcel_id, type
    FROM parcels;
    -- result
     cid | parcel_id |    type
    -----+-----------+-------------
       1 | 005       | commercial
       1 | 003       | commercial
       2 | 007       | commercial
       0 | 001       | commercial
       1 | 004       | residential
       0 | 002       | residential
       2 | 006       | residential
    (7 rows)

### See Also

ST_ClusterDBSCAN, ST_ClusterIntersecting, ST_ClusterWithin, ST_Subdivide

ST_ClusterWithin

Aggregate. Returns an array of GeometryCollections, where each GeometryCollection represents a set of geometries separated by no more than the specified distance.

                geometry[] ST_ClusterWithin
                geometry set  g
                float8  distance

### Description

ST_ClusterWithin is an aggregate function that returns an array of GeometryCollections, where each GeometryCollection represents a set of geometries separated by no more than the specified distance. (Distances are Cartesian distances in the units of the SRID.)

Availability: 2.2.0 - requires GEOS

### Examples

    WITH testdata AS
      (SELECT unnest(ARRAY['LINESTRING (0 0, 1 1)'::geometry,
    		       'LINESTRING (5 5, 4 4)'::geometry,
    		       'LINESTRING (6 6, 7 7)'::geometry,
    		       'LINESTRING (0 0, -1 -1)'::geometry,
    		       'POLYGON ((0 0, 4 0, 4 4, 0 4, 0 0))'::geometry]) AS geom)

    SELECT ST_AsText(unnest(ST_ClusterWithin(geom, 1.4))) FROM testdata;

    --result

    st_astext
    ---------
    GEOMETRYCOLLECTION(LINESTRING(0 0,1 1),LINESTRING(5 5,4 4),LINESTRING(0 0,-1 -1),POLYGON((0 0,4 0,4 4,0 4,0 0)))
    GEOMETRYCOLLECTION(LINESTRING(6 6,7 7))

### See Also

ST_ClusterDBSCAN, ST_ClusterKMeans, ST_ClusterIntersecting

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 ST_ContainsProperly 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.

Do not call with a `GEOMETRYCOLLECTION` as an argument

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_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). 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 ST_Relate

From JTS docs slightly reworded: The advantage to using this predicate over ST_Contains and ST_Intersects 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.

Availability: 1.4.0 - requires GEOS >= 3.1.0.

Do not call with a `GEOMETRYCOLLECTION` as an argument

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

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

Performed by the GEOS module

Do not call with a `GEOMETRYCOLLECTION` as an argument

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.

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 - requires GEOS >= 3.0

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_Contains, ST_CoveredBy, ST_Within

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

Performed by the GEOS module

Do not call with a `GEOMETRYCOLLECTION` as an argument

Do not use this function with invalid geometries. You will get unexpected results.

Availability: 1.2.2 - requires GEOS >= 3.0

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_Contains, ST_Covers, ST_ExteriorRing, ST_Within

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:

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.

Do not call with a `GEOMETRYCOLLECTION` as an argument

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_Crosses

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.

Do not call with a `GEOMETRYCOLLECTION` as an argument

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_Distance

For geometry type returns the 2D Cartesian distance between two geometries in projected units (based on spatial reference system). For geography type defaults to return minimum geodesic distance between two geographies in meters.

    			float ST_Distance

    			geometry
    			g1

    			geometry
    			g2

    			float ST_Distance

    			geography
    			gg1

    			geography
    			gg2

    			float ST_Distance

    			geography
    			gg1

    			geography
    			gg2

    			boolean
    			use_spheroid

### Description

For geometry type returns the minimum 2D Cartesian distance between two geometries in projected units (spatial ref units). For geography type defaults to return the minimum geodesic distance between two geographies in meters. If use_spheroid is false, a faster sphere calculation is used instead of a spheroid.

&sfs_compliant;

&sqlmm_compliant; SQL-MM 3: 5.1.23

&curve_support;

&sfcgal_enhanced;

Availability: 1.5.0 geography support was introduced in 1.5. Speed improvements for planar to better handle large or many vertex geometries

Enhanced: 2.1.0 improved speed for geography. See Making Geography faster for details.

Enhanced: 2.1.0 - support for curved geometries was introduced.

Enhanced: 2.2.0 - measurement on spheroid performed with GeographicLib for improved accuracy and robustness. Requires Proj >= 4.9.0 to take advantage of the new feature.

### Basic Geometry Examples

    --Geometry example - units in planar degrees 4326 is WGS 84 long lat unit=degrees
    SELECT ST_Distance(
    		'SRID=4326;POINT(-72.1235 42.3521)'::geometry,
    		'SRID=4326;LINESTRING(-72.1260 42.45, -72.123 42.1546)'::geometry
    	);
    st_distance
    -----------------
    0.00150567726382282

    -- Geometry example - units in meters (SRID: 3857, proportional to pixels on popular web maps)
    -- although the value is off, nearby ones can be compared correctly,
    -- which makes it a good choice for algorithms like KNN or KMeans.
    SELECT ST_Distance(
    			ST_Transform('SRID=4326;POINT(-72.1235 42.3521)'::geometry, 3857),
    			ST_Transform('SRID=4326;LINESTRING(-72.1260 42.45, -72.123 42.1546)'::geometry, 3857)
    		);
    st_distance
    -----------------
    167.441410065196

    -- Geometry example - units in meters (SRID: 3857 as above, but corrected by cos(lat) to account for distortion)
    SELECT ST_Distance(
    			ST_Transform('SRID=4326;POINT(-72.1235 42.3521)'::geometry, 3857),
    			ST_Transform('SRID=4326;LINESTRING(-72.1260 42.45, -72.123 42.1546)'::geometry, 3857)
    		) * cosd(42.3521);
    st_distance
    -----------------
    123.742351254151

    -- Geometry example - units in meters (SRID: 26986 Massachusetts state plane meters) (most accurate for Massachusetts)
    SELECT ST_Distance(
    			ST_Transform('SRID=4326;POINT(-72.1235 42.3521)'::geometry, 26986),
    			ST_Transform('SRID=4326;LINESTRING(-72.1260 42.45, -72.123 42.1546)'::geometry, 26986)
    		);
    st_distance
    -----------------
    123.797937878454

    -- Geometry example - units in meters (SRID: 2163 US National Atlas Equal area) (least accurate)
    SELECT ST_Distance(
    			ST_Transform('SRID=4326;POINT(-72.1235 42.3521)'::geometry, 2163),
    			ST_Transform('SRID=4326;LINESTRING(-72.1260 42.45, -72.123 42.1546)'::geometry, 2163)
    		);

    st_distance
    ------------------
    126.664256056812

### Geography Examples

    -- same as geometry example but note units in meters - use sphere for slightly faster less accurate
    SELECT ST_Distance(gg1, gg2) As spheroid_dist, ST_Distance(gg1, gg2, false) As sphere_dist
    FROM (SELECT
    	'SRID=4326;POINT(-72.1235 42.3521)'::geography as gg1,
    	'SRID=4326;LINESTRING(-72.1260 42.45, -72.123 42.1546)'::geography as gg2
    	) As foo  ;

      spheroid_dist   |   sphere_dist
    ------------------+------------------
     123.802076746848 | 123.475736916397

### See Also

ST_3DDistance, ST_DWithin, ST_DistanceSphere, ST_Distance_Spheroid, ST_MaxDistance, ST_HausdorffDistance, ST_FrechetDistance, ST_Transform

ST_MinimumClearance

Returns the minimum clearance of a geometry, a measure of a geometry's robustness.

    					float ST_MinimumClearance
    					geometry g

### Description

It is not uncommon to have a geometry that, while meeting the criteria for validity according to ST_IsValid (polygons) or ST_IsSimple (lines), would become invalid if one of the vertices moved by a slight distance, as can happen during conversion to text-based formats (such as WKT, KML, GML GeoJSON), or binary formats that do not use double-precision floating point coordinates (MapInfo TAB).

A geometry's "minimum clearance" is the smallest distance by which a vertex of the geometry could be moved to produce an invalid geometry. It can be thought of as a quantitative measure of a geometry's robustness, where increasing values of minimum clearance indicate increasing robustness.

If a geometry has a minimum clearance of `e`, it can be said that:

- No two distinct vertices in the geometry are separated by less than `e`.

- No vertex is closer than `e` to a line segement of which it is not an endpoint.

If no minimum clearance exists for a geometry (for example, a single point, or a multipoint whose points are identical), then ST_MinimumClearance will return Infinity.

Availability: 2.3.0 - requires GEOS >= 3.6.0

### Examples

    SELECT ST_MinimumClearance('POLYGON ((0 0, 1 0, 1 1, 0.5 3.2e-4, 0 0))');
     st_minimumclearance
    ---------------------
                 0.00032

### See Also

ST_MinimumClearanceLine

ST_MinimumClearanceLine

Returns the two-point LineString spanning a geometry's minimum clearance.

    			Geometry ST_MinimumClearanceLine

    			geometry
    			g

### Description

Returns the two-point LineString spanning a geometry's minimum clearance. If the geometry does not have a minimum clearance, `LINESTRING EMPTY` will be returned.

Availability: 2.3.0 - requires GEOS >= 3.6.0

### Examples

    SELECT ST_AsText(ST_MinimumClearanceLine('POLYGON ((0 0, 1 0, 1 1, 0.5 3.2e-4, 0 0))'));
    st_astext
    -------------------------------
    LINESTRING(0.5 0.00032,0.5 0)

### See Also

ST_MinimumClearance

ST_HausdorffDistance

Returns the Hausdorff distance between two geometries. Basically a measure of how similar or dissimilar 2 geometries are. Units are in the units of the spatial reference system of the geometries.

    			float ST_HausdorffDistance

    			geometry
    			g1

    			geometry
    			g2

    			float ST_HausdorffDistance

    			geometry
    			g1

    			geometry
    			g2

    			float
    			densifyFrac

### Description

Implements algorithm for computing a distance metric which can be thought of as the "Discrete Hausdorff Distance". This is the Hausdorff distance restricted to discrete points for one of the geometries. Wikipedia article on Hausdorff distance Martin Davis note on how Hausdorff Distance calculation was used to prove correctness of the CascadePolygonUnion approach.

When densifyFrac is specified, this function performs a segment densification before computing the discrete hausdorff distance. The densifyFrac parameter sets the fraction by which to densify each segment. Each segment will be split into a number of equal-length subsegments, whose fraction of the total length is closest to the given fraction.

The current implementation supports only vertices as the discrete locations. This could be extended to allow an arbitrary density of points to be used.

This algorithm is NOT equivalent to the standard Hausdorff distance. However, it computes an approximation that is correct for a large subset of useful cases. One important part of this subset is Linestrings that are roughly parallel to each other, and roughly equal in length. This is a useful metric for line matching.

Availability: 1.5.0 - requires GEOS >= 3.2.0

### Examples

For each building, find the parcel that best represents it. First we require the parcel intersect with the geometry. DISTINCT ON guarantees we get each building listed only once, the ORDER BY .. ST_HausdorffDistance gives us a preference of parcel that is most similar to the building.

    SELECT DISTINCT ON(buildings.gid) buildings.gid, parcels.parcel_id
       FROM buildings INNER JOIN parcels ON ST_Intersects(buildings.geom,parcels.geom)
         ORDER BY buildings.gid, ST_HausdorffDistance(buildings.geom, parcels.geom);

    postgis=# SELECT ST_HausdorffDistance(
    				'LINESTRING (0 0, 2 0)'::geometry,
    				'MULTIPOINT (0 1, 1 0, 2 1)'::geometry);
     st_hausdorffdistance
     ----------------------
    					 1
    (1 row)

    postgis=# SELECT st_hausdorffdistance('LINESTRING (130 0, 0 0, 0 150)'::geometry, 'LINESTRING (10 10, 10 150, 130 10)'::geometry, 0.5);
     st_hausdorffdistance
     ----------------------
    					70
    (1 row)

### See Also

ST_FrechetDistance

ST_FrechetDistance

Returns the Fréchet distance between two geometries. This is a measure of similarity between curves that takes into account the location and ordering of the points along the curves. Units are in the units of the spatial reference system of the geometries.

    			float ST_FrechetDistance

    			geometry
    			g1

    			geometry
    			g2

    			float
    			densifyFrac = -1

### Description

Implements algorithm for computing the Fréchet distance restricted to discrete points for both geometries, based on Computing Discrete Fréchet Distance. The Fréchet distance is a measure of similarity between curves that takes into account the location and ordering of the points along the curves. Therefore it is often better than the Hausdorff distance.

When the optional densifyFrac is specified, this function performs a segment densification before computing the discrete Fréchet distance. The densifyFrac parameter sets the fraction by which to densify each segment. Each segment will be split into a number of equal-length subsegments, whose fraction of the total length is closest to the given fraction.

The current implementation supports only vertices as the discrete locations. This could be extended to allow an arbitrary density of points to be used.

The smaller densifyFrac we specify, the more acurate Fréchet distance we get. But, the computation time and the memory usage increase with the square of the number of subsegments.

Availability: 2.4.0 - requires GEOS >= 3.7.0

### Examples

    postgres=# SELECT st_frechetdistance('LINESTRING (0 0, 100 0)'::geometry, 'LINESTRING (0 0, 50 50, 100 0)'::geometry);
     st_frechetdistance
    --------------------
       70.7106781186548
    (1 row)

    SELECT st_frechetdistance('LINESTRING (0 0, 100 0)'::geometry, 'LINESTRING (0 0, 50 50, 100 0)'::geometry, 0.5);
     st_frechetdistance
    --------------------
                     50
    (1 row)

### See Also

ST_HausdorffDistance

ST_MaxDistance

Returns the 2-dimensional largest distance between two geometries in projected units.

            float ST_MaxDistance
            geometry  g1
            geometry  g2

### Description

Returns the 2-dimensional maximum distance between two geometries in projected units. If g1 and g2 is the same geometry the function will return the distance between the two vertices most far from each other in that geometry.

Availability: 1.5.0

### Examples

Basic furthest distance the point is to any part of the line

    postgis=# SELECT ST_MaxDistance('POINT(0 0)'::geometry, 'LINESTRING ( 2 0, 0 2 )'::geometry);
       st_maxdistance
    -----------------
     2
    (1 row)

    postgis=# SELECT ST_MaxDistance('POINT(0 0)'::geometry, 'LINESTRING ( 2 2, 2 2 )'::geometry);
      st_maxdistance
    ------------------
     2.82842712474619
    (1 row)

### See Also

ST_Distance, ST_LongestLine, ST_DFullyWithin

ST_DistanceSphere

Returns minimum distance in meters between two lon/lat geometries. Uses a spherical earth and radius derived from the spheroid defined by the SRID. Faster than ST_DistanceSpheroid ST_Distance_Spheroid, but less accurate. PostGIS versions prior to 1.5 only implemented for points.

    			float ST_DistanceSphere
    			geometry  geomlonlatA
    			geometry  geomlonlatB

### Description

Returns minimum distance in meters between two lon/lat points. Uses a spherical earth and radius derived from the spheroid defined by the SRID. Faster than ST_Distance_Spheroid, but less accurate. PostGIS Versions prior to 1.5 only implemented for points.

Availability: 1.5 - support for other geometry types besides points was introduced. Prior versions only work with points.

Changed: 2.2.0 In prior versions this used to be called ST_Distance_Sphere

### Examples

    SELECT round(CAST(ST_DistanceSphere(ST_Centroid(the_geom), ST_GeomFromText('POINT(-118 38)',4326)) As numeric),2) As dist_meters,
    round(CAST(ST_Distance(ST_Transform(ST_Centroid(the_geom),32611),
    		ST_Transform(ST_GeomFromText('POINT(-118 38)', 4326),32611)) As numeric),2) As dist_utm11_meters,
    round(CAST(ST_Distance(ST_Centroid(the_geom), ST_GeomFromText('POINT(-118 38)', 4326)) As numeric),5) As dist_degrees,
    round(CAST(ST_Distance(ST_Transform(the_geom,32611),
    		ST_Transform(ST_GeomFromText('POINT(-118 38)', 4326),32611)) As numeric),2) As min_dist_line_point_meters
    FROM
    	(SELECT ST_GeomFromText('LINESTRING(-118.584 38.374,-118.583 38.5)', 4326) As the_geom) as foo;
    	 dist_meters | dist_utm11_meters | dist_degrees | min_dist_line_point_meters
    	-------------+-------------------+--------------+----------------------------
    		70424.47 |          70438.00 |      0.72900 |                   65871.18

### See Also

ST_Distance, ST_Distance_Spheroid

ST_DistanceSpheroid

Returns the minimum distance between two lon/lat geometries given a particular spheroid. PostGIS versions prior to 1.5 only support points.

    			float ST_DistanceSpheroid
    			geometry  geomlonlatA
    			geometry  geomlonlatB
    			spheroid  measurement_spheroid

### Description

Returns minimum distance in meters between two lon/lat geometries given a particular spheroid. See the explanation of spheroids given for ST_Length_Spheroid. PostGIS version prior to 1.5 only support points.

This function currently does not look at the SRID of a geometry and will always assume its represented in the coordinates of the passed in spheroid. Prior versions of this function only support points.

Availability: 1.5 - support for other geometry types besides points was introduced. Prior versions only work with points.

Changed: 2.2.0 In prior versions this used to be called ST_Distance_Spheroid

### Examples

    SELECT round(CAST(
    		ST_DistanceSpheroid(ST_Centroid(the_geom), ST_GeomFromText('POINT(-118 38)',4326), 'SPHEROID["WGS 84",6378137,298.257223563]')
    			As numeric),2) As dist_meters_spheroid,
    		round(CAST(ST_DistanceSphere(ST_Centroid(the_geom), ST_GeomFromText('POINT(-118 38)',4326)) As numeric),2) As dist_meters_sphere,
    round(CAST(ST_Distance(ST_Transform(ST_Centroid(the_geom),32611),
    		ST_Transform(ST_GeomFromText('POINT(-118 38)', 4326),32611)) As numeric),2) As dist_utm11_meters
    FROM
    	(SELECT ST_GeomFromText('LINESTRING(-118.584 38.374,-118.583 38.5)', 4326) As the_geom) as foo;
     dist_meters_spheroid | dist_meters_sphere | dist_utm11_meters
    ----------------------+--------------------+-------------------
    			 70454.92 |           70424.47 |          70438.00

### See Also

ST_Distance, ST_DistanceSphere

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_MaxDistance, ST_DWithin

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 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

ST_Distance, ST_Expand, ST_3DDWithin

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.

Do not call with a GEOMETRYCOLLECTION as an argument.

&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_GeometricMedian

Returns the geometric median of a MultiPoint.

    			geometry

    					ST_GeometricMedian

    					geometry

    					g

    					float8

    					tolerance

    					int

    					max_iter

    					boolean

    					fail_if_not_converged

### Description

Computes the approximate geometric median of a MultiPoint geometry using the Weiszfeld algorithm. The geometric median provides a centrality measure that is less sensitive to outlier points than the centroid.

The algorithm will iterate until the distance change between successive iterations is less than the supplied `tolerance` parameter. If this condition has not been met after `max_iterations` iterations, the function will produce an error and exit, unless `fail_if_not_converged` is set to false.

If a `tolerance` value is not provided, a default tolerance value will be calculated based on the extent of the input geometry.

M value of points, if present, is interpreted as their relative weight.

Availability: 2.3.0

Enhanced: 2.5.0 Added support for M as weight of points.

&Z_support;

&M_support;

### Examples

Comparison of the centroid (turquoise point) and geometric median (red point) of a four-point MultiPoint (yellow points).

    WITH test AS (
    SELECT 'MULTIPOINT((0 0), (1 1), (2 2), (200 200))'::geometry geom)
    SELECT
      ST_AsText(ST_Centroid(geom)) centroid,
      ST_AsText(ST_GeometricMedian(geom)) median
    FROM test;
          centroid      |                 median
    --------------------+----------------------------------------
     POINT(50.75 50.75) | POINT(1.9761550281255 1.9761550281255)
    (1 row)

### See Also

ST_Centroid

ST_HasArc

Returns true if a geometry or geometry collection contains a circular string

    			boolean ST_HasArc
    			geometry  geomA

### Description

Returns true if a geometry or geometry collection contains a circular string

Availability: 1.2.3?

&Z_support;

&curve_support;

### Examples

    SELECT ST_HasArc(ST_Collect('LINESTRING(1 2, 3 4, 5 6)', 'CIRCULARSTRING(1 1, 2 3, 4 5, 6 7, 5 6)'));
    		st_hasarc
    		--------
    		t

### See Also

ST_CurveToLine, ST_LineToCurve

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)

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.

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(
    		ST_GeographyFromText('SRID=4326;LINESTRING(-43.23456 72.4567,-43.23456 72.4568)'),
    		ST_GeographyFromText('SRID=4326;POINT(-43.23456 72.4567772)')
    		);

     st_intersects
    ---------------
    t

### See Also

ST_3DIntersects, ST_Disjoint

ST_Length

Returns the 2D length of the geometry if it is a LineString or MultiLineString. geometry are in units of spatial reference and geography are in meters (default spheroid)

    			  float ST_Length
    				geometry a_2dlinestring

    			  float ST_Length
    				geography geog
    				boolean use_spheroid=true

### Description

For geometry: Returns the 2D Cartesian length of the geometry if it is a LineString, MultiLineString, ST_Curve, ST_MultiCurve. 0 is returned for areal geometries. For areal geometries use ST_Perimeter. For geometry types, units for length measures are specified by the spatial reference system of the geometry.

For geography types, the calculations are performed using the inverse geodesic problem, where length units are in meters. If PostGIS is compiled with PROJ version 4.8.0 or later, the spheroid is specified by the SRID, otherwise it is exclusive to WGS84. If `use_spheroid=false`, then calculations will approximate a sphere instead of a spheroid.

Currently for geometry this is an alias for ST_Length2D, but this may change to support higher dimensions.

Changed: 2.0.0 Breaking change -- in prior versions applying this to a MULTI/POLYGON of type geography would give you the perimeter of the POLYGON/MULTIPOLYGON. In 2.0.0 this was changed to return 0 to be in line with geometry behavior. Please use ST_Perimeter if you want the perimeter of a polygon

For geography measurement defaults spheroid measurement. To use the faster less accurate sphere use ST_Length(gg,false);

&sfs_compliant; s2.1.5.1

&sqlmm_compliant; SQL-MM 3: 7.1.2, 9.3.4

Availability: 1.5.0 geography support was introduced in 1.5.

&sfcgal_enhanced;

### Geometry Examples

Return length in feet for line string. Note this is in feet because EPSG:2249 is Massachusetts State Plane Feet

    SELECT ST_Length(ST_GeomFromText('LINESTRING(743238 2967416,743238 2967450,743265 2967450,
    743265.625 2967416,743238 2967416)',2249));
    st_length
    ---------
     122.630744000095

    --Transforming WGS 84 LineString to Massachusetts state plane meters
    SELECT ST_Length(
    	ST_Transform(
    		ST_GeomFromEWKT('SRID=4326;LINESTRING(-72.1260 42.45, -72.1240 42.45666, -72.123 42.1546)'),
    		26986
    	)
    );
    st_length
    ---------
    34309.4563576191

### Geography Examples

Return length of WGS 84 geography line

    			-- default calculation is using a sphere rather than spheroid
    SELECT ST_Length(the_geog) As length_spheroid,  ST_Length(the_geog,false) As length_sphere
    FROM (SELECT ST_GeographyFromText(
    'SRID=4326;LINESTRING(-72.1260 42.45, -72.1240 42.45666, -72.123 42.1546)') As the_geog)
     As foo;
     length_spheroid  |  length_sphere
    ------------------+------------------
     34310.5703627288 | 34346.2060960742

### See Also

ST_GeographyFromText, ST_GeomFromEWKT, ST_Length_Spheroid, ST_Perimeter, ST_Transform

ST_Length2D

Returns the 2-dimensional length of the geometry if it is a linestring or multi-linestring. This is an alias for `ST_Length`

    			float ST_Length2D
    			geometry  a_2dlinestring

### Description

Returns the 2-dimensional length of the geometry if it is a linestring or multi-linestring. This is an alias for `ST_Length`

### See Also

ST_Length, ST_3DLength

ST_3DLength

Returns the 3-dimensional or 2-dimensional length of the geometry if it is a linestring or multi-linestring.

    			float ST_3DLength
    			geometry  a_3dlinestring

### Description

Returns the 3-dimensional or 2-dimensional length of the geometry if it is a linestring or multi-linestring. For 2-d lines it will just return the 2-d length (same as ST_Length and ST_Length2D)

&Z_support;

Changed: 2.0.0 In prior versions this used to be called ST_Length3D

### Examples

Return length in feet for a 3D cable. Note this is in feet because EPSG:2249 is Massachusetts State Plane Feet

    SELECT ST_3DLength(ST_GeomFromText('LINESTRING(743238 2967416 1,743238 2967450 1,743265 2967450 3,
    743265.625 2967416 3,743238 2967416 3)',2249));
    ST_3DLength
    -----------
    122.704716741457

### See Also

ST_Length, ST_Length2D

ST_LengthSpheroid

Calculates the 2D or 3D length/perimeter of a geometry on an ellipsoid. This is useful if the coordinates of the geometry are in longitude/latitude and a length is desired without reprojection.

    			float ST_LengthSpheroid
    			geometry  a_geometry
    			spheroid  a_spheroid

### Description

Calculates the length/perimeter of a geometry on an ellipsoid. This is useful if the coordinates of the geometry are in longitude/latitude and a length is desired without reprojection. The ellipsoid is a separate database type and can be constructed as follows:

    SPHEROID[<NAME>,<SEMI-MAJOR AXIS>,<INVERSE FLATTENING>]

    SPHEROID["GRS_1980",6378137,298.257222101]

Availability: 1.2.2

Changed: 2.2.0 In prior versions this used to be called ST_Length_Spheroid and used to have a ST_3DLength_Spheroid alias

&Z_support;

### Examples

    SELECT ST_LengthSpheroid( geometry_column,
    			  'SPHEROID["GRS_1980",6378137,298.257222101]' )
    			  FROM geometry_table;

    SELECT ST_LengthSpheroid( the_geom, sph_m ) As tot_len,
    ST_LengthSpheroid(ST_GeometryN(the_geom,1), sph_m) As len_line1,
    ST_LengthSpheroid(ST_GeometryN(the_geom,2), sph_m) As len_line2
    			  FROM (SELECT ST_GeomFromText('MULTILINESTRING((-118.584 38.374,-118.583 38.5),
    	(-71.05957 42.3589 , -71.061 43))') As the_geom,
    CAST('SPHEROID["GRS_1980",6378137,298.257222101]' As spheroid) As sph_m)  as foo;
    	tot_len      |    len_line1     |    len_line2
    ------------------+------------------+------------------
     85204.5207562955 | 13986.8725229309 | 71217.6482333646

     --3D
    SELECT ST_LengthSpheroid( the_geom, sph_m ) As tot_len,
    ST_LengthSpheroid(ST_GeometryN(the_geom,1), sph_m) As len_line1,
    ST_LengthSpheroid(ST_GeometryN(the_geom,2), sph_m) As len_line2
    			  FROM (SELECT ST_GeomFromEWKT('MULTILINESTRING((-118.584 38.374 20,-118.583 38.5 30),
    	(-71.05957 42.3589 75, -71.061 43 90))') As the_geom,
    CAST('SPHEROID["GRS_1980",6378137,298.257222101]' As spheroid) As sph_m)  as foo;

    	 tot_len      |    len_line1    |    len_line2
    ------------------+-----------------+------------------
     85204.5259107402 | 13986.876097711 | 71217.6498130292

### See Also

ST_GeometryN, ST_Length

ST_Length2D_Spheroid

Calculates the 2D length/perimeter of a geometry on an ellipsoid. This is useful if the coordinates of the geometry are in longitude/latitude and a length is desired without reprojection.

    			float ST_Length2D_Spheroid
    			geometry  a_geometry
    			spheroid  a_spheroid

### Description

Calculates the 2D length/perimeter of a geometry on an ellipsoid. This is useful if the coordinates of the geometry are in longitude/latitude and a length is desired without reprojection. The ellipsoid is a separate database type and can be constructed as follows:

    SPHEROID[<NAME>,<SEMI-MAJOR AXIS>,<INVERSE FLATTENING>]

    SPHEROID["GRS_1980",6378137,298.257222101]

This is much like ST_Length_Spheroid except it will ignore the Z ordinate in calculations.

### Examples

    SELECT ST_Length2D_Spheroid( geometry_column,
    			  'SPHEROID["GRS_1980",6378137,298.257222101]' )
    			  FROM geometry_table;

    SELECT ST_Length2D_Spheroid( the_geom, sph_m ) As tot_len,
    ST_Length2D_Spheroid(ST_GeometryN(the_geom,1), sph_m) As len_line1,
    ST_Length2D_Spheroid(ST_GeometryN(the_geom,2), sph_m) As len_line2
    			  FROM (SELECT ST_GeomFromText('MULTILINESTRING((-118.584 38.374,-118.583 38.5),
    	(-71.05957 42.3589 , -71.061 43))') As the_geom,
    CAST('SPHEROID["GRS_1980",6378137,298.257222101]' As spheroid) As sph_m)  as foo;
    	tot_len      |    len_line1     |    len_line2
    ------------------+------------------+------------------
     85204.5207562955 | 13986.8725229309 | 71217.6482333646

     --3D Observe same answer
    SELECT ST_Length2D_Spheroid( the_geom, sph_m ) As tot_len,
    ST_Length2D_Spheroid(ST_GeometryN(the_geom,1), sph_m) As len_line1,
    ST_Length2D_Spheroid(ST_GeometryN(the_geom,2), sph_m) As len_line2
    			  FROM (SELECT ST_GeomFromEWKT('MULTILINESTRING((-118.584 38.374 20,-118.583 38.5 30),
    	(-71.05957 42.3589 75, -71.061 43 90))') As the_geom,
    CAST('SPHEROID["GRS_1980",6378137,298.257222101]' As spheroid) As sph_m)  as foo;

    	tot_len      |    len_line1     |    len_line2
    ------------------+------------------+------------------
     85204.5207562955 | 13986.8725229309 | 71217.6482333646

### See Also

ST_GeometryN, ST_Length_Spheroid

ST_LongestLine

Returns the 2-dimensional longest line points of two geometries. The function will only return the first longest line if more than one, that the function finds. The line returned will always start in g1 and end in g2. The length of the line this function returns will always be the same as st_maxdistance returns for g1 and g2.

    			geometry ST_LongestLine

    			geometry
    			g1

    			geometry
    			g2

### Description

Returns the 2-dimensional longest line between the points of two geometries.

Availability: 1.5.0

### Examples

Longest line between point and line
    SELECT ST_AsText(
    	ST_LongestLine('POINT(100 100)'::geometry,
    		'LINESTRING (20 80, 98 190, 110 180, 50 75 )'::geometry)
    	) As lline;

       lline
    -----------------
    LINESTRING(100 100,98 190)
| longest line between polygon and polygon
    SELECT ST_AsText(
    	ST_LongestLine(
    		ST_GeomFromText('POLYGON((175 150, 20 40,
    			50 60, 125 100, 175 150))'),
    		ST_Buffer(ST_GeomFromText('POINT(110 170)'), 20)
    		)
    	) As llinewkt;

       lline
    -----------------
    LINESTRING(20 40,121.111404660392 186.629392246051)

longest straight distance to travel from one part of an elegant city to the other Note the max distance = to the length of the line.
    SELECT ST_AsText(ST_LongestLine(c.the_geom, c.the_geom)) As llinewkt,
    	ST_MaxDistance(c.the_geom,c.the_geom) As max_dist,
    	ST_Length(ST_LongestLine(c.the_geom, c.the_geom)) As lenll
    FROM (SELECT ST_BuildArea(ST_Collect(the_geom)) As the_geom
    	FROM (SELECT ST_Translate(ST_SnapToGrid(ST_Buffer(ST_Point(50 ,generate_series(50,190, 50)
    			),40, 'quad_segs=2'),1), x, 0)  As the_geom
    			FROM generate_series(1,100,50) As x)  AS foo
    ) As c;

              llinewkt          |     max_dist     |      lenll
    ---------------------------+------------------+------------------
     LINESTRING(23 22,129 178) | 188.605408193933 | 188.605408193933

### See Also

ST_MaxDistance, ST_ShortestLine, ST_LongestLine

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_Equals, ST_Reverse

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

Do not call with a GeometryCollection as an argument

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_Contains, ST_Crosses, ST_Dimension, ST_Intersects

ST_Perimeter

Return the length measurement of the boundary of an ST_Surface or ST_MultiSurface geometry or geography. (Polygon, MultiPolygon). geometry measurement is in units of spatial reference and geography is in meters.

    			  float ST_Perimeter
    				geometry g1

    			  float ST_Perimeter
    				geography geog
    				boolean use_spheroid=true

### Description

Returns the 2D perimeter of the geometry/geography if it is a ST_Surface, ST_MultiSurface (Polygon, MultiPolygon). 0 is returned for non-areal geometries. For linear geometries use ST_Length. For geometry types, units for perimeter measures are specified by the spatial reference system of the geometry.

For geography types, the calculations are performed using the inverse geodesic problem, where perimeter units are in meters. If PostGIS is compiled with PROJ version 4.8.0 or later, the spheroid is specified by the SRID, otherwise it is exclusive to WGS84. If `use_spheroid=false`, then calculations will approximate a sphere instead of a spheroid.

Currently this is an alias for ST_Perimeter2D, but this may change to support higher dimensions.

&sfs_compliant; s2.1.5.1

&sqlmm_compliant; SQL-MM 3: 8.1.3, 9.5.4

Availability 2.0.0: Support for geography was introduced

### Examples: Geometry

Return perimeter in feet for Polygon and MultiPolygon. Note this is in feet because EPSG:2249 is Massachusetts State Plane Feet

    SELECT ST_Perimeter(ST_GeomFromText('POLYGON((743238 2967416,743238 2967450,743265 2967450,
    743265.625 2967416,743238 2967416))', 2249));
    st_perimeter
    ---------
     122.630744000095
    (1 row)

    SELECT ST_Perimeter(ST_GeomFromText('MULTIPOLYGON(((763104.471273676 2949418.44119003,
    763104.477769673 2949418.42538203,
    763104.189609677 2949418.22343004,763104.471273676 2949418.44119003)),
    ((763104.471273676 2949418.44119003,763095.804579742 2949436.33850239,
    763086.132105649 2949451.46730207,763078.452329651 2949462.11549407,
    763075.354136904 2949466.17407812,763064.362142565 2949477.64291974,
    763059.953961626 2949481.28983009,762994.637609571 2949532.04103014,
    762990.568508415 2949535.06640477,762986.710889563 2949539.61421415,
    763117.237897679 2949709.50493431,763235.236617789 2949617.95619822,
    763287.718121842 2949562.20592617,763111.553321674 2949423.91664605,
    763104.471273676 2949418.44119003)))', 2249));
    st_perimeter
    ---------
     845.227713366825
    (1 row)

### Examples: Geography

Return perimeter in meters and feet for Polygon and MultiPolygon. Note this is geography (WGS 84 long lat)

    SELECT  ST_Perimeter(geog) As per_meters, ST_Perimeter(geog)/0.3048 As per_ft
    FROM ST_GeogFromText('POLYGON((-71.1776848522251 42.3902896512902,-71.1776843766326 42.3903829478009,
    -71.1775844305465 42.3903826677917,-71.1775825927231 42.3902893647987,-71.1776848522251 42.3902896512902))') As geog;

       per_meters    |      per_ft
    -----------------+------------------
    37.3790462565251 | 122.634666195949

    -- MultiPolygon example --
    SELECT  ST_Perimeter(geog) As per_meters, ST_Perimeter(geog,false) As per_sphere_meters,  ST_Perimeter(geog)/0.3048 As per_ft
    FROM ST_GeogFromText('MULTIPOLYGON(((-71.1044543107478 42.340674480411,-71.1044542869917 42.3406744369506,
    -71.1044553562977 42.340673886454,-71.1044543107478 42.340674480411)),
    ((-71.1044543107478 42.340674480411,-71.1044860600303 42.3407237015564,-71.1045215770124 42.3407653385914,
    -71.1045498002983 42.3407946553165,-71.1045611902745 42.3408058316308,-71.1046016507427 42.340837442371,
    -71.104617893173 42.3408475056957,-71.1048586153981 42.3409875993595,-71.1048736143677 42.3409959528211,
    -71.1048878050242 42.3410084812078,-71.1044020965803 42.3414730072048,
    -71.1039672113619 42.3412202916693,-71.1037740497748 42.3410666421308,
    -71.1044280218456 42.3406894151355,-71.1044543107478 42.340674480411)))') As geog;

        per_meters    | per_sphere_meters |      per_ft
    ------------------+-------------------+------------------
     257.634283683311 |  257.412311446337 | 845.256836231335

### See Also

ST_GeogFromText, ST_GeomFromText, ST_Length

ST_Perimeter2D

Returns the 2-dimensional perimeter of the geometry, if it is a polygon or multi-polygon. This is currently an alias for ST_Perimeter.

    			float ST_Perimeter2D
    			geometry  geomA

### Description

Returns the 2-dimensional perimeter of the geometry, if it is a polygon or multi-polygon.

This is currently an alias for ST_Perimeter. In future versions ST_Perimeter may return the highest dimension perimeter for a geometry. This is still under consideration

### See Also

ST_Perimeter

ST_3DPerimeter

Returns the 3-dimensional perimeter of the geometry, if it is a polygon or multi-polygon.

    			float ST_3DPerimeter
    			geometry  geomA

### Description

Returns the 3-dimensional perimeter of the geometry, if it is a polygon or multi-polygon. If the geometry is 2-dimensional, then the 2-dimensional perimeter is returned.

&Z_support;

Changed: 2.0.0 In prior versions this used to be called ST_Perimeter3D

### Examples

Perimeter of a slightly elevated polygon in the air in Massachusetts state plane feet

    SELECT ST_3DPerimeter(the_geom), ST_Perimeter2d(the_geom), ST_Perimeter(the_geom) FROM
    			(SELECT ST_GeomFromEWKT('SRID=2249;POLYGON((743238 2967416 2,743238 2967450 1,
    743265.625 2967416 1,743238 2967416 2))') As the_geom) As foo;

      ST_3DPerimeter  |  st_perimeter2d  |   st_perimeter
    ------------------+------------------+------------------
     105.465793597674 | 105.432997272188 | 105.432997272188

### See Also

ST_GeomFromEWKT, ST_Perimeter, ST_Perimeter2D

ST_PointOnSurface

Returns a `POINT` guaranteed to lie on the surface.

    			geometry ST_PointOnSurface

    			geometry
    			g1

### Description

Returns a `POINT` guaranteed to intersect a surface.

&sfs_compliant; s3.2.14.2 // s3.2.18.2

&sqlmm_compliant; SQL-MM 3: 8.1.5, 9.5.6. According to the specs, ST_PointOnSurface works for surface geometries (POLYGONs, MULTIPOLYGONS, CURVED POLYGONS). So PostGIS seems to be extending what the spec allows here. Most databases Oracle,DB II, ESRI SDE seem to only support this function for surfaces. SQL Server 2008 like PostGIS supports for all common geometries.

&Z_support;

### Examples

    SELECT ST_AsText(ST_PointOnSurface('POINT(0 5)'::geometry));
     st_astext
    ------------
     POINT(0 5)
    (1 row)

    SELECT ST_AsText(ST_PointOnSurface('LINESTRING(0 5, 0 10)'::geometry));
     st_astext
    ------------
     POINT(0 5)
    (1 row)

    SELECT ST_AsText(ST_PointOnSurface('POLYGON((0 0, 0 5, 5 5, 5 0, 0 0))'::geometry));
       st_astext
    ----------------
     POINT(2.5 2.5)
    (1 row)

    SELECT ST_AsEWKT(ST_PointOnSurface(ST_GeomFromEWKT('LINESTRING(0 5 1, 0 0 1, 0 10 2)')));
       st_asewkt
    ----------------
     POINT(0 0 1)
    (1 row)

### See Also

ST_Centroid, ST_Point_Inside_Circle

ST_Project

Returns a `POINT` projected from a start point using a distance in meters and bearing (azimuth) in radians.

    				geography ST_Project

    				geography
    				g1
    				float
    				distance
    				float
    				azimuth

### Description

Returns a `POINT` projected along a geodesic from a start point using an azimuth (bearing) measured in radians and distance measured in meters. This is also called a direct geodesic problem.

The azimuth is sometimes called the heading or the bearing in navigation. It is measured relative to true north (azimuth zero). East is azimuth 90 (π/2), south is azimuth 180 (π), west is azimuth 270 (3π/2).

The distance is given in meters.

Availability: 2.0.0

Enhanced: 2.4.0 Allow negative distance and non-normalized azimuth.

### Example: Using degrees - projected point 100,000 meters and bearing 45 degrees

    SELECT ST_AsText(ST_Project('POINT(0 0)'::geography, 100000, radians(45.0)));

                     st_astext
    --------------------------------------------
     POINT(0.635231029125537 0.639472334729198)
    (1 row)

### See Also

ST_Azimuth, ST_Distance, PostgreSQL Math Functions

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.

Do not call with a GeometryCollection as an argument

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 DE-9IM

Version 3: same as version 2, but allows to specify a boundary node rule (1:OGC/MOD2, 2:Endpoint, 3:MultivalentEndpoint, 4:MonovalentEndpoint)

Do not call with a GeometryCollection as an argument

not in OGC spec, but implied. see s2.1.13.2

Performed by the GEOS module

&sfs_compliant; s2.1.1.2 // s2.1.13.3

&sqlmm_compliant; SQL-MM 3: 5.1.25

Enhanced: 2.0.0 - added support for specifying boundary node rule (requires GEOS >= 3.0).

### 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_Crosses, DE-9IM, ST_Disjoint, ST_Intersects, ST_Touches

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 DE-9IM.

Availability: 2.0.0 - requires GEOS >= 3.3.0.

### 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

DE-9IM, ST_Relate

ST_ShortestLine

Returns the 2-dimensional shortest line between two geometries

    			geometry ST_ShortestLine

    			geometry
    			g1

    			geometry
    			g2

### Description

Returns the 2-dimensional shortest line between two geometries. The function will only return the first shortest line if more than one, that the function finds. If g1 and g2 intersects in just one point the function will return a line with both start and end in that intersection-point. If g1 and g2 are intersecting with more than one point the function will return a line with start and end in the same point but it can be any of the intersecting points. The line returned will always start in g1 and end in g2. The length of the line this function returns will always be the same as ST_Distance returns for g1 and g2.

Availability: 1.5.0

### Examples

Shortest line between point and linestring
    SELECT ST_AsText(
    	ST_ShortestLine('POINT(100 100)'::geometry,
    		'LINESTRING (20 80, 98 190, 110 180, 50 75 )'::geometry)
    	) As sline;

       sline
    -----------------
    LINESTRING(100 100,73.0769230769231 115.384615384615)
| shortest line between polygon and polygon
    SELECT ST_AsText(
    		ST_ShortestLine(
    			ST_GeomFromText('POLYGON((175 150, 20 40, 50 60, 125 100, 175 150))'),
    			ST_Buffer(ST_GeomFromText('POINT(110 170)'), 20)
    			)
    		) As slinewkt;

     LINESTRING(140.752120669087 125.695053378061,121.111404660392 153.370607753949)

### See Also

ST_ClosestPoint, ST_Distance, ST_LongestLine, ST_MaxDistance

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****`

Do not call with a `GEOMETRYCOLLECTION` as an argument

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.

Do not call with a `GEOMETRYCOLLECTION` as an argument

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

ST_Contains, ST_Equals, ST_IsValid