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 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 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) , ,, 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 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 ? Availability: 2.0.0 -- 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 ,,,, , 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 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 -- 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 ,,, 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 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; -- 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 , , , ST_3DIntersects Returns TRUE if the Geometries "spatially intersect" in 3d - only for points and linestrings boolean ST_3DIntersects geometry geomA geometry geomB 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. &Z_support; &P_support; &sqlmm_compliant; SQL-MM 3: ? 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) ST_3DLongestLine Returns the 3-dimensional longest line between two geometries geometry ST_3DLongestLine geometry g1 geometry g2 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 returns for g1 and g2. Availability: 2.0.0 &Z_support; &P_support; 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) , , , , 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 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 -- 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 ,,, ST_3DShortestLine Returns the 3-dimensional shortest line between two geometries geometry ST_3DShortestLine geometry g1 geometry g2 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 returns for g1 and g2. Availability: 2.0.0 &Z_support; &P_support; 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) , , , , ST_Area Returns the area of the surface if it is a polygon or multi-polygon. For "geometry" type area is in SRID units. For "geography" area is in square meters. float ST_Area geometry g1 float ST_Area geography g1 float ST_Area geography g1 boolean use_spheroid Returns the area of the geometry if it is a polygon or multi-polygon. Return the area measurement of an ST_Surface or ST_MultiSurface value. For geometry Area is in the units of the srid. For geography area is in square meters and defaults to measuring about the spheroid of the geography (currently only WGS84). To measure around the faster but less accurate sphere -- ST_Area(geog,false). Enhanced: 2.0.0 - support for 2D polyhedral surfaces was introduced. &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. 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 2249 is Mass 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 (26986) to get square meters. Note this is in square feet because 2249 is Mass State Plane Feet and transformed area is in square meters since 26986 is state plane mass 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 -----------------+------------------+------------------ 928.684405217197 | 927.186481558724 | 86.2776044452694 --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; , , , ST_Azimuth Returns the angle in radians from the horizontal of the vector defined by pointA and pointB float ST_Azimuth geometry pointA geometry pointB Returns the azimuth of the segment defined by the given Point geometries, or NULL if the two points are coincident. Return value is in radians. The Azimuth is mathematical concept defined as the angle, in this case measured in radian, between a reference plane and a point Availability: 1.1.0 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. --Azimuth in degrees SELECT ST_Azimuth(ST_MakePoint(1,2), ST_MakePoint(3,4))/(2*pi())*360 as degAz, ST_Azimuth(ST_MakePoint(3,4), ST_MakePoint(1,2))/(2*pi())*360 As degAzrev degaz degazrev ------ --------- 45 225 , ST_Centroid Returns the geometric center of a geometry. geometry ST_Centroid geometry g1 Computes the geometric center of a geometry, or equivalently, the center of mass of the geometry as a POINT. For [MULTI]POINTs, this is computed as the arithmetric mean of the input coordinates. For [MULTI]LINESTRINGs, this is computed as the weighted length of each line segment. For [MULTI]POLYGONs, "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. 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). Computation will be more accurate if performed by the GEOS module (enabled at compile time). &sfs_compliant; &sqlmm_compliant; SQL-MM 3: 8.1.4, 9.5.5 In each of the following illustrations, the blue 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) 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 Returns the 2-dimensional point on g1 that is closest to g2. This is the first point of the shortest line. Availability: 1.5.0 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) , , , 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 Geometry A contains Geometry B if and only if no points of B lie in the exterior of A, and at least one point of the interior of B lies in the interior of A. An important subtlety of this definition is that A does not contain its boundary, but A does contain itself. Contrast that to where geometry A does not Contain Properly itself. Returns TRUE if geometry B is completely inside geometry A. For this function to make sense, the source geometries must both be of the same coordinate projection, having the same SRID. ST_Contains is the inverse of ST_Within. So ST_Contains(A,B) implies ST_Within(B,A) except in the case of invalid geometries where the result is always false regardless or not defined. Performed by the GEOS module 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 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 , , ,, , 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 Returns true if B intersects the interior of A but not the boundary (or exterior). A does not contain properly itself, but does contain itself. Every point of the other geometry is a point of this geometry's interior. The DE-9IM Intersection Matrix for the two geometries matches [T**FF*FF*] used in From JTS docs slightly reworded: The advantage to using this predicate over and is that it can be computed efficiently, with no need to compute topology at individual points. An example use case for this predicate is computing the intersections of a set of geometries with a large polygonal geometry. Since intersection is a fairly slow operation, it can be more efficient to use containsProperly to filter out test geometries which lie wholly inside the area. In these cases the intersection is known a priori to be exactly the original test geometry. 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. --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 , , , ,, ,, 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 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 For geography only Polygon covers point is supported. 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. Availability: 1.2.2 - requires GEOS >= 3.0 Availability: 1.5 - support for geography was introduced. 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 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 , , 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 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 --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) , , , ST_Crosses Returns TRUE if the supplied geometries have some, but not all, interior points in common. boolean ST_Crosses geometry g1 geometry g2 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 the maximum dimension of the two input geometries. Additionally, the intersection of the two geometries must not equal either of the source geometries. Otherwise, it returns FALSE. In mathematical terms, this is expressed as: TODO: Insert appropriate MathML markup here or use a gif. Simple HTML markup does not work well in both IE and Firefox. The DE-9IM Intersection Matrix for the two geometries is: T*T****** (for Point/Line, Point/Area, and Line/Area situations) T*****T** (for Line/Point, Area/Point, and Area/Line situations) 0******** (for Line/Line situations) For any other combination of dimensions this predicate returns false. The OpenGIS Simple Features Specification defines this predicate only for Point/Line, Point/Area, Line/Line, and Line/Area situations. JTS / GEOS extends the definition to apply to Line/Point, Area/Point and Area/Line situations as well. This makes the relation symmetric. 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 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 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 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; 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 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 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) ST_Intersects ST_Distance For geometry type Returns the 2-dimensional cartesian minimum distance (based on spatial ref) between two geometries in projected units. For geography type defaults to return spheroidal minimum 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 For geometry type returns the 2-dimensional minimum cartesian distance between two geometries in projected units (spatial ref units). For geography type defaults to return the minimum distance around WGS 84 spheroid between two geographies in meters. Pass in false to return answer in sphere instead of spheroid. &sfs_compliant; &sqlmm_compliant; SQL-MM 3: 5.1.23 Availability: 1.5.0 geography support was introduced in 1.5. Speed improvements for planar to better handle large or many vertex geometries --Geometry example - units in planar degrees 4326 is WGS 84 long lat unit=degrees SELECT ST_Distance( ST_GeomFromText('POINT(-72.1235 42.3521)',4326), ST_GeomFromText('LINESTRING(-72.1260 42.45, -72.123 42.1546)', 4326) ); st_distance ----------------- 0.00150567726382282 -- Geometry example - units in meters (SRID: 26986 Massachusetts state plane meters) (most accurate for Massachusetts) SELECT ST_Distance( ST_Transform(ST_GeomFromText('POINT(-72.1235 42.3521)',4326),26986), ST_Transform(ST_GeomFromText('LINESTRING(-72.1260 42.45, -72.123 42.1546)', 4326),26986) ); st_distance ----------------- 123.797937878454 -- Geometry example - units in meters (SRID: 2163 US National Atlas Equal area) (least accurate) SELECT 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) ); st_distance ------------------ 126.664256056812 -- Geography example -- same 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 ST_GeographyFromText('SRID=4326;POINT(-72.1235 42.3521)') As gg1, ST_GeographyFromText('SRID=4326;LINESTRING(-72.1260 42.45, -72.123 42.1546)') As gg2 ) As foo ; spheroid_dist | sphere_dist ------------------+------------------ 123.802076746848 | 123.475736916397 ,, , , , 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 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 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) ST_MaxDistance Returns the 2-dimensional largest distance between two geometries in projected units. float ST_MaxDistance geometry g1 geometry g2 Some useful description here. Returns the 2-dimensional maximum distance between two linestrings 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 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) , ST_Distance_Sphere Returns minimum distance in meters between two lon/lat geometries. Uses a spherical earth and radius of 6370986 meters. Faster than ST_Distance_Spheroid , but less accurate. PostGIS versions prior to 1.5 only implemented for points. float ST_Distance_Sphere geometry geomlonlatA geometry geomlonlatB Returns minimum distance in meters between two lon/lat points. Uses a spherical earth and radius of 6370986 meters. Faster than , but less accurate. PostGIS Versions prior to 1.5 only implemented for points. This function currently does not look at the SRID of a geometry and will always assume its in WGS 84 long lat. 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. SELECT round(CAST(ST_Distance_Sphere(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 , ST_Distance_Spheroid Returns the minimum distance between two lon/lat geometries given a particular spheroid. PostGIS versions prior to 1.5 only support points. float ST_Distance_Spheroid geometry geomlonlatA geometry geomlonlatB spheroid measurement_spheroid Returns minimum distance in meters between two lon/lat geometries given a particular spheroid. See the explanation of spheroids given for . 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. SELECT round(CAST( ST_Distance_Spheroid(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_Distance_Sphere(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 , 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 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 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 | , 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 Returns true if the geometries are within the specified distance of one another. For Geometries: 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 (measure around WGS 84 spheroid), 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 --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.the_geom, h.hospital_name FROM schools s LEFT JOIN hospitals h ON ST_DWithin(s.the_geom, h.the_geom, 3000) ORDER BY s.gid, ST_Distance(s.the_geom, h.the_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.the_geom, h.the_geom, 3000) WHERE h.gid IS NULL; , ST_Equals Returns true if the given geometries represent the same geometry. Directionality is ignored. boolean ST_Equals geometry A geometry B 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 even if they are binary equal. &sfs_compliant; s2.1.1.2 &sqlmm_compliant; SQL-MM 3: 5.1.24 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) , , , ST_HasArc Returns true if a geometry or geometry collection contains a circular string boolean ST_HasArc geometry geomA Returns true if a geometry or geometry collection contains a circular string Availability: 1.2.3? &Z_support; &curve_support; 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 , 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 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. Do not call with a GEOMETRYCOLLECTION as an argument for geometry version. The geography version supports GEOMETRYCOLLECTION since its a thin wrapper around distance implementation. 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 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) 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 , 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 gg float ST_Length geography gg boolean use_spheroid For geometry: Returns the cartesian 2D 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. Geometry: Measurements are in the units of the spatial reference system of the geometry. Geography: Units are in meters and also acts as a Perimeter function for areal geogs. Currently for geometry this is an alias for ST_Length2D, but this may change to support higher dimensions. Currently applying this to a MULTI/POLYGON of type geography will give you the perimeter of the POLYGON/MULTIPOLYGON. This is not the case with the geometry implementation. 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. Return length in feet for line string. Note this is in feet because 2249 is Mass 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 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 ------------------+------------------ 34310.5703627305 | 34346.2060960742 (1 row) , , , , 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 Returns the 2-dimensional length of the geometry if it is a linestring or multi-linestring. This is an alias for ST_Length , 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 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; Return length in feet for a 3D cable. Note this is in feet because 2249 is Mass 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 , ST_Length_Spheroid Calculates the 2D or 3D length of a linestring/multilinestring 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_Length_Spheroid geometry a_linestring spheroid a_spheroid Calculates the length 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] Will return 0 for anything that is not a MULTILINESTRING or LINESTRING &Z_support; SELECT ST_Length_Spheroid( geometry_column, 'SPHEROID["GRS_1980",6378137,298.257222101]' ) FROM geometry_table; SELECT ST_Length_Spheroid( the_geom, sph_m ) As tot_len, ST_Length_Spheroid(ST_GeometryN(the_geom,1), sph_m) As len_line1, ST_Length_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 SELECT ST_Length_Spheroid( the_geom, sph_m ) As tot_len, ST_Length_Spheroid(ST_GeometryN(the_geom,1), sph_m) As len_line1, ST_Length_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 ------------------+-----------------+------------------ 85204.5259107402 | 13986.876097711 | 71217.6498130292 , , ST_Length2D_Spheroid Calculates the 2D length of a linestring/multilinestring 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_linestring spheroid a_spheroid Calculates the 2D length 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] Will return 0 for anything that is not a MULTILINESTRING or LINESTRING This is much like and except it will throw away the Z coordinate in calculations. 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 , , ST_3DLength_Spheroid Calculates the length of a geometry on an ellipsoid, taking the elevation into account. This is just an alias for ST_Length_Spheroid. float ST_3DLength_Spheroid geometry a_linestring spheroid a_spheroid Calculates the length of a geometry on an ellipsoid, taking the elevation into account. This is just an alias for ST_Length_Spheroid. Will return 0 for anything that is not a MULTILINESTRING or LINESTRING This function is just an alias for ST_Length_Spheroid. &Z_support; See 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 Returns the 2-dimensional longest line between the points of two geometries. Availability: 1.5.0 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 , , 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 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 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) , 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 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 --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 puffered 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 , , , ST_Perimeter Return the length measurement of the boundary of an ST_Surface or ST_MultiSurface value. (Polygon, Multipolygon) float ST_Perimeter geometry g1 Returns the 2D perimeter of the geometry if it is a ST_Surface, ST_MultiSurface (Polygon, Multipolygon). 0 is returned for non-areal geometries. For linestrings use ST_Length. Measurements are in the units of the spatial reference system of the geometry. 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 Return perimeter in feet for polygon and multipolygon. Note this is in feet because 2249 is Mass 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) 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 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 ST_3DPerimeter Returns the 3-dimensional perimeter of the geometry, if it is a polygon or multi-polygon. float ST_3DPerimeter geometry geomA 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; 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 , , ST_PointOnSurface Returns a POINT guaranteed to lie on the surface. geometry ST_PointOnSurface geometry g1 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; 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) , 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 int BoundaryNodeRule 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 intersectionMatrixPattern. 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 Version 3: same as version 2 bu 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). --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 , , , , ST_RelateMatch Returns true if intersectionMattrixPattern1 implies intersectionMatrixPattern2 boolean ST_RelateMatch text intersectionMatrix text intersectionMatrixPattern Takes intersectionMatrix and intersectionMatrixPattern and Returns true if the intersectionMatrix satisfies the intersectionMatrixPattern. For more information refer to . Availability: 2.0.0 - requires GEOS >= 3.3.0. 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); , ST_ShortestLine Returns the 2-dimensional shortest line between two geometries geometry ST_ShortestLine geometry g1 geometry g2 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 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) , , , 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 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 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 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 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 --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) , ,