<?xml version="1.0" encoding="UTF-8"?>
  <sect1 id="Spatial_Relationships_Measurements">
	<title>Spatial Relationships and Measurements</title>
	<refentry id="ST_3DClosestPoint">
		  <refnamediv>
			<refname>ST_3DClosestPoint</refname>

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

		  <refsynopsisdiv>
			<funcsynopsis>
			  <funcprototype>
				<funcdef>geometry <function>ST_3DClosestPoint</function></funcdef>

				<paramdef><type>geometry </type>
				<parameter>g1</parameter></paramdef>

				<paramdef><type>geometry </type>
				<parameter>g2</parameter></paramdef>
			  </funcprototype>
			</funcsynopsis>
		  </refsynopsisdiv>

		  <refsection>
			<title>Description</title>

			<para>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.
			</para>
			<para>&Z_support;</para>
			<!-- Optionally mention supports Polyhedral Surface  -->
			<para>&P_support;</para>
			<para>Availability: 2.0.0</para>
			<para>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.</para>
		  </refsection>

		  <refsection>
			<title>Examples</title>
				<informaltable>
					  <tgroup cols="1">
						<tbody>
						  <row>
							<entry><para>linestring and point -- both 3d and 2d closest point
					<programlisting>
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)
					</programlisting>
							  </para></entry>
						    </row>
						    <row>
							<entry><para>linestring and multipoint -- both 3d and 2d closest point
					<programlisting>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)
					</programlisting>
							  </para></entry>
						  </row>
						  <row>
						  <entry><para>Multilinestring and polygon both 3d and 2d closest point
					<programlisting>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)
             </programlisting>
							  </para></entry>
						  </row>
			</tbody>
		</tgroup>
	</informaltable>

		  </refsection>

		  <refsection>
			<title>See Also</title>

			<para><xref linkend="ST_AsEWKT" />, <xref linkend="ST_ClosestPoint"/>, <xref linkend="ST_3DDistance"/>, <xref linkend="ST_3DShortestLine"/></para>
		  </refsection>
	</refentry>
	<refentry id="ST_3DDistance">
	  <refnamediv>
		<refname>ST_3DDistance</refname>

		<refpurpose>For geometry type Returns the 3-dimensional cartesian minimum distance (based on spatial ref) between two geometries in
		projected units. </refpurpose>
	  </refnamediv>
	  <refsynopsisdiv>
		<funcsynopsis>
		  <funcprototype>
			<funcdef>float <function>ST_3DDistance</function></funcdef>

			<paramdef><type>geometry </type>
			<parameter>g1</parameter></paramdef>

			<paramdef><type>geometry </type>
			<parameter>g2</parameter></paramdef>
		  </funcprototype>
		</funcsynopsis>
	  </refsynopsisdiv>

	  <refsection>
		<title>Description</title>

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

		<para>&Z_support;</para>
		<!-- Optionally mention supports Polyhedral Surface  -->
		<para>&P_support;</para>
		<para>&sqlmm_compliant; SQL-MM ?</para>
        <para>&sfcgal_enhanced;</para>

		<para>Availability: 2.0.0</para>
		<para>Changed: 2.2.0 - In case of 2D and 3D, Z is no longer assumed to be 0 for missing Z.</para>
	  </refsection>

	  <refsection>
		<title>Examples</title>

		<programlisting>
-- 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
</programlisting>
<programlisting>
-- 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
</programlisting>
	  </refsection>

	  <refsection>
		<title>See Also</title>

		<para><xref linkend="ST_Distance"/>, <xref linkend="ST_3DClosestPoint"/>, <xref linkend="ST_3DDWithin"/>, <xref linkend="ST_3DMaxDistance" />, <xref linkend="ST_3DShortestLine"/>, <xref linkend="ST_Transform" /></para>
	  </refsection>
	</refentry>

	<refentry id="ST_3DDWithin">
	  <refnamediv>
		<refname>ST_3DDWithin</refname>

		<refpurpose>For 3d (z) geometry type Returns true if two geometries 3d distance is within number of units. </refpurpose>
	  </refnamediv>
	  <refsynopsisdiv>
		<funcsynopsis>
		  <funcprototype>
			<funcdef>boolean <function>ST_3DDWithin</function></funcdef>

			<paramdef><type>geometry </type>
			<parameter>g1</parameter></paramdef>

			<paramdef><type>geometry </type>
			<parameter>g2</parameter></paramdef>

			<paramdef><type>double precision </type>
			<parameter>distance_of_srid</parameter></paramdef>
		  </funcprototype>
		</funcsynopsis>
	  </refsynopsisdiv>

	  <refsection>
		<title>Description</title>

		<para>For geometry type returns true if the 3d distance between two objects is within distance_of_srid specified
		projected units (spatial ref units). </para>

        <para>&Z_support;</para>
        <!-- Optionally mention supports Polyhedral Surface  -->
        <para>&P_support;</para>
		<para>&sqlmm_compliant; SQL-MM ?</para>

		<para>Availability: 2.0.0</para>
	  </refsection>

	  <refsection>
		<title>Examples</title>

		<programlisting>
-- 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
</programlisting>
	  </refsection>

	  <refsection>
		<title>See Also</title>

		<para><xref linkend="ST_3DDistance"/>, <xref linkend="ST_Distance"/>, <xref linkend="ST_DWithin"/>, <xref linkend="ST_3DMaxDistance" />, <xref linkend="ST_Transform" /></para>
	  </refsection>
	</refentry>

<refentry id="ST_3DDFullyWithin">
	  <refnamediv>
		<refname>ST_3DDFullyWithin</refname>

		<refpurpose>Returns true if all of the 3D geometries are within the specified
		distance of one another. </refpurpose>
	  </refnamediv>

	  <refsynopsisdiv>
		<funcsynopsis>
		  <funcprototype>
			<funcdef>boolean <function>ST_3DDFullyWithin</function></funcdef>

			<paramdef><type>geometry </type>
			<parameter>g1</parameter></paramdef>

			<paramdef><type>geometry </type>
			<parameter>g2</parameter></paramdef>

			<paramdef><type>double precision </type>
			<parameter>distance</parameter></paramdef>
		  </funcprototype>
		</funcsynopsis>
	  </refsynopsisdiv>

	  <refsection>
		<title>Description</title>

		<para>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.</para>

		<note>
		  <para>This function call will automatically include a bounding box
		  comparison that will make use of any indexes that are available on
		  the geometries.</para>
		</note>

		<para>Availability: 2.0.0</para>
        <para>&Z_support;</para>
        <!-- Optionally mention supports Polyhedral Surface  -->
        <para>&P_support;</para>

	  </refsection>

	  <refsection>
		<title>Examples</title>
		<programlisting>
		-- 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 </programlisting>
	  </refsection>

	  <refsection>
		<title>See Also</title>

		<para><xref linkend="ST_3DMaxDistance"/>, <xref linkend="ST_3DDWithin"/>, <xref linkend="ST_DWithin"/>, <xref linkend="ST_DFullyWithin"/></para>
	  </refsection>
	</refentry>

	<refentry id="ST_3DIntersects">
		<refnamediv>
			<refname>ST_3DIntersects</refname>

			<refpurpose>Returns TRUE if the Geometries "spatially
			intersect" in 3d - only for points, linestrings, polygons, polyhedral surface (area).  With SFCGAL backend enabled also supports TINS
			</refpurpose>
		</refnamediv>
		<refsynopsisdiv>
			<funcsynopsis>
				<funcprototype>
					<funcdef>boolean <function>ST_3DIntersects</function></funcdef>
					<paramdef>
						<type>geometry</type>
						<parameter>geomA</parameter>
					</paramdef>
					<paramdef>
						<type>geometry</type>
						<parameter>geomB</parameter>
					</paramdef>
				</funcprototype>
			</funcsynopsis>
		</refsynopsisdiv>
		<refsection>
			<title>Description</title>
			<para>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.</para>



			<para>Availability: 2.0.0</para>
			<note>
			  <para>This function call will automatically include a bounding box
			  comparison that will make use of any indexes that are available on the
			  geometries.</para>
			</note>

			<note><para>In order to take advantage of support for TINS, you need to enable the SFCGAL backend.  This can be done at session time with: <code>set postgis.backend = sfcgal;</code> or at the database or system level.  Database level can be done with <code>ALTER DATABASE gisdb SET postgis.backend = sfcgal;</code>.</para></note>
			<para>&Z_support;</para>
			<!-- Optionally mention supports Polyhedral Surface  -->
			<para>&P_support;</para>
			<para>&T_support;</para>
			<para>&sfcgal_enhanced;</para>
			<para>&sqlmm_compliant; SQL-MM 3: ?</para>
		</refsection>
		<refsection>
		<title>Geometry Examples</title>
<programlisting>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)
		</programlisting>
		</refsection>

		<refsection><title>TIN Examples</title>
		    <programlisting>set postgis.backend = sfcgal;
SELECT ST_3DIntersects('TIN(((0 0,1 0,0 1,0 0)))'::geometry, 'POINT(.1 .1)'::geometry);
 st_3dintersects
-----------------
 t</programlisting></refsection>

		<refsection>
			<title>See Also</title>
			<para><xref linkend="ST_Intersects"/></para>
		</refsection>
	</refentry>

	<refentry id="ST_3DLongestLine">
	  <refnamediv>
		<refname>ST_3DLongestLine</refname>

		<refpurpose>Returns the 3-dimensional longest line between two geometries</refpurpose>
	  </refnamediv>

	  <refsynopsisdiv>
		<funcsynopsis>
		  <funcprototype>
			<funcdef>geometry <function>ST_3DLongestLine</function></funcdef>

			<paramdef><type>geometry </type>
			<parameter>g1</parameter></paramdef>

			<paramdef><type>geometry </type>
			<parameter>g2</parameter></paramdef>
		  </funcprototype>
		</funcsynopsis>
	  </refsynopsisdiv>

	  <refsection>
		<title>Description</title>

		<para>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 <xref linkend="ST_3DMaxDistance" /> returns for g1 and g2.
		</para>

		<para>Availability: 2.0.0</para>
		<para>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.</para>
		<para>&Z_support;</para>
		<!-- Optionally mention supports Polyhedral Surface  -->
		<para>&P_support;</para>
	  </refsection>

	  <refsection>
		<title>Examples</title>
				<informaltable>
					  <tgroup cols="1">
						<tbody>
						  <row>
							<entry><para>linestring and point -- both 3d and 2d longest line
					<programlisting>
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)
					</programlisting>
							  </para></entry>
						    </row>
						    <row>
							<entry><para>linestring and multipoint -- both 3d and 2d longest line
					<programlisting>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)
					</programlisting>
							  </para></entry>
						  </row>
						  <row>
						  <entry><para>Multilinestring and polygon both 3d and 2d longest line
					<programlisting>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)
             </programlisting>
							  </para></entry>
						  </row>
			</tbody>
		</tgroup>
	</informaltable>

	  </refsection>

	  <refsection>
		<title>See Also</title>

		<para><xref linkend="ST_3DClosestPoint"/>, <xref linkend="ST_3DDistance"/>, <xref linkend="ST_LongestLine"/>, <xref linkend="ST_3DShortestLine"/>, <xref linkend="ST_3DMaxDistance"/></para>
	  </refsection>
	</refentry>

	<refentry id="ST_3DMaxDistance">
	  <refnamediv>
		<refname>ST_3DMaxDistance</refname>

		<refpurpose>For geometry type Returns the 3-dimensional cartesian maximum distance (based on spatial ref) between two geometries in
		projected units.  </refpurpose>
	  </refnamediv>
	  <refsynopsisdiv>
		<funcsynopsis>
		  <funcprototype>
			<funcdef>float <function>ST_3DMaxDistance</function></funcdef>

			<paramdef><type>geometry </type>
			<parameter>g1</parameter></paramdef>

			<paramdef><type>geometry </type>
			<parameter>g2</parameter></paramdef>
		  </funcprototype>
		</funcsynopsis>
	  </refsynopsisdiv>

	  <refsection>
		<title>Description</title>

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

        <para>&Z_support;</para>
        <!-- Optionally mention supports Polyhedral Surface  -->
        <para>&P_support;</para>

		<para>Availability: 2.0.0</para>
		<para>Changed: 2.2.0 - In case of 2D and 3D, Z is no longer assumed to be 0 for missing Z.</para>
	  </refsection>

	  <refsection>
		<title>Examples</title>

		<programlisting>
-- 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
</programlisting>
	  </refsection>

	  <refsection>
		<title>See Also</title>

		<para><xref linkend="ST_Distance"/>, <xref linkend="ST_3DDWithin"/>, <xref linkend="ST_3DMaxDistance" />, <xref linkend="ST_Transform" /></para>
	  </refsection>
	</refentry>
	<refentry id="ST_3DShortestLine">
	  <refnamediv>
		<refname>ST_3DShortestLine</refname>

		<refpurpose>Returns the 3-dimensional shortest line between two geometries</refpurpose>
	  </refnamediv>

	  <refsynopsisdiv>
		<funcsynopsis>
		  <funcprototype>
			<funcdef>geometry <function>ST_3DShortestLine</function></funcdef>

			<paramdef><type>geometry </type>
			<parameter>g1</parameter></paramdef>

			<paramdef><type>geometry </type>
			<parameter>g2</parameter></paramdef>
		  </funcprototype>
		</funcsynopsis>
	  </refsynopsisdiv>

	  <refsection>
		<title>Description</title>

		<para>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 <xref linkend="ST_3DDistance" /> returns for g1 and g2.
		</para>

		<para>Availability: 2.0.0</para>
		<para>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.</para>
		<para>&Z_support;</para>
		<!-- Optionally mention supports Polyhedral Surface  -->
		<para>&P_support;</para>
	  </refsection>

	  <refsection>
		<title>Examples</title>
				<informaltable>
					  <tgroup cols="1">
						<tbody>
						  <row>
							<entry><para>linestring and point -- both 3d and 2d shortest line
					<programlisting>
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)
					</programlisting>
							  </para></entry>
						    </row>
						    <row>
							<entry><para>linestring and multipoint -- both 3d and 2d shortest line
					<programlisting>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)
					</programlisting>
							  </para></entry>
						  </row>
						  <row>
						  <entry><para>Multilinestring and polygon both 3d and 2d shortest line
					<programlisting>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)
             </programlisting>
							  </para></entry>
						  </row>
			</tbody>
		</tgroup>
	</informaltable>

	  </refsection>

	  <refsection>
		<title>See Also</title>

		<para><xref linkend="ST_3DClosestPoint"/>, <xref linkend="ST_3DDistance"/>, <xref linkend="ST_LongestLine"/>, <xref linkend="ST_ShortestLine"/>, <xref linkend="ST_3DMaxDistance"/></para>
	  </refsection>
	</refentry>
	<refentry id="ST_Area">
		<refnamediv>
		  <refname>ST_Area</refname>

		  <refpurpose>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.</refpurpose>
		</refnamediv>
		<refsynopsisdiv>
		  <funcsynopsis>
			<funcprototype>
			  <funcdef>float <function>ST_Area</function></funcdef>
				<paramdef><type>geometry </type><parameter>g1</parameter></paramdef>
			</funcprototype>

			<funcprototype>
			  <funcdef>float <function>ST_Area</function></funcdef>
				<paramdef><type>geography </type><parameter>geog</parameter></paramdef>
				<paramdef choice="opt"><type>boolean </type><parameter>use_spheroid=true</parameter></paramdef>
			</funcprototype>
		  </funcsynopsis>
		</refsynopsisdiv>
		<refsection>
			<title>Description</title>

			<para>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).
		  </para>
			<para>Enhanced: 2.0.0 - support for 2D polyhedral surfaces was introduced.</para>
			<para>Enhanced: 2.2.0 - measurement on spheroid performed with GeographicLib for improved accuracy and robustness.  Requires Proj &gt;= 4.9.0 to take advantage of the new feature.</para>
			<para>&sfs_compliant;</para>
			<para>&sqlmm_compliant; SQL-MM 3: 8.1.2, 9.5.3</para>
			<para>&P_support;</para>
			<note><para>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.</para></note>
                        <para>&sfcgal_enhanced;</para>
		</refsection>

		  <refsection>
			<title>Examples</title>
			<para>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 </para>
			<programlisting>
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
</programlisting>
<para>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 </para>
<programlisting>

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
			</programlisting>

<para>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.</para>
<programlisting>

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;</programlisting>
		  </refsection>
		<refsection>
			<title>See Also</title>
			<para><xref linkend="ST_GeomFromText" />, <xref linkend="ST_GeographyFromText" />, <xref linkend="ST_SetSRID" />, <xref linkend="ST_Transform" /></para>
		</refsection>
	</refentry>

	<refentry id="ST_Azimuth">
		<refnamediv>
		  <refname>ST_Azimuth</refname>

		  <refpurpose>Returns the north-based azimuth as the angle in radians measured clockwise from the vertical on pointA to pointB.</refpurpose>
		</refnamediv>
		<refsynopsisdiv>
		  <funcsynopsis>
			<funcprototype>
			  <funcdef>float <function>ST_Azimuth</function></funcdef>
			  <paramdef><type>geometry </type><parameter>pointA</parameter></paramdef>
			  <paramdef><type>geometry </type><parameter>pointB</parameter></paramdef>
			</funcprototype>
			<funcprototype>
			  <funcdef>float <function>ST_Azimuth</function></funcdef>
			  <paramdef><type>geography </type><parameter>pointA</parameter></paramdef>
			  <paramdef><type>geography </type><parameter>pointB</parameter></paramdef>
			</funcprototype>
		  </funcsynopsis>
		</refsynopsisdiv>
		<refsection>
			<title>Description</title>

			<para>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 = &#x03C0;/2; South = &#x03C0;; West = 3&#x03C0;/2.</para>
			<para>For the geography type, the forward azimuth is solved as part of the inverse geodesic problem.</para>
			<para>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.</para>

			<para>Availability: 1.1.0</para>
			<para>Enhanced: 2.0.0 support for geography was introduced.</para>
			<para>Enhanced: 2.2.0 measurement on spheroid performed with GeographicLib for improved accuracy and robustness.  Requires Proj &gt;= 4.9.0 to take advantage of the new feature.</para>
			<para>Azimuth is especially useful in conjunction with ST_Translate for shifting an object along its perpendicular axis. See
				 upgis_lineshift <ulink url="http://trac.osgeo.org/postgis/wiki/UsersWikiplpgsqlfunctions">Plpgsqlfunctions PostGIS wiki section</ulink> for example of this.</para>
		</refsection>

		<refsection>
		<title>Examples</title>
		<para>Geometry Azimuth in degrees </para>
<programlisting>
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
</programlisting>
		<informaltable>
		  <tgroup cols="2">
			<tbody>
				<row>
				<entry><para><informalfigure>
					<mediaobject>
					  <imageobject>
						<imagedata fileref="images/st_azimuth01.png" />
					  </imageobject>
					  <caption><para>Green: the start Point(25,45) with its vertical. Yellow: degA_B as the path to travel (azimuth).</para></caption>
					</mediaobject>
				  </informalfigure>
				</para></entry>
				<entry><para><informalfigure>
					<mediaobject>
					  <imageobject>
						<imagedata fileref="images/st_azimuth02.png" />
					  </imageobject>
					  <caption><para>Green: the start Point(75,100) with its vertical. Yellow: degB_A as the path to travel (azimuth).</para></caption>
					</mediaobject>
				  </informalfigure>
				</para></entry>
				</row>
			</tbody>
			</tgroup>
		</informaltable>
		</refsection>
		<refsection>
			<title>See Also</title>
			<para><xref linkend="ST_Point" />, <xref linkend="ST_Translate" />, <xref linkend="ST_Project" />, <ulink url="http://www.postgresql.org/docs/current/interactive/functions-math.html">PostgreSQL Math Functions</ulink></para>
		</refsection>

  </refentry>

  <refentry id="ST_Centroid">
	<refnamediv>
	  <refname>ST_Centroid</refname>

	  <refpurpose>Returns the geometric center of a geometry.</refpurpose>
	</refnamediv>

	<refsynopsisdiv>
	  <funcsynopsis>
		<funcprototype>
		  <funcdef>geometry <function>ST_Centroid</function></funcdef>

		  <paramdef><type>geometry </type>
		  <parameter>g1</parameter></paramdef>
		</funcprototype>
	  </funcsynopsis>
	</refsynopsisdiv>

	<refsection>
	  <title>Description</title>

	  <para>Computes the geometric center of a geometry, or equivalently,
	  the center of mass of the geometry as a <varname>POINT</varname>. For
	  [<varname>MULTI</varname>]<varname>POINT</varname>s, this is computed
	  as the arithmetic mean of the input coordinates. For
	  [<varname>MULTI</varname>]<varname>LINESTRING</varname>s, this is
	  computed as the weighted length of each line segment. For
	  [<varname>MULTI</varname>]<varname>POLYGON</varname>s, "weight" is
	  thought in terms of area. If an empty geometry is supplied, an empty
	  <varname>GEOMETRYCOLLECTION</varname> is returned. If
	  <varname>NULL</varname> is supplied, <varname>NULL</varname> is
	  returned.
	  If <varname>CIRCULARSTRING</varname> or <varname>COMPOUNDCURVE</varname>
	  are supplied, they are converted to linestring wtih CurveToLine first,
	  then same than for  <varname>LINESTRING</varname>
	  </para>
	  <para>New in 2.3.0 : support <varname>CIRCULARSTRING</varname> and <varname>COMPOUNDCURVE</varname> (using CurveToLine)</para>

	  <para>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).</para>

	  <para>&sfs_compliant;</para>
	  <para>&sqlmm_compliant; SQL-MM 3: 8.1.4, 9.5.5</para>
	</refsection>

	<refsection>
	  <title>Examples</title>

	  <para>In each of the following illustrations, the blue dot represents
	  the centroid of the source geometry.</para>

	  <informaltable>
		<tgroup cols="2">
		  <tbody>
			<row>
			  <entry><para><informalfigure>
				  <mediaobject>
					<imageobject>
					  <imagedata fileref="images/st_centroid01.png" />
					</imageobject>

					<caption><para>Centroid of a
					<varname>MULTIPOINT</varname></para></caption>
				  </mediaobject>
				</informalfigure></para></entry>

			  <entry><para><informalfigure>
				  <mediaobject>
					<imageobject>
					  <imagedata fileref="images/st_centroid02.png" />
					</imageobject>

					<caption><para>Centroid of a
					<varname>LINESTRING</varname></para></caption>
				  </mediaobject>
				</informalfigure></para></entry>
			</row>

			<row>
			  <entry><para><informalfigure>
				  <mediaobject>
					<imageobject>
					  <imagedata fileref="images/st_centroid03.png" />
					</imageobject>

					<caption><para>Centroid of a
					<varname>POLYGON</varname></para></caption>
				  </mediaobject>
				</informalfigure></para></entry>

			  <entry><para><informalfigure>
				  <mediaobject>
					<imageobject>
					  <imagedata fileref="images/st_centroid04.png" />
					</imageobject>

					<caption><para>Centroid of a
					<varname>GEOMETRYCOLLECTION</varname></para></caption>
				  </mediaobject>
				</informalfigure></para></entry>
			</row>
		  </tbody>
		</tgroup>
	  </informaltable>

	  <programlisting>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)

</programlisting>
	</refsection>

	<refsection>
	  <title>See Also</title>

	  <para><xref linkend="ST_PointOnSurface" /></para>
	</refsection>
  </refentry>

<refentry id="ST_ClosestPoint">
	  <refnamediv>
		<refname>ST_ClosestPoint</refname>

		<refpurpose>Returns the 2-dimensional point on g1 that is closest to g2.  This is the first point of
			the shortest line.</refpurpose>
	  </refnamediv>

	  <refsynopsisdiv>
		<funcsynopsis>
		  <funcprototype>
			<funcdef>geometry <function>ST_ClosestPoint</function></funcdef>

			<paramdef><type>geometry </type>
			<parameter>g1</parameter></paramdef>

			<paramdef><type>geometry </type>
			<parameter>g2</parameter></paramdef>
		  </funcprototype>
		</funcsynopsis>
	  </refsynopsisdiv>

	  <refsection>
		<title>Description</title>

		<para>Returns the 2-dimensional point on g1 that is closest to g2.  This is the first point of
			the shortest line.
		</para>
		<note><para>If you have a 3D Geometry, you may prefer to use <xref linkend="ST_3DClosestPoint" />.</para></note>
		<para>Availability: 1.5.0</para>
	  </refsection>

	  <refsection>
		<title>Examples</title>
			<informaltable>
				  <tgroup cols="2">
					<tbody>
					  <row>
						<entry><para><informalfigure>
							<mediaobject>
							  <imageobject>
								<imagedata fileref="images/st_closestpoint01.png" />
							  </imageobject>
							  <caption><para>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.</para></caption>
							</mediaobject>
						  </informalfigure>
				<programlisting>
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)
				</programlisting>
						  </para></entry>

						<entry><para><informalfigure>
							<mediaobject>
							  <imageobject>
								<imagedata fileref="images/st_closestpoint02.png" />
							  </imageobject>
							  <caption><para>closest point on polygon A to polygon B</para></caption>
							</mediaobject>
						  </informalfigure>
				<programlisting>
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)
				</programlisting>
						</para></entry>
					  </row>
		</tbody>
	</tgroup>
</informaltable>

	  </refsection>

	  <refsection>
		<title>See Also</title>

		<para><xref linkend="ST_3DClosestPoint" />,<xref linkend="ST_Distance"/>, <xref linkend="ST_LongestLine"/>, <xref linkend="ST_ShortestLine"/>, <xref linkend="ST_MaxDistance"/></para>
	  </refsection>
</refentry>

    <refentry id="ST_ClusterDBSCAN">
	  <refnamediv>
		<refname>ST_ClusterDBSCAN</refname>

        <refpurpose>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.</refpurpose>
    </refnamediv>

	  <refsynopsisdiv>
		<funcsynopsis>
		  <funcprototype>
			<funcdef>integer <function>ST_ClusterDBSCAN</function></funcdef>

			<paramdef><type>geometry winset </type>
			<parameter>geom</parameter></paramdef>

			<paramdef><type>float8 </type>
			<parameter>eps</parameter></paramdef>

			<paramdef><type>integer </type>
			<parameter>minpoints</parameter></paramdef>
		  </funcprototype>
		</funcsynopsis>
	  </refsynopsisdiv>

	  <refsection>
      <title>Description</title>

	  <para>
		  Returns cluster number for each input geometry, based on a 2D implementation of the
          <ulink url="https://en.wikipedia.org/wiki/DBSCAN">Density-based spatial clustering of applications with noise (DBSCAN)</ulink>
		  algorithm.  Unlike <xref linkend="ST_ClusterKMeans" />, it does not require the number of clusters to be specified, but instead
		  uses the desired distance (<varname>eps</varname>) and density(<varname>minpoints</varname>) parameters to construct each cluster.
	  </para>

	  <para>
		  An input geometry will be added to a cluster if it is either:
		  <itemizedlist>
              <listitem>
                  <para>
                      A "core" geometry, that is within <varname>eps</varname> distance (Cartesian) of at least <varname>minpoints</varname> input geometries (including itself) or
                  </para>
			  </listitem>
			  <listitem>
                  <para>
                      A "border" geometry, that is within <varname>eps</varname> distance of a core geometry.
                  </para>
			  </listitem>
		  </itemizedlist>
		</para>

		<para>
		  Note that border geometries may be within <varname>eps</varname> 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 <varname>minpoints</varname> 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.
	  </para>

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

      <para>Availability: 2.3.0 - requires GEOS </para>
    </refsection>

    <refsection>
      <title>Examples</title>
      <para>
          Assigning a cluster number to each parcel point:
      </para>
		    <programlisting>
SELECT parcel_id, ST_ClusterDBSCAN(geom, eps := 0.5, minpoints := 5) over () AS cid
FROM parcels;
</programlisting>


        <para>
            Combining parcels with the same cluster number into a single geometry. This uses named argument calling
        </para>
		    <programlisting>
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;
    </programlisting>
    </refsection>

    <refsection>
		  <title>See Also</title>
          <para>
              <xref linkend="ST_ClusterKMeans"/>,
              <xref linkend="ST_ClusterIntersecting"/>,
              <xref linkend="ST_ClusterWithin"/>
          </para>
	  </refsection>

    </refentry>

    <refentry id="ST_ClusterIntersecting">
      <refnamediv>
        <refname>ST_ClusterIntersecting</refname>

        <refpurpose>Aggregate.  Returns an array with the connected components of a set of geometries</refpurpose>
      </refnamediv>

      <refsynopsisdiv>
        <funcsynopsis>
          <funcprototype>
            <funcdef>geometry[] <function>ST_ClusterIntersecting</function></funcdef>
            <paramdef><type>geometry set</type> <parameter>g</parameter></paramdef>
          </funcprototype>
        </funcsynopsis>
      </refsynopsisdiv>

      <refsection>
        <title>Description</title>

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

        <para>Availability: 2.2.0 - requires GEOS </para>
      </refsection>

      <refsection>
        <title>Examples</title>
        <programlisting>
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))
        </programlisting>
      </refsection>
      <refsection>
        <title>See Also</title>
        <para>
            <xref linkend="ST_ClusterDBSCAN" />,
            <xref linkend="ST_ClusterKMeans" />,
            <xref linkend="ST_ClusterWithin" />
        </para>
      </refsection>

    </refentry>


	<refentry id="ST_ClusterKMeans">
	  <refnamediv>
		<refname>ST_ClusterKMeans</refname>

		<refpurpose>Windowing function that returns integer id for the cluster each input geometry is in.</refpurpose>
	  </refnamediv>

	  <refsynopsisdiv>
		<funcsynopsis>
		  <funcprototype>
			<funcdef>integer <function>ST_ClusterKMeans</function></funcdef>

			<paramdef><type>geometry winset </type>
			<parameter>geom</parameter></paramdef>

			<paramdef><type>integer </type>
			<parameter>number_of_clusters</parameter></paramdef>
		  </funcprototype>
		</funcsynopsis>
	  </refsynopsisdiv>

	  <refsection>
      <title>Description</title>

      <para>Returns 2D distance based
        <ulink url="https://en.wikipedia.org/wiki/K-means_clustering">k-means</ulink>
        cluster number for each input geometry. The distance used for clustering is the
        distance between the centroids of the geometries.
      </para>
      <para>Availability: 2.3.0 - requires GEOS </para>
    </refsection>

    <refsection>
      <title>Examples</title>
		<para>Generate dummy set of parcels for examples</para>
		<programlisting>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;
</programlisting>

	<informaltable>
			  <tgroup cols="1">
				<tbody>
				  <row>
					<entry>
						<para><informalfigure>
						<mediaobject>
						  <imageobject>
							<imagedata fileref="images/st_clusterkmeans01.png" />
						  </imageobject>
						  <caption><para>Original Parcels</para></caption>
						</mediaobject>
						</informalfigure>
						</para>
					</entry>
					<entry><para><informalfigure>
						<mediaobject>
						  <imageobject>
							<imagedata fileref="images/st_clusterkmeans02.png" />
						  </imageobject>
						  <caption><para>Parcels color-coded by cluster number (cid)</para></caption>
						</mediaobject>
					  </informalfigure>
						<programlisting>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)</programlisting>
					</para></entry>
				  </row>
			</tbody>
			</tgroup>
		</informaltable>

		    <programlisting> -- 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)</programlisting>

    </refsection>

    <refsection>
		  <title>See Also</title>
          <para>
              <xref linkend="ST_ClusterDBSCAN"/>,
              <xref linkend="ST_ClusterIntersecting" />,
              <xref linkend="ST_ClusterWithin" />, <xref linkend="ST_Subdivide" />
          </para>
	  </refsection>
	</refentry>

	<refentry id="ST_ClusterWithin">
      <refnamediv>
        <refname>ST_ClusterWithin</refname>

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

      <refsynopsisdiv>
        <funcsynopsis>
          <funcprototype>
            <funcdef>geometry[] <function>ST_ClusterWithin</function></funcdef>
            <paramdef><type>geometry set </type> <parameter>g</parameter></paramdef>
            <paramdef><type>float8 </type> <parameter>distance</parameter></paramdef>
          </funcprototype>
        </funcsynopsis>
      </refsynopsisdiv>

      <refsection>
        <title>Description</title>

        <para>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.)</para>

        <para>Availability: 2.2.0 - requires GEOS</para>
      </refsection>

      <refsection>
        <title>Examples</title>
        <programlisting>
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))
        </programlisting>
      </refsection>
      <refsection>
        <title>See Also</title>
        <para>
          <xref linkend="ST_ClusterDBSCAN" />,
          <xref linkend="ST_ClusterKMeans" />,
          <xref linkend="ST_ClusterIntersecting" />
        </para>
      </refsection>

    </refentry>

  <refentry id="ST_Contains">
	  <refnamediv>
		<refname>ST_Contains</refname>

		<refpurpose>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. </refpurpose>
	  </refnamediv>

	  <refsynopsisdiv>
		<funcsynopsis>
		  <funcprototype>
			<funcdef>boolean <function>ST_Contains</function></funcdef>

			<paramdef><type>geometry </type>
			<parameter>geomA</parameter></paramdef>

			<paramdef><type>geometry </type>
			<parameter>geomB</parameter></paramdef>
		  </funcprototype>
		</funcsynopsis>
	  </refsynopsisdiv>

	  <refsection>
		<title>Description</title>

		<para>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 <xref linkend="ST_ContainsProperly" /> where geometry
		A does not Contain Properly itself.</para>

		<para>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.</para>

		<para>Performed by the GEOS module</para>
		<para>Enhanced: 2.3.0 Enhancement to PIP short-circuit extended to support MultiPoints with few points. Prior versions only supported point in polygon.</para>

		<important>
		  <para>Do not call with a <varname>GEOMETRYCOLLECTION</varname> as an argument</para>
		</important>

		<important>
		  <para>Do not use this function with invalid geometries. You will get unexpected results.</para>
		</important>

		<para>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.</para>

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

		<para>&sfs_compliant; s2.1.1.2 // s2.1.13.3
		- same as within(geometry B, geometry A)</para>
		<para>&sqlmm_compliant;	SQL-MM 3: 5.1.31</para>

		<para>There are certain subtleties to ST_Contains and ST_Within that are not intuitively obvious.
			For details check out <ulink url="http://lin-ear-th-inking.blogspot.com/2007/06/subtleties-of-ogc-covers-spatial.html">Subtleties of OGC Covers, Contains, Within</ulink></para>
	  </refsection>

	  <refsection>
		<title>Examples</title>

		<para>The <function>ST_Contains</function> predicate returns <varname>TRUE</varname> in all the following illustrations.</para>

		<informaltable>
		  <tgroup cols="2">
			<tbody>
			  <row>
				<entry><para><informalfigure>
					<mediaobject>
					  <imageobject>
						<imagedata fileref="images/st_contains01.png" />
					  </imageobject>

					  <caption><para><varname>LINESTRING</varname> / <varname>MULTIPOINT</varname></para></caption>
					</mediaobject>
				  </informalfigure></para></entry>

				<entry><para><informalfigure>
					<mediaobject>
					  <imageobject>
						<imagedata fileref="images/st_contains02.png" />
					  </imageobject>

					  <caption><para><varname>POLYGON</varname> / <varname>POINT</varname></para></caption>
					</mediaobject>
				  </informalfigure></para></entry>
			  </row>
			  <row>
				<entry><para><informalfigure>
					<mediaobject>
					  <imageobject>
						<imagedata fileref="images/st_contains03.png" />
					  </imageobject>

					  <caption><para><varname>POLYGON</varname> / <varname>LINESTRING</varname></para></caption>
					</mediaobject>
				  </informalfigure></para></entry>

				<entry><para><informalfigure>
					<mediaobject>
					  <imageobject>
						<imagedata fileref="images/st_contains04.png" />
					  </imageobject>

					  <caption><para><varname>POLYGON</varname> / <varname>POLYGON</varname></para></caption>
					</mediaobject>
				  </informalfigure></para></entry>
			  </row>
			</tbody>
		  </tgroup>
		</informaltable>

		<para>The <function>ST_Contains</function> predicate returns <varname>FALSE</varname> in all the following illustrations.</para>

		<informaltable>
		  <tgroup cols="2">
			<tbody>
			  <row>
				<entry><para><informalfigure>
					<mediaobject>
					  <imageobject>
						<imagedata fileref="images/st_contains05.png" />
					  </imageobject>

					  <caption><para><varname>POLYGON</varname> / <varname>MULTIPOINT</varname></para></caption>
					</mediaobject>
				  </informalfigure></para></entry>

				<entry><para><informalfigure>
					<mediaobject>
					  <imageobject>
						<imagedata fileref="images/st_contains06.png" />
					  </imageobject>

					  <caption><para><varname>POLYGON</varname> / <varname>LINESTRING</varname></para></caption>
					</mediaobject>
				  </informalfigure></para></entry>
			  </row>
			</tbody>
		  </tgroup>
		</informaltable>

		  <programlisting>
-- 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

 </programlisting>
	  </refsection>

	  <refsection>
		<title>See Also</title>
		<para><xref linkend="ST_Boundary" />, <xref linkend="ST_ContainsProperly" />, <xref linkend="ST_Covers" />, <xref linkend="ST_CoveredBy" />, <xref linkend="ST_Equals"/>, <xref linkend="ST_Within"/></para>
	  </refsection>
 </refentry>

 <refentry id="ST_ContainsProperly">
	  <refnamediv>
		<refname>ST_ContainsProperly</refname>

		<refpurpose>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.</refpurpose>
	  </refnamediv>

	  <refsynopsisdiv>
		<funcsynopsis>
		  <funcprototype>
			<funcdef>boolean <function>ST_ContainsProperly</function></funcdef>

			<paramdef><type>geometry </type>
			<parameter>geomA</parameter></paramdef>

			<paramdef><type>geometry </type>
			<parameter>geomB</parameter></paramdef>
		  </funcprototype>
		</funcsynopsis>
	  </refsynopsisdiv>

	  <refsection>
		<title>Description</title>

		<para>Returns true if B intersects the interior of A but not the boundary (or exterior).</para>

		<para>A does not contain properly itself, but does contain itself.</para>
		<para>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 <xref linkend="ST_Relate" /></para>

		<note>
		  <para>From JTS docs slightly reworded: The advantage to using this predicate over <xref linkend="ST_Contains" /> and <xref linkend="ST_Intersects" /> is that it can be computed
	  efficiently, with no need to compute topology at individual points.</para>
		<para>
			 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.
	 </para>
		</note>

		<para>Availability: 1.4.0 - requires GEOS &gt;= 3.1.0.</para>

		<important>
		  <para>Do not call with a <varname>GEOMETRYCOLLECTION</varname> as an argument</para>
		</important>

		<important>
		  <para>Do not use this function with invalid geometries. You will get unexpected results.</para>
		</important>

		<para>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.</para>

	  </refsection>

	  <refsection>
		<title>Examples</title>
		  <programlisting>
	--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
 </programlisting>
	  </refsection>

	  <refsection>
		<title>See Also</title>
		<para><xref linkend="ST_GeometryType" />, <xref linkend="ST_Boundary" />, <xref linkend="ST_Contains" />, <xref linkend="ST_Covers" />, <xref linkend="ST_CoveredBy" />, <xref linkend="ST_Equals"/>, <xref linkend="ST_Relate" />, <xref linkend="ST_Within"/></para>
	  </refsection>
 </refentry>

  <refentry id="ST_Covers">
	  <refnamediv>
		<refname>ST_Covers</refname>

		<refpurpose>Returns 1 (TRUE) if no point in Geometry B is outside
			Geometry A</refpurpose>
	  </refnamediv>

	  <refsynopsisdiv>
		<funcsynopsis>
		  <funcprototype>
			<funcdef>boolean <function>ST_Covers</function></funcdef>

			<paramdef><type>geometry </type>
			<parameter>geomA</parameter></paramdef>

			<paramdef><type>geometry </type>
			<parameter>geomB</parameter></paramdef>
		  </funcprototype>
		  <funcprototype>
			<funcdef>boolean <function>ST_Covers</function></funcdef>

			<paramdef><type>geography </type>
			<parameter>geogpolyA</parameter></paramdef>

			<paramdef><type>geography </type>
			<parameter>geogpointB</parameter></paramdef>
		  </funcprototype>
		</funcsynopsis>
	  </refsynopsisdiv>

	  <refsection>
		<title>Description</title>

		  <para>Returns 1 (TRUE) if no point in Geometry/Geography B is outside
			Geometry/Geography A</para>

		<para>Performed by the GEOS module</para>

		<important>
		  <para>Do not call with a <varname>GEOMETRYCOLLECTION</varname> as an argument</para>
		</important>

		<important>
		  <para>For geography only Polygon covers point is supported.</para>
		</important>

		<important>
		  <para>Do not use this function with invalid geometries. You will get unexpected results.</para>
		</important>

		<para>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.</para>

		<para>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.</para>
		<para>Availability: 1.5 - support for geography was introduced. </para>
		<para>Availability: 1.2.2 - requires GEOS &gt;= 3.0</para>

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

		<para>Not an OGC standard, but Oracle has it too.</para>
		<para>There are certain subtleties to ST_Contains and ST_Within that are not intuitively obvious.
			For details check out <ulink url="http://lin-ear-th-inking.blogspot.com/2007/06/subtleties-of-ogc-covers-spatial.html">Subtleties of OGC Covers, Contains, Within</ulink></para>
	  </refsection>

	  <refsection>
		<title>Examples</title>
			<para> Geometry example </para>
		  <programlisting>
	--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)	</programlisting>
		<para>Geeography Example</para>
		<programlisting>
-- 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
		</programlisting>
	  </refsection>

	  <refsection>
		<title>See Also</title>
		<para><xref linkend="ST_Contains"/>, <xref linkend="ST_CoveredBy" />, <xref linkend="ST_Within"/></para>
	  </refsection>
 </refentry>

  <refentry id="ST_CoveredBy">
	  <refnamediv>
		<refname>ST_CoveredBy</refname>

		<refpurpose>Returns 1 (TRUE) if no point in Geometry/Geography A is outside
			Geometry/Geography B</refpurpose>
	  </refnamediv>

	  <refsynopsisdiv>
		<funcsynopsis>
		  <funcprototype>
			<funcdef>boolean <function>ST_CoveredBy</function></funcdef>

			<paramdef><type>geometry </type>
			<parameter>geomA</parameter></paramdef>

			<paramdef><type>geometry </type>
			<parameter>geomB</parameter></paramdef>
		  </funcprototype>

		  <funcprototype>
			<funcdef>boolean <function>ST_CoveredBy</function></funcdef>

			<paramdef><type>geography </type>
			<parameter>geogA</parameter></paramdef>

			<paramdef><type>geography </type>
			<parameter>geogB</parameter></paramdef>
		  </funcprototype>
		</funcsynopsis>
	  </refsynopsisdiv>

	  <refsection>
		<title>Description</title>

		  <para>Returns 1 (TRUE) if no point in Geometry/Geography A is outside
			Geometry/Geography B</para>

		<para>Performed by the GEOS module</para>

		<important>
		  <para>Do not call with a <varname>GEOMETRYCOLLECTION</varname> as an argument</para>
		</important>

		<important>
		  <para>Do not use this function with invalid geometries. You will get unexpected results.</para>
		</important>
		<para>Availability: 1.2.2 - requires GEOS &gt;= 3.0</para>
		<para>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.</para>

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

		<para>Not an OGC standard, but Oracle has it too.</para>
		<para>There are certain subtleties to ST_Contains and ST_Within that are not intuitively obvious.
			For details check out <ulink url="http://lin-ear-th-inking.blogspot.com/2007/06/subtleties-of-ogc-covers-spatial.html">Subtleties of OGC Covers, Contains, Within</ulink></para>
	  </refsection>

	  <refsection>
		<title>Examples</title>
		  <programlisting>
	--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)	</programlisting>
	  </refsection>

	  <refsection>
		<title>See Also</title>
		<para><xref linkend="ST_Contains"/>, <xref linkend="ST_Covers" />, <xref linkend="ST_ExteriorRing"/>, <xref linkend="ST_Within"/></para>
	  </refsection>
 </refentry>

  <refentry id="ST_Crosses">
	<refnamediv>
	  <refname>ST_Crosses</refname>

	  <refpurpose>Returns <varname>TRUE</varname> if the supplied geometries have some, but not all,
	  interior points in common.</refpurpose>
	</refnamediv>

	<refsynopsisdiv>
	  <funcsynopsis>
		<funcprototype>
		  <funcdef>boolean <function>ST_Crosses</function></funcdef>

		  <paramdef><type>geometry </type><parameter>g1</parameter></paramdef>

		  <paramdef><type>geometry </type><parameter>g2</parameter></paramdef>
		</funcprototype>
	  </funcsynopsis>
	</refsynopsisdiv>

	<refsection>
	  <title>Description</title>

	  <para><function>ST_Crosses</function> takes two geometry objects and
	  returns <varname>TRUE</varname> 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 <varname>FALSE</varname>.</para>

	  <para>In mathematical terms, this is expressed as:</para>

	  <remark>TODO: Insert appropriate MathML markup here or use a gif.
	  Simple HTML markup does not work well in both IE and Firefox.</remark>

	  <informalfigure>
		<mediaobject>
		  <imageobject>
			<imagedata fileref="images/st_crosses-math.gif" />
		  </imageobject>
		</mediaobject>
	  </informalfigure>

	  <para>The DE-9IM Intersection Matrix for the two geometries is:</para>

	  <itemizedlist>
		<listitem>
		  <para><markup>T*T******</markup> (for Point/Line, Point/Area, and
		  Line/Area situations)</para>
		</listitem>

		<listitem>
		  <para><markup>T*****T**</markup> (for Line/Point, Area/Point, and
		  Area/Line situations)</para>
		</listitem>

		<listitem>
		  <para><markup>0********</markup> (for Line/Line situations)</para>
		</listitem>
	  </itemizedlist>

	  <para>For any other combination of dimensions this predicate returns
	  false.</para>

	  <para>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.</para>

	  <important>
		<para>Do not call with a <varname>GEOMETRYCOLLECTION</varname> as an argument</para>
	  </important>

	<note>
	  <para>This function call will automatically include a bounding box
	  comparison that will make use of any indexes that are available on the
	  geometries.</para>
	</note>

	<para>&sfs_compliant; s2.1.13.3</para>
	<para>&sqlmm_compliant; SQL-MM 3: 5.1.29</para>
	</refsection>

	<refsection>
	  <title>Examples</title>

	  <para>The following illustrations all return <varname>TRUE</varname>.</para>

	  <informaltable>
		<tgroup cols="2">
		  <tbody>
			<row>
			  <entry><para><informalfigure>
				  <mediaobject>
					<imageobject>
					  <imagedata fileref="images/st_crosses01.png" />
					</imageobject>

					<caption><para><varname>MULTIPOINT</varname> / <varname>LINESTRING</varname></para></caption>
				  </mediaobject>
				</informalfigure></para></entry>

			  <entry><para><informalfigure>
				  <mediaobject>
					<imageobject>
					  <imagedata fileref="images/st_crosses02.png" />
					</imageobject>

					<caption><para><varname>MULTIPOINT</varname> / <varname>POLYGON</varname></para></caption>
				  </mediaobject>
				</informalfigure></para></entry>
			</row>

			<row>
			  <entry><para><informalfigure>
				  <mediaobject>
					<imageobject>
					  <imagedata fileref="images/st_crosses03.png" />
					</imageobject>

					<caption><para><varname>LINESTRING</varname> / <varname>POLYGON</varname></para></caption>
				  </mediaobject>
				</informalfigure></para></entry>

			  <entry><para><informalfigure>
				  <mediaobject>
					<imageobject>
					  <imagedata fileref="images/st_crosses04.png" />
					</imageobject>

					<caption><para><varname>LINESTRING</varname> / <varname>LINESTRING</varname></para></caption>
				  </mediaobject>
				</informalfigure></para></entry>
			</row>
		  </tbody>
		</tgroup>
	  </informaltable>

	  <para>Consider a situation where a user has two tables: a table of roads
	  and a table of highways.</para>

	  <informaltable>
		<tgroup cols="2">
		  <tbody>
			<row>
			  <entry><para> <informalexample>
				  <programlisting>CREATE TABLE roads (
  id serial NOT NULL,
  the_geom geometry,
  CONSTRAINT roads_pkey PRIMARY KEY (road_id)
);</programlisting>
				</informalexample> </para></entry>

			  <entry><para> <informalexample>
				  <programlisting>CREATE TABLE highways (
  id serial NOT NULL,
  the_gem geometry,
  CONSTRAINT roads_pkey PRIMARY KEY (road_id)
);</programlisting>
				</informalexample> </para></entry>
			</row>
		  </tbody>
		</tgroup>
	  </informaltable>

	  <para>To determine a list of roads that cross a highway, use a query
	  similiar to:</para>

	  <para><informalexample>
		  <programlisting>SELECT roads.id
FROM roads, highways
WHERE ST_Crosses(roads.the_geom, highways.the_geom);</programlisting>
		</informalexample></para>
	</refsection>
  </refentry>

  <refentry id="ST_LineCrossingDirection">
	<refnamediv>
	  <refname>ST_LineCrossingDirection</refname>

	  <refpurpose>Given 2 linestrings, returns a number between -3 and 3 denoting what kind of crossing behavior. 0 is no crossing.</refpurpose>
	</refnamediv>

	<refsynopsisdiv>
	  <funcsynopsis>
		<funcprototype>
		  <funcdef>integer <function>ST_LineCrossingDirection</function></funcdef>
		  <paramdef><type>geometry </type> <parameter>linestringA</parameter></paramdef>
		  <paramdef><type>geometry </type> <parameter>linestringB</parameter></paramdef>
		</funcprototype>
	  </funcsynopsis>
	</refsynopsisdiv>

	<refsection>
	  <title>Description</title>

	  <para>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 <varname>LINESTRING</varname></para>
	  <para>Definition of integer constants is as follows:
		   <itemizedlist>
				<listitem>
				  <para> 0: LINE NO CROSS</para>
				</listitem>
				<listitem>
				  <para>-1: LINE CROSS LEFT</para>
				</listitem>
				<listitem>
				  <para> 1: LINE CROSS RIGHT</para>
				</listitem>
				<listitem>
				  <para>-2: LINE MULTICROSS END LEFT</para>
				</listitem>
				<listitem>
					<para> 2: LINE MULTICROSS END RIGHT</para>
				</listitem>
				<listitem>
				  <para>-3: LINE MULTICROSS END SAME FIRST LEFT</para>
				</listitem>
				<listitem>
				  <para> 3: LINE MULTICROSS END SAME FIRST RIGHT</para>
				</listitem>
			</itemizedlist>
	  </para>
	  <para>Availability: 1.4</para>
	  <!-- optionally mention that this function uses indexes if appropriate -->

	</refsection>


	<refsection>
	  <title>Examples</title>
  <!-- TODO: We really badly need diagrams here and more examples -->
		<informaltable>
		  <tgroup cols="2">
			<tbody>
			  <row>
				<entry><para><informalfigure>
					<mediaobject>
					  <imageobject>
						<imagedata fileref="images/st_linecrossingdirection01.png" />
					  </imageobject>
					  <caption><para>Line 1 (green), Line 2 ball is start point,
					triangle are end points. Query below. </para></caption>
					</mediaobject>
				  </informalfigure>
				  <programlisting>
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
				</programlisting>
			</para>
		</entry>

		<entry>
			<para><informalfigure>
				<mediaobject>
				  <imageobject>
					<imagedata fileref="images/st_linecrossingdirection02.png" />
				  </imageobject>
				  <caption><para>Line 1 (green), Line 2 (blue) ball is start point,
						triangle are end points. Query below.</para></caption>
				</mediaobject>
			  </informalfigure>
			  <programlisting>
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
				</programlisting>
			</para>
		</entry>
	  </row>
	  <row>
				<entry><para><informalfigure>
					<mediaobject>
					  <imageobject>
						<imagedata fileref="images/st_linecrossingdirection03.png" />
					  </imageobject>
					  <caption><para>Line 1 (green), Line 2 (blue) ball is start point,
					triangle are end points. Query below. </para></caption>
					</mediaobject>
				  </informalfigure>
				  <programlisting>
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
				</programlisting>
			</para>
		</entry>

		<entry>
			<para><informalfigure>
				<mediaobject>
				  <imageobject>
					<imagedata fileref="images/st_linecrossingdirection04.png" />
				  </imageobject>
				  <caption><para>Line 1 (green), Line 2 (blue) ball is start point,
						triangle are end points. Query below.</para></caption>
				</mediaobject>
			  </informalfigure>
			  <programlisting>
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
				</programlisting>
			</para>
		</entry>
	  </row>
	  </tbody>
	</tgroup>
</informaltable>

<programlisting>
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 &amp;&amp; s2.the_geom )
WHERE ST_CrossingDirection(s1.the_geom, s2.the_geom) > 0;
</programlisting>
	</refsection>

	<!-- Optionally add a "See Also" section -->
	<refsection>
	  <title>See Also</title>

	  <para><xref linkend="ST_Crosses" /></para>
	</refsection>
  </refentry>

  <refentry id="ST_Disjoint">
		<refnamediv>
			<refname>ST_Disjoint</refname>

			<refpurpose>Returns TRUE if the Geometries do not "spatially
			intersect" - if they do not share any space together.
			</refpurpose>
		</refnamediv>
		<refsynopsisdiv>
			<funcsynopsis>
				<funcprototype>
					<funcdef>boolean <function>ST_Disjoint</function></funcdef>
					<paramdef>
						<type>geometry</type>
						<parameter>A</parameter>
					</paramdef>
					<paramdef>
						<type>geometry</type>
						<parameter>B</parameter>
					</paramdef>
				</funcprototype>
			</funcsynopsis>
		</refsynopsisdiv>
		<refsection>
			<title>Description</title>
			<para>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.</para>

			<important>
				<para>Do not call with a <varname>GEOMETRYCOLLECTION</varname> as an argument</para>
			</important>

			<para>Performed by the GEOS module</para>
			<note>
			  <para>This function call does not use indexes</para>

			</note>
			<note>
			  <para>NOTE: this is the "allowable" version that returns a
			boolean, not an integer.</para>
			</note>
			<para>&sfs_compliant; s2.1.1.2 //s2.1.13.3
			- a.Relate(b, 'FF*FF****')</para>
			<para>&sqlmm_compliant; SQL-MM 3: 5.1.26</para>
		</refsection>
		<refsection>
		<title>Examples</title>

		<programlisting>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)
		</programlisting>
		</refsection>

		<refsection>
			<title>See Also</title>
			<para><xref linkend="ST_Intersects"/>ST_Intersects</para>
		</refsection>
	</refentry>

	<refentry id="ST_Distance">
	  <refnamediv>
		<refname>ST_Distance</refname>

		<refpurpose>For geometry type Returns the 2D Cartesian distance between two geometries in
		projected units (based on spatial ref).  For geography type defaults to return minimum geodesic distance between two geographies in meters.</refpurpose>
	  </refnamediv>
	  <refsynopsisdiv>
		<funcsynopsis>
		  <funcprototype>
			<funcdef>float <function>ST_Distance</function></funcdef>

			<paramdef><type>geometry </type>
			<parameter>g1</parameter></paramdef>

			<paramdef><type>geometry </type>
			<parameter>g2</parameter></paramdef>
		  </funcprototype>
		  <funcprototype>
			<funcdef>float <function>ST_Distance</function></funcdef>

			<paramdef><type>geography </type>
			<parameter>gg1</parameter></paramdef>

			<paramdef><type>geography </type>
			<parameter>gg2</parameter></paramdef>
		  </funcprototype>

		  <funcprototype>
			<funcdef>float <function>ST_Distance</function></funcdef>

			<paramdef><type>geography </type>
			<parameter>gg1</parameter></paramdef>

			<paramdef><type>geography </type>
			<parameter>gg2</parameter></paramdef>

			<paramdef><type>boolean </type>
			<parameter>use_spheroid</parameter></paramdef>
		  </funcprototype>
		</funcsynopsis>
	  </refsynopsisdiv>

	  <refsection>
		<title>Description</title>

		<para>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.</para>

		<para>&sfs_compliant;</para>
		<para>&sqlmm_compliant; SQL-MM 3: 5.1.23</para>
		<para>&curve_support;</para>
		<para>&sfcgal_enhanced;</para>

		<para>Availability: 1.5.0 geography support was introduced in 1.5.  Speed improvements for planar to better handle large or many vertex geometries</para>
		<para>Enhanced: 2.1.0 improved speed for geography. See <ulink url="http://boundlessgeo.com/2012/07/making-geography-faster/">Making Geography faster</ulink> for details.</para>
		<para>Enhanced: 2.1.0 - support for curved geometries was introduced.</para>
		<para>Enhanced: 2.2.0 - measurement on spheroid performed with GeographicLib for improved accuracy and robustness. Requires Proj &gt;= 4.9.0 to take advantage of the new feature.</para>
	  </refsection>

	  <refsection>
		<title>Basic Geometry Examples</title>

		<programlisting>
--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
</programlisting>
	</refsection>
	  <refsection>
		<title>Geography Examples</title>
<programlisting>-- 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
	ST_GeogFromText('SRID=4326;POINT(-72.1235 42.3521)') As gg1,
	ST_GeogFromText('SRID=4326;LINESTRING(-72.1260 42.45, -72.123 42.1546)') As gg2
	) As foo  ;

  spheroid_dist   |   sphere_dist
------------------+------------------
 123.802076746848 | 123.475736916397
</programlisting>
	</refsection>



	  <refsection>
		<title>See Also</title>

		<para><xref linkend="ST_3DDistance"/>, <xref linkend="ST_DWithin"/>, <xref linkend="ST_DistanceSphere"/>, <xref linkend="ST_Distance_Spheroid"/>,
		<xref linkend="ST_MaxDistance" />, <xref linkend="ST_HausdorffDistance" />, <xref linkend="ST_Transform" /></para>
	  </refsection>
	</refentry>

	<refentry id="ST_MinimumClearance">
		<refnamediv>
			<refname>ST_MinimumClearance</refname>
			<refpurpose>Returns the minimum clearance of a geometry, a measure of a geometry's robustness.</refpurpose>
		</refnamediv>

		<refsynopsisdiv>
			<funcsynopsis>
				<funcprototype>
					<funcdef>float <function>ST_MinimumClearance</function></funcdef>
					<paramdef><type>geometry </type><parameter>g</parameter></paramdef>
				</funcprototype>
			</funcsynopsis>
		</refsynopsisdiv>

	  <refsection>
		<title>Description</title>

		<para>
			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).
		</para>

		<para>
			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.
		</para>

		<para>
			If a geometry has a minimum clearance of <varname>e</varname>, it can be said that:
			<itemizedlist>
				<listitem>
					<para>
						No two distinct vertices in the geometry are separated by less than <varname>e</varname>.
					</para>
				</listitem>
				<listitem>
					<para>
						No vertex is closer than <varname>e</varname> to a line segement of which it is not an endpoint.
					</para>
				</listitem>
			</itemizedlist>
		</para>

		<para>
			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.
		</para>

		<para>Availability: 2.3.0 - requires GEOS &gt;= 3.6.0</para>

	  </refsection>

	  <refsection>
		<title>Examples</title>
		<programlisting>
SELECT ST_MinimumClearance('POLYGON ((0 0, 1 0, 1 1, 0.5 3.2e-4, 0 0))');
 st_minimumclearance
---------------------
             0.00032
     </programlisting>

	  </refsection>

	  <refsection>
		<title>See Also</title>

		<para>
			<xref linkend="ST_MinimumClearanceLine" />
		</para>
	  </refsection>
	</refentry>

	<refentry id="ST_MinimumClearanceLine">
		<refnamediv>
			<refname>ST_MinimumClearanceLine</refname>
			<refpurpose>Returns the two-point LineString spanning a geometry's minimum clearance.</refpurpose>
		</refnamediv>

	  <refsynopsisdiv>
		<funcsynopsis>
		  <funcprototype>
			<funcdef>Geometry <function>ST_MinimumClearanceLine</function></funcdef>

			<paramdef><type>geometry </type>
			<parameter>g</parameter></paramdef>

		  </funcprototype>
		</funcsynopsis>
	  </refsynopsisdiv>

	  <refsection>
		<title>Description</title>

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

		<para>Availability: 2.3.0 - requires GEOS &gt;= 3.6.0</para>

	  </refsection>

	  <refsection>
		  <title>Examples</title>
		  <programlisting>
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)
		  </programlisting>
	  </refsection>

	  <refsection>
		<title>See Also</title>

		<para>
			<xref linkend="ST_MinimumClearance" />
		</para>
	  </refsection>

	</refentry>


	<refentry id="ST_HausdorffDistance">
	  <refnamediv>
		<refname>ST_HausdorffDistance</refname>

		<refpurpose>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.</refpurpose>
	  </refnamediv>

	  <refsynopsisdiv>
		<funcsynopsis>
		  <funcprototype>
			<funcdef>float <function>ST_HausdorffDistance</function></funcdef>

			<paramdef><type>geometry </type>
			<parameter>g1</parameter></paramdef>

			<paramdef><type>geometry </type>
			<parameter>g2</parameter></paramdef>
		  </funcprototype>
		  <funcprototype>
			<funcdef>float <function>ST_HausdorffDistance</function></funcdef>

			<paramdef><type>geometry </type>
			<parameter>g1</parameter></paramdef>

			<paramdef><type>geometry </type>
			<parameter>g2</parameter></paramdef>

			<paramdef><type>float</type>
			<parameter>densifyFrac</parameter></paramdef>
		  </funcprototype>
		</funcsynopsis>
	  </refsynopsisdiv>

	  <refsection>
		<title>Description</title>

		<para>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. <ulink url="http://en.wikipedia.org/wiki/Hausdorff_distance">Wikipedia article on Hausdorff distance</ulink>
	<ulink url="http://lin-ear-th-inking.blogspot.com/2009/01/computing-geometric-similarity.html">Martin Davis note on how Hausdorff Distance calculation was used to prove correctness of the CascadePolygonUnion approach.</ulink></para>
		<para>
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.
		</para>

		<note>
			<para>
The current implementation supports only vertices as the discrete locations. This could be extended to allow an arbitrary density of points to be used.
			</para>
		</note>
		<note>
			<para>
				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.
			</para>
		</note>
		<para>Availability: 1.5.0 - requires GEOS &gt;= 3.2.0</para>

	  </refsection>

	  <refsection>
		<title>Examples</title>
		    <para>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.</para>
		<programlisting>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);</programlisting>

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

	  </refsection>
	</refentry>

<refentry id="ST_MaxDistance">
  <refnamediv>
    <refname>ST_MaxDistance</refname>

    <refpurpose>Returns the 2-dimensional largest distance between two geometries in
		projected units.</refpurpose>
  </refnamediv>

  <refsynopsisdiv>
    <funcsynopsis>
      <funcprototype>
        <funcdef>float <function>ST_MaxDistance</function></funcdef>
        <paramdef><type>geometry </type> <parameter>g1</parameter></paramdef>
        <paramdef><type>geometry </type> <parameter>g2</parameter></paramdef>
      </funcprototype>
    </funcsynopsis>
  </refsynopsisdiv>

  <refsection>
    <title>Description</title>

    <!-- optionally mention that this function uses indexes if appropriate -->
    <note>
      <para>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.</para>
    </note>

	<para>Availability: 1.5.0</para>
  </refsection>
  <refsection>
    <title>Examples</title>

     <para>Basic furthest distance the point is to any part of the line</para>
		<programlisting>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)</programlisting>
  </refsection>

  <!-- Optionally add a "See Also" section -->
  <refsection>
    <title>See Also</title>
<para><xref linkend="ST_Distance"/>, <xref linkend="ST_LongestLine"/>, <xref linkend="ST_DFullyWithin" /></para>
  </refsection>
</refentry>

<refentry id="ST_DistanceSphere">
	  <refnamediv>
		<refname>ST_DistanceSphere</refname>

		<refpurpose>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 <xref linkend="ST_Distance_Spheroid" />, but less
				accurate. PostGIS versions prior to 1.5 only implemented for points.</refpurpose>
	  </refnamediv>

	  <refsynopsisdiv>
		<funcsynopsis>
		  <funcprototype>
			<funcdef>float <function>ST_DistanceSphere</function></funcdef>
			<paramdef><type>geometry </type> <parameter>geomlonlatA</parameter></paramdef>
			<paramdef><type>geometry </type> <parameter>geomlonlatB</parameter></paramdef>
		  </funcprototype>
		</funcsynopsis>
	  </refsynopsisdiv>

	  <refsection>
		<title>Description</title>

		<para>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 <xref linkend="ST_Distance_Spheroid"/>, but less
				accurate. PostGIS Versions prior to 1.5 only implemented for points.</para>

		<para>Availability: 1.5 - support for other geometry types besides points was introduced. Prior versions only work with points.</para>
		<para>Changed: 2.2.0 In prior versions this used to be called ST_Distance_Sphere</para>
	  </refsection>


	  <refsection>
		<title>Examples</title>

		<programlisting>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

	</programlisting>
	  </refsection>

	  <!-- Optionally add a "See Also" section -->
	  <refsection>
		<title>See Also</title>

		<para><xref linkend="ST_Distance" />, <xref linkend="ST_Distance_Spheroid" /></para>
	  </refsection>
	</refentry>

	<refentry id="ST_Distance_Spheroid">
	  <refnamediv>
		<refname>ST_DistanceSpheroid</refname>

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

	  <refsynopsisdiv>
		<funcsynopsis>
		  <funcprototype>
			<funcdef>float <function>ST_DistanceSpheroid</function></funcdef>
			<paramdef><type>geometry </type> <parameter>geomlonlatA</parameter></paramdef>
			<paramdef><type>geometry </type> <parameter>geomlonlatB</parameter></paramdef>
			<paramdef><type>spheroid </type> <parameter>measurement_spheroid</parameter></paramdef>
		  </funcprototype>
		</funcsynopsis>
	  </refsynopsisdiv>

	  <refsection>
		<title>Description</title>

		<para>Returns minimum distance in meters between two lon/lat
				geometries given a particular spheroid. See the explanation of spheroids given for
			<xref linkend="ST_Length_Spheroid" />. PostGIS version prior to 1.5 only support points.</para>
		<note>
			<para>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.</para>
		</note>

		<para>Availability: 1.5 - support for other geometry types besides points was introduced. Prior versions only work with points.</para>
		<para>Changed: 2.2.0 In prior versions this used to be called ST_Distance_Spheroid</para>
	  </refsection>


	  <refsection>
		<title>Examples</title>

		<programlisting>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

	</programlisting>
	  </refsection>

	  <!-- Optionally add a "See Also" section -->
	  <refsection>
		<title>See Also</title>

		<para><xref linkend="ST_Distance" />, <xref linkend="ST_DistanceSphere" /></para>
	  </refsection>
	</refentry>

	<refentry id="ST_DFullyWithin">
	  <refnamediv>
		<refname>ST_DFullyWithin</refname>

		<refpurpose>Returns true if all of the geometries are within the specified
		distance of one another</refpurpose>
	  </refnamediv>

	  <refsynopsisdiv>
		<funcsynopsis>
		  <funcprototype>
			<funcdef>boolean <function>ST_DFullyWithin</function></funcdef>

			<paramdef><type>geometry </type>
			<parameter>g1</parameter></paramdef>

			<paramdef><type>geometry </type>
			<parameter>g2</parameter></paramdef>

			<paramdef><type>double precision </type>
			<parameter>distance</parameter></paramdef>
		  </funcprototype>
		</funcsynopsis>
	  </refsynopsisdiv>

	  <refsection>
		<title>Description</title>

		<para>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.</para>

		<note>
		  <para>This function call will automatically include a bounding box
		  comparison that will make use of any indexes that are available on
		  the geometries.</para>
		</note>

		<para>Availability: 1.5.0</para>
	  </refsection>

	  <refsection>
		<title>Examples</title>
		<programlisting>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             |  </programlisting>
	  </refsection>

	  <refsection>
		<title>See Also</title>

		<para><xref linkend="ST_MaxDistance"/>, <xref linkend="ST_DWithin"/></para>
	  </refsection>
	</refentry>

	<refentry id="ST_DWithin">
	  <refnamediv>
		<refname>ST_DWithin</refname>

		<refpurpose>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.</refpurpose>
	  </refnamediv>

	  <refsynopsisdiv>
		<funcsynopsis>
		  <funcprototype>
				<funcdef>boolean <function>ST_DWithin</function></funcdef>
				<paramdef><type>geometry </type>
				<parameter>g1</parameter></paramdef>

				<paramdef><type>geometry </type>
				<parameter>g2</parameter></paramdef>

				<paramdef><type>double precision </type>
				<parameter>distance_of_srid</parameter></paramdef>
		  </funcprototype>

		  <funcprototype>
				<funcdef>boolean <function>ST_DWithin</function></funcdef>
				<paramdef><type>geography </type>
				<parameter>gg1</parameter></paramdef>

				<paramdef><type>geography </type>
				<parameter>gg2</parameter></paramdef>

				<paramdef><type>double precision </type>
				<parameter>distance_meters</parameter></paramdef>
		  </funcprototype>

		  <funcprototype>
				<funcdef>boolean <function>ST_DWithin</function></funcdef>
				<paramdef><type>geography </type>
				<parameter>gg1</parameter></paramdef>

				<paramdef><type>geography </type>
				<parameter>gg2</parameter></paramdef>

				<paramdef><type>double precision </type>
				<parameter>distance_meters</parameter></paramdef>

				<paramdef><type>boolean </type>
				<parameter>use_spheroid</parameter></paramdef>
		  </funcprototype>
		</funcsynopsis>
	  </refsynopsisdiv>

	  <refsection>
		<title>Description</title>

		<para>Returns true if the geometries are within the specified distance
		of one another.</para>
		<para>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.</para>

		<para>For geography units are in meters and measurement is
		defaulted to use_spheroid=true, for faster check, use_spheroid=false to measure along sphere.
		</para>
		<note>
		  <para>This function call will automatically include a bounding box
		  comparison that will make use of any indexes that are available on
		  the geometries.</para>
		</note>

		<note>
		  <para>Prior to 1.3, ST_Expand was commonly used in conjunction with &amp;&amp; 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.</para>
		</note>

		<note><para>Use ST_3DDWithin if you have 3D geometries.</para></note>

		<para>&sfs_compliant;</para>
		<para>Availability: 1.5.0 support for geography was introduced</para>
		<para>Enhanced: 2.1.0 improved speed for geography. See <ulink url="http://blog.opengeo.org/2012/07/12/making-geography-faster/">Making Geography faster</ulink> for details.</para>
		<para>Enhanced: 2.1.0 support for curved geometries was introduced.</para>
	  </refsection>

	  <refsection>
		<title>Examples</title>
		  <programlisting>
--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;
			  </programlisting>
	  </refsection>

	  <refsection>
		<title>See Also</title>

		<para><xref linkend="ST_Distance"/>, <xref linkend="ST_Expand"/></para>
	  </refsection>
	</refentry>

	<refentry id="ST_Equals">
	  <refnamediv>
		<refname>ST_Equals</refname>

		<refpurpose>Returns true if the given geometries represent the same geometry. Directionality
			is ignored.</refpurpose>
	  </refnamediv>

	  <refsynopsisdiv>
		<funcsynopsis>
		  <funcprototype>
			<funcdef>boolean <function>ST_Equals</function></funcdef>
			<paramdef><type>geometry </type> <parameter>A</parameter></paramdef>
			<paramdef><type>geometry </type> <parameter>B</parameter></paramdef>
		  </funcprototype>
		</funcsynopsis>
	  </refsynopsisdiv>

	  <refsection>
		<title>Description</title>

		<para>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).</para>

		<important>
		  <para>This function will return false if either geometry is invalid except in the case where they are binary equal.</para>
		</important>

		<para>&sfs_compliant; s2.1.1.2</para>
		<para>&sqlmm_compliant; SQL-MM 3: 5.1.24</para>
        <para>Changed: 2.2.0 Returns true even for invalid geometries if they are binary equal</para>
	  </refsection>

	  <refsection>
		<title>Examples</title>

		<programlisting>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)
</programlisting>
	  </refsection>

	  <refsection>
		<title>See Also</title>

		<para><xref linkend="ST_IsValid"/>, <xref linkend="ST_OrderingEquals"/>, <xref linkend="ST_Reverse"/>, <xref linkend="ST_Within" /></para>
	  </refsection>

	</refentry>

	<refentry id="ST_GeometricMedian">
	  <refnamediv>
		  <refname>
			  ST_GeometricMedian
		  </refname>

		<refpurpose>
			Returns the geometric median of a MultiPoint.
		</refpurpose>
	  </refnamediv>

	<refsynopsisdiv>
	  <funcsynopsis>
		<funcprototype>
			<funcdef>geometry
				<function>
					ST_GeometricMedian
				</function>
			</funcdef>

			<paramdef>
				<type>
					geometry
				</type>
				<parameter>
					g
				</parameter>
			</paramdef>

			<paramdef>
				<type>
					float8
				</type>
				<parameter>
					tolerance
				</parameter>
			</paramdef>

			<paramdef>
				<type>
					int
				</type>
				<parameter>
					max_iter
				</parameter>
			</paramdef>

			<paramdef>
				<type>
					boolean
				</type>
				<parameter>
					fail_if_not_converged
				</parameter>
			</paramdef>

		</funcprototype>
	  </funcsynopsis>
	</refsynopsisdiv>

	<refsection>
	  <title>Description</title>

	  <para>
		  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 <varname>tolerance</varname>
		  parameter.  If this condition has not been met after <varname>max_iterations</varname>
		  iterations, the function will produce an error and exit, unless <varname>fail_if_not_converged</varname>
		  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.
	  </para>

	  <para>Availability: 2.3.0</para>
	  <para>&Z_support;</para>
  </refsection>
    <refsection>
      <title>Examples</title>
	  <para>
		  <informalfigure>
			  <mediaobject>
					<imageobject>
						<imagedata fileref="images/st_geometricmedian01.png" />
					</imageobject>

					<caption>
						<para>
						Comparison of the centroid (turquoise point) and geometric
						median (red point) of a four-point MultiPoint (yellow points).
						</para>
					</caption>
			  </mediaobject>
		</informalfigure>
	  </para>
	  <programlisting>
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)
	  </programlisting>
	</refsection>

	<refsection>
	  <title>See Also</title>

	  <para><xref linkend="ST_Centroid"/></para>
	</refsection>

	</refentry>

	<refentry id="ST_HasArc">
	  <refnamediv>
		<refname>ST_HasArc</refname>

		<refpurpose>Returns true if a geometry or geometry collection contains a circular string</refpurpose>
	  </refnamediv>

	  <refsynopsisdiv>
		<funcsynopsis>
		  <funcprototype>
			<funcdef>boolean <function>ST_HasArc</function></funcdef>
			<paramdef><type>geometry </type> <parameter>geomA</parameter></paramdef>
		  </funcprototype>
		</funcsynopsis>
	  </refsynopsisdiv>

	  <refsection>
		<title>Description</title>

		<para>Returns true if a geometry or geometry collection contains a circular string</para>

		<para>Availability: 1.2.3?</para>
		<para>&Z_support;</para>
		<para>&curve_support;</para>
	  </refsection>


	  <refsection>
		<title>Examples</title>

		<programlisting>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
		</programlisting>
	  </refsection>

	  <!-- Optionally add a "See Also" section -->
	  <refsection>
		<title>See Also</title>

		<para><xref linkend="ST_CurveToLine" />, <xref linkend="ST_LineToCurve" /></para>
	  </refsection>
	</refentry>

	<refentry id="ST_Intersects">
		<refnamediv>
			<refname>ST_Intersects</refname>

			<refpurpose>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)
			</refpurpose>
		</refnamediv>
		<refsynopsisdiv>
			<funcsynopsis>
				<funcprototype>
					<funcdef>boolean <function>ST_Intersects</function></funcdef>
					<paramdef>
						<type>geometry</type>
						<parameter>geomA</parameter>
					</paramdef>
					<paramdef>
						<type>geometry</type>
						<parameter>geomB</parameter>
					</paramdef>
				</funcprototype>
				<funcprototype>
					<funcdef>boolean <function>ST_Intersects</function></funcdef>
					<paramdef>
						<type>geography</type>
						<parameter>geogA</parameter>
					</paramdef>
					<paramdef>
						<type>geography</type>
						<parameter>geogB</parameter>
					</paramdef>
				</funcprototype>
			</funcsynopsis>
		</refsynopsisdiv>
		<refsection>
			<title>Description</title>
			<para>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)</para>
			<para>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.</para>

	  <important>
		<para>Do not call with a <varname>GEOMETRYCOLLECTION</varname> as an argument for geometry version.  The geography
			version supports GEOMETRYCOLLECTION since its a thin wrapper around distance implementation.</para>
	  </important>
	  <para>Enhanced: 2.3.0 Enhancement to PIP short-circuit extended to support MultiPoints with few points. Prior versions only supported point in polygon.</para>

			<para>Performed by the GEOS module (for geometry), geography is native</para>
			<para>Availability: 1.5 support for geography was introduced.</para>
			<note>
			  <para>This function call will automatically include a bounding box
			  comparison that will make use of any indexes that are available on the
			  geometries.</para>
			</note>
			<note>
			  <para>For geography, this function has a distance tolerance of about 0.00001 meters and uses the sphere rather
				than spheroid calculation.</para>
			</note>
			<note>
			  <para>NOTE: this is the "allowable" version that returns a
			boolean, not an integer.</para>
			</note>
			<para>&sfs_compliant; s2.1.1.2 //s2.1.13.3
			  - ST_Intersects(g1, g2 ) --&gt; Not (ST_Disjoint(g1, g2 ))
			</para>
			<para>&sqlmm_compliant; SQL-MM 3: 5.1.27</para>
                        <para>&sfcgal_enhanced;</para>
		</refsection>
		<refsection>
		<title>Geometry Examples</title>
<programlisting>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)
		</programlisting>
		</refsection>
		<refsection>
		<title>Geography Examples</title>
<programlisting>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
</programlisting>
		</refsection>
		<refsection>
			<title>See Also</title>
			<para> <xref linkend="ST_3DIntersects" />, <xref linkend="ST_Disjoint"/></para>
		</refsection>
	</refentry>
	<refentry id="ST_Length">
		<refnamediv>
		  <refname>ST_Length</refname>

		  <refpurpose>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)</refpurpose>
		</refnamediv>
		<refsynopsisdiv>
		  <funcsynopsis>
			<funcprototype>
			  <funcdef>float <function>ST_Length</function></funcdef>
				<paramdef><type>geometry </type><parameter>a_2dlinestring</parameter></paramdef>
			</funcprototype>
			<funcprototype>
			  <funcdef>float <function>ST_Length</function></funcdef>
				<paramdef><type>geography </type><parameter>geog</parameter></paramdef>
				<paramdef choice="opt"><type>boolean </type><parameter>use_spheroid=true</parameter></paramdef>
			</funcprototype>
		  </funcsynopsis>
		</refsynopsisdiv>
		<refsection>
			<title>Description</title>

			<para>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 <xref linkend="ST_Perimeter" />. For geometry types, units for length measures are specified by the
				spatial reference system of the geometry.</para>
			<para>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 <varname>use_spheroid=false</varname>, then calculations will approximate a sphere instead of a spheroid.</para>

			<para>Currently for geometry this is an alias for ST_Length2D, but this may change to support higher dimensions.</para>
			<warning><para>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</para></warning>
			<note><para>For geography measurement defaults spheroid measurement.  To use the faster less accurate sphere use ST_Length(gg,false);</para></note>
			<para>&sfs_compliant; s2.1.5.1</para>
			<para>&sqlmm_compliant; SQL-MM 3: 7.1.2, 9.3.4</para>
			<para>Availability: 1.5.0 geography support was introduced in 1.5.</para>
			<para>&sfcgal_enhanced;</para>
		</refsection>

		  <refsection>
			<title>Geometry Examples</title>
			<para>Return length in feet for line string. Note this is in feet because EPSG:2249 is
				Massachusetts State Plane Feet</para>
			<programlisting>
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
			</programlisting>
		  </refsection>
		  <refsection>
			<title>Geography Examples</title>
			<para>Return length of WGS 84 geography line</para>
			<programlisting>
			-- 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
			</programlisting>
		  </refsection>
		<refsection>
			<title>See Also</title>
			<para><xref linkend="ST_GeographyFromText" />, <xref linkend="ST_GeomFromEWKT" />, <xref linkend="ST_Length_Spheroid" />, <xref linkend="ST_Perimeter" />, <xref linkend="ST_Transform" /></para>
		</refsection>
	</refentry>

	<refentry id="ST_Length2D">
	  <refnamediv>
		<refname>ST_Length2D</refname>

		<refpurpose>Returns the 2-dimensional length of the geometry if it is a
				linestring or multi-linestring. This is an alias for <varname>ST_Length</varname></refpurpose>
	  </refnamediv>

	  <refsynopsisdiv>
		<funcsynopsis>
		  <funcprototype>
			<funcdef>float <function>ST_Length2D</function></funcdef>
			<paramdef><type>geometry </type> <parameter>a_2dlinestring</parameter></paramdef>
		  </funcprototype>
		</funcsynopsis>
	  </refsynopsisdiv>

	  <refsection>
		<title>Description</title>

		<para>Returns the 2-dimensional length of the geometry if it is a
				linestring or multi-linestring. This is an alias for <varname>ST_Length</varname></para>

	  </refsection>

	  <!-- Optionally add a "See Also" section -->
	  <refsection>
		<title>See Also</title>

		<para><xref linkend="ST_Length" />, <xref linkend="ST_3DLength" /></para>
	  </refsection>
	</refentry>

	<refentry id="ST_3DLength">
	  <refnamediv>
		<refname>ST_3DLength</refname>

		<refpurpose>Returns the 3-dimensional or 2-dimensional length of the geometry if it is a
			linestring or multi-linestring. </refpurpose>
	  </refnamediv>

	  <refsynopsisdiv>
		<funcsynopsis>
		  <funcprototype>
			<funcdef>float <function>ST_3DLength</function></funcdef>
			<paramdef><type>geometry </type> <parameter>a_3dlinestring</parameter></paramdef>
		  </funcprototype>
		</funcsynopsis>
	  </refsynopsisdiv>

	  <refsection>
		<title>Description</title>

		<para>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)</para>
		<para>&Z_support;</para>
		<para>Changed: 2.0.0 In prior versions this used to be called ST_Length3D</para>
	  </refsection>


	  <refsection>
		<title>Examples</title>

		<para>Return length in feet for a 3D cable. Note this is in feet because EPSG:2249 is
				Massachusetts State Plane Feet</para>
		<programlisting>
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
		</programlisting>
	  </refsection>

	  <!-- Optionally add a "See Also" section -->
	  <refsection>
		<title>See Also</title>

		<para><xref linkend="ST_Length" />, <xref linkend="ST_Length2D" /></para>
	  </refsection>
	</refentry>

	<refentry id="ST_Length_Spheroid">
	  <refnamediv>
		<refname>ST_LengthSpheroid</refname>

        <refpurpose>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.</refpurpose>
	  </refnamediv>

	  <refsynopsisdiv>
		<funcsynopsis>
		  <funcprototype>
			<funcdef>float <function>ST_LengthSpheroid</function></funcdef>
			<paramdef><type>geometry </type> <parameter>a_geometry</parameter></paramdef>
			<paramdef><type>spheroid </type> <parameter>a_spheroid</parameter></paramdef>
		  </funcprototype>
		</funcsynopsis>
	  </refsynopsisdiv>

	  <refsection>
		<title>Description</title>

        <para>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:</para>

		<literallayout>SPHEROID[&lt;NAME&gt;,&lt;SEMI-MAJOR AXIS&gt;,&lt;INVERSE FLATTENING&gt;]</literallayout>

		<literallayout>SPHEROID["GRS_1980",6378137,298.257222101]</literallayout>

		<para>Availability: 1.2.2</para>
		<para>Changed: 2.2.0 In prior versions this used to be called ST_Length_Spheroid and used to have a ST_3DLength_Spheroid alias</para>
		<para>&Z_support;</para>
	  </refsection>

	  <refsection>
		<title>Examples</title>

		<programlisting>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

</programlisting>
	  </refsection>

	  <!-- Optionally add a "See Also" section -->
	  <refsection>
		<title>See Also</title>

		<para><xref linkend="ST_GeometryN" />, <xref linkend="ST_Length" /></para>
	  </refsection>
	</refentry>

	<refentry id="ST_Length2D_Spheroid">
	  <refnamediv>
		<refname>ST_Length2D_Spheroid</refname>

        <refpurpose>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.  </refpurpose>
	  </refnamediv>

	  <refsynopsisdiv>
		<funcsynopsis>
		  <funcprototype>
			<funcdef>float <function>ST_Length2D_Spheroid</function></funcdef>
			<paramdef><type>geometry </type> <parameter>a_geometry</parameter></paramdef>
			<paramdef><type>spheroid </type> <parameter>a_spheroid</parameter></paramdef>
		  </funcprototype>
		</funcsynopsis>
	  </refsynopsisdiv>

	  <refsection>
		<title>Description</title>

        <para>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:</para>

		<literallayout>SPHEROID[&lt;NAME&gt;,&lt;SEMI-MAJOR AXIS&gt;,&lt;INVERSE FLATTENING&gt;]</literallayout>

		<literallayout>SPHEROID["GRS_1980",6378137,298.257222101]</literallayout>
		<note><para>This is much like <xref linkend="ST_Length_Spheroid" /> except it will ignore the Z ordinate in calculations.</para></note>
	  </refsection>


	  <refsection>
		<title>Examples</title>

		<programlisting>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

</programlisting>
	  </refsection>

	  <!-- Optionally add a "See Also" section -->
	  <refsection>
		<title>See Also</title>

		<para><xref linkend="ST_GeometryN" />, <xref linkend="ST_Length_Spheroid" /></para>
	  </refsection>
	</refentry>

<refentry id="ST_LongestLine">
	  <refnamediv>
		<refname>ST_LongestLine</refname>

		<refpurpose>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.</refpurpose>
	  </refnamediv>

	  <refsynopsisdiv>
		<funcsynopsis>
		  <funcprototype>
			<funcdef>geometry <function>ST_LongestLine</function></funcdef>

			<paramdef><type>geometry </type>
			<parameter>g1</parameter></paramdef>

			<paramdef><type>geometry </type>
			<parameter>g2</parameter></paramdef>
		  </funcprototype>
		</funcsynopsis>
	  </refsynopsisdiv>

	  <refsection>
		<title>Description</title>

		<para>Returns the 2-dimensional longest line between the points of two geometries.
		</para>

		<para>Availability: 1.5.0</para>

	  </refsection>

	  <refsection>
		<title>Examples</title>
			<informaltable>
				  <tgroup cols="2">
					<tbody>
					  <row>
						<entry><para><informalfigure>
							<mediaobject>
							  <imageobject>
								<imagedata fileref="images/st_longestline01.png" />
							  </imageobject>
							  <caption><para>Longest line between point and line</para></caption>
							</mediaobject>
						  </informalfigure>
				<programlisting>
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)
				</programlisting>
						  </para></entry>

						<entry><para><informalfigure>
							<mediaobject>
							  <imageobject>
								<imagedata fileref="images/st_longestline02.png" />
							  </imageobject>
							  <caption><para>longest line between polygon and polygon</para></caption>
							</mediaobject>
						  </informalfigure>
				<programlisting>
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)
				</programlisting>
						</para></entry>
					  </row>
		</tbody>
	</tgroup>
</informaltable>

<informaltable>
	  <tgroup cols="1">
		<tbody>
		  <row>
			<entry><para><informalfigure>
							<mediaobject>
							  <imageobject>
								<imagedata fileref="images/st_longestline03.png" />
							  </imageobject>
							  <caption><para>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.</para></caption>
							</mediaobject>
						  </informalfigure>
				<programlisting>
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
				</programlisting>
						</para></entry>
		</row>
	</tbody>
</tgroup>
</informaltable>
	  </refsection>

	  <refsection>
		<title>See Also</title>

		<para><xref linkend="ST_MaxDistance"/>, <xref linkend="ST_ShortestLine"/>, <xref linkend="ST_LongestLine"/></para>
	  </refsection>
	</refentry>

	<refentry id="ST_OrderingEquals">
	  <refnamediv>
		<refname>ST_OrderingEquals</refname>

		<refpurpose>Returns true if the given geometries represent the same geometry
		and points are in the same directional order.</refpurpose>
	  </refnamediv>

	  <refsynopsisdiv>
		<funcsynopsis>
		  <funcprototype>
			<funcdef>boolean <function>ST_OrderingEquals</function></funcdef>
			<paramdef><type>geometry </type> <parameter>A</parameter></paramdef>
			<paramdef><type>geometry </type> <parameter>B</parameter></paramdef>
		  </funcprototype>
		</funcsynopsis>
	  </refsynopsisdiv>

	  <refsection>
		<title>Description</title>

		<para>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).</para>

		<note>
			<para>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</para>
		</note>
		<para>&sqlmm_compliant; SQL-MM 3: 5.1.43</para>
	  </refsection>

	  <refsection>
		<title>Examples</title>

		<programlisting>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)
</programlisting>
		  </refsection>
		  <refsection>
			<title>See Also</title>
			<para><xref linkend="ST_Equals"/>, <xref linkend="ST_Reverse"/></para>
		  </refsection>
	</refentry>

	<refentry id="ST_Overlaps">
	  <refnamediv>
		<refname>ST_Overlaps</refname>

		<refpurpose>Returns TRUE if the Geometries share space, are of the same dimension, but are not completely contained by each other.</refpurpose>
	  </refnamediv>

	  <refsynopsisdiv>
		<funcsynopsis>
		  <funcprototype>
			<funcdef>boolean <function>ST_Overlaps</function></funcdef>
			<paramdef><type>geometry </type> <parameter>A</parameter></paramdef>
			<paramdef><type>geometry </type> <parameter>B</parameter></paramdef>
		  </funcprototype>
		</funcsynopsis>
	  </refsynopsisdiv>

	  <refsection>
		<title>Description</title>

		<para>Returns TRUE if the Geometries "spatially
			overlap".  By that we mean they intersect, but one does not completely contain another. </para>

		 <para>Performed by the GEOS module</para>

		<note><para>Do not call with a GeometryCollection as an argument</para></note>

		<para>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.</para>

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

		<para>&sfs_compliant; s2.1.1.2 // s2.1.13.3</para>
		<para>&sqlmm_compliant; SQL-MM 3: 5.1.32</para>
	  </refsection>

	  <refsection>
		<title>Examples</title>
          <para>The following illustrations all return <varname>TRUE</varname>.</para>

	  <informaltable>
		<tgroup cols="3">
		  <tbody>
			<row>
			  <entry><para><informalfigure>
				  <mediaobject>
					<imageobject>
					  <imagedata fileref="images/st_overlaps01.png" />
					</imageobject>
					<caption><para><varname>MULTIPOINT</varname> / <varname>MULTIPOINT</varname></para></caption>
				  </mediaobject>
				</informalfigure></para></entry>

			  <entry><para><informalfigure>
				  <mediaobject>
					<imageobject>
					  <imagedata fileref="images/st_overlaps02.png" />
					</imageobject>
					<caption><para><varname>LINESTRING</varname> / <varname>LINESTRING</varname></para></caption>
				  </mediaobject>
				</informalfigure></para></entry>
			  <entry><para><informalfigure>
				  <mediaobject>
					<imageobject>
					  <imagedata fileref="images/st_overlaps03.png" />
					</imageobject>
					<caption><para><varname>POLYGON</varname> / <varname>POLYGON</varname></para></caption>
				  </mediaobject>
				</informalfigure></para></entry>
			</row>
		  </tbody>
		</tgroup>
	  </informaltable>
		<programlisting>--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
</programlisting>


	  </refsection>

	  <refsection>
		<title>See Also</title>

		<para><xref linkend="ST_Contains"/>, <xref linkend="ST_Crosses"/>, <xref linkend="ST_Dimension"/>, <xref linkend="ST_Intersects"/></para>
	  </refsection>
	</refentry>
	<refentry id="ST_Perimeter">
		<refnamediv>
		  <refname>ST_Perimeter</refname>

		  <refpurpose>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.</refpurpose>
		</refnamediv>
		<refsynopsisdiv>
		  <funcsynopsis>
			<funcprototype>
			  <funcdef>float <function>ST_Perimeter</function></funcdef>
				<paramdef><type>geometry </type><parameter>g1</parameter></paramdef>
			</funcprototype>

			<funcprototype>
			  <funcdef>float <function>ST_Perimeter</function></funcdef>
				<paramdef><type>geography </type><parameter>geog</parameter></paramdef>
				<paramdef choice="opt"><type>boolean </type><parameter>use_spheroid=true</parameter></paramdef>
			</funcprototype>
		  </funcsynopsis>
		</refsynopsisdiv>
		<refsection>
			<title>Description</title>

			<para>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 <xref linkend="ST_Length" />.  For geometry types, units for perimeter measures are specified by the
				spatial reference system of the geometry.</para>
			<para>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 <varname>use_spheroid=false</varname>, then calculations will approximate a sphere instead of a spheroid.</para>

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

			<para>&sfs_compliant; s2.1.5.1</para>
			<para>&sqlmm_compliant; SQL-MM 3: 8.1.3, 9.5.4</para>
			<para>Availability 2.0.0: Support for geography was introduced</para>
		</refsection>

		<refsection>
			<title>Examples: Geometry</title>
			<para>Return perimeter in feet for Polygon and MultiPolygon. Note this is in feet because EPSG:2249 is
				Massachusetts State Plane Feet</para>
			<programlisting>
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)
			</programlisting>
		  </refsection>
		  <refsection>
			<title>Examples: Geography</title>
			<para>Return perimeter in meters and feet for Polygon and MultiPolygon. Note this is geography (WGS 84 long lat)</para>
			<programlisting>
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
			</programlisting>
		  </refsection>
		<refsection>
			<title>See Also</title>
			<para><xref linkend="ST_GeogFromText" />, <xref linkend="ST_GeomFromText" />, <xref linkend="ST_Length" /></para>
		</refsection>
	</refentry>

	<refentry id="ST_Perimeter2D">
	  <refnamediv>
		<refname>ST_Perimeter2D</refname>

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

	  <refsynopsisdiv>
		<funcsynopsis>
		  <funcprototype>
			<funcdef>float <function>ST_Perimeter2D</function></funcdef>
			<paramdef><type>geometry </type> <parameter>geomA</parameter></paramdef>
		  </funcprototype>
		</funcsynopsis>
	  </refsynopsisdiv>

	  <refsection>
		<title>Description</title>

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

		<!-- optionally mention that this function uses indexes if appropriate -->
		<note>
		  <para> 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</para>
		</note>
	  </refsection>

	  <!-- Optionally add a "See Also" section -->
	  <refsection>
		<title>See Also</title>

		<para><xref linkend="ST_Perimeter" /></para>
	  </refsection>
	</refentry>

	<refentry id="ST_3DPerimeter">
	  <refnamediv>
		<refname>ST_3DPerimeter</refname>

		<refpurpose>Returns the 3-dimensional perimeter of the geometry, if it
			is a polygon or multi-polygon.</refpurpose>
	  </refnamediv>

	  <refsynopsisdiv>
		<funcsynopsis>
		  <funcprototype>
			<funcdef>float <function>ST_3DPerimeter</function></funcdef>
			<paramdef><type>geometry </type> <parameter>geomA</parameter></paramdef>
		  </funcprototype>
		</funcsynopsis>
	  </refsynopsisdiv>

	  <refsection>
		<title>Description</title>

		<para>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.  </para>
		<para>&Z_support;</para>
		<para>Changed: 2.0.0 In prior versions this used to be called ST_Perimeter3D</para>
	  </refsection>


	  <refsection>
		<title>Examples</title>
		<para>Perimeter of a slightly elevated polygon in the air in Massachusetts state plane feet</para>
		<programlisting>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

</programlisting>
	  </refsection>

	  <!-- Optionally add a "See Also" section -->
	  <refsection>
		<title>See Also</title>

		<para><xref linkend="ST_GeomFromEWKT" />, <xref linkend="ST_Perimeter" />, <xref linkend="ST_Perimeter2D" /></para>
	  </refsection>
	</refentry>

	<refentry id="ST_PointOnSurface">
	  <refnamediv>
		<refname>ST_PointOnSurface</refname>

		<refpurpose>Returns a <varname>POINT</varname> guaranteed to lie on the surface.</refpurpose>
	  </refnamediv>

	  <refsynopsisdiv>
		<funcsynopsis>
		  <funcprototype>
			<funcdef>geometry <function>ST_PointOnSurface</function></funcdef>

			<paramdef><type>geometry </type>
			<parameter>g1</parameter></paramdef>
		  </funcprototype>
		</funcsynopsis>
	  </refsynopsisdiv>

	  <refsection>
		<title>Description</title>

		<para>Returns a <varname>POINT</varname> guaranteed to intersect a surface.</para>

		<para>&sfs_compliant; s3.2.14.2 // s3.2.18.2</para>
		<para>&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.</para>
		<para>&Z_support;</para>
	  </refsection>

	  <refsection>
		<title>Examples</title>

		<programlisting>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)
</programlisting>
	  </refsection>

	  <refsection>
		<title>See Also</title>

		<para><xref linkend="ST_Centroid" />, <xref linkend="ST_Point_Inside_Circle" /></para>
	  </refsection>
	</refentry>

	<refentry id="ST_Project">
		  <refnamediv>
			<refname>ST_Project</refname>

			<refpurpose>Returns a <varname>POINT</varname> projected from a start point using a distance in meters and bearing (azimuth) in radians.</refpurpose>
		  </refnamediv>

		  <refsynopsisdiv>
			<funcsynopsis>
			  <funcprototype>
				<funcdef>geography <function>ST_Project</function></funcdef>

				<paramdef><type>geography </type>
				<parameter>g1</parameter></paramdef>
				<paramdef><type>float </type>
				<parameter>distance</parameter></paramdef>
				<paramdef><type>float </type>
				<parameter>azimuth</parameter></paramdef>
			  </funcprototype>
			</funcsynopsis>
		  </refsynopsisdiv>

		  <refsection>
			<title>Description</title>

			<para>Returns a <varname>POINT</varname> 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.</para>
			<para>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 (&#x03C0;/2), south is azimuth 180 (&#x03C0;), west is azimuth 270 (3&#x03C0;/2).</para>
			<para>The distance is given in meters.</para>

			<para>Availability: 2.0.0</para>

		  </refsection>

		  <refsection>
			<title>Example: Using degrees - projected point 100,000 meters and bearing 45 degrees </title>

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

                 st_astext
--------------------------------------------
 POINT(0.635231029125537 0.639472334729198)
(1 row)
      </programlisting>
		  </refsection>

		  <refsection>
			<title>See Also</title>

			<para><xref linkend="ST_Azimuth" />, <xref linkend="ST_Distance" />, <ulink url="http://www.postgresql.org/docs/current/interactive/functions-math.html">PostgreSQL Math Functions</ulink></para>
		  </refsection>
	</refentry>

	<refentry id="ST_Relate">
		<refnamediv>
			<refname>ST_Relate</refname>

			<refpurpose>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.</refpurpose>
		</refnamediv>

		<refsynopsisdiv>
			<funcsynopsis>
			  <funcprototype>
				<funcdef>boolean <function>ST_Relate</function></funcdef>
				<paramdef><type>geometry </type> <parameter>geomA</parameter></paramdef>
				<paramdef><type>geometry </type> <parameter>geomB</parameter></paramdef>
				<paramdef><type>text </type> <parameter>intersectionMatrixPattern</parameter></paramdef>
			  </funcprototype>

			  <funcprototype>
				<funcdef>text <function>ST_Relate</function></funcdef>
				<paramdef><type>geometry </type> <parameter>geomA</parameter></paramdef>
				<paramdef><type>geometry </type> <parameter>geomB</parameter></paramdef>
			  </funcprototype>

			  <funcprototype>
				<funcdef>text <function>ST_Relate</function></funcdef>
				<paramdef><type>geometry </type> <parameter>geomA</parameter></paramdef>
				<paramdef><type>geometry </type> <parameter>geomB</parameter></paramdef>
				<paramdef><type>integer </type> <parameter>BoundaryNodeRule</parameter></paramdef>
			  </funcprototype>
			</funcsynopsis>
		</refsynopsisdiv>

		<refsection>
			<title>Description</title>

			<para>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 <ulink url="http://en.wikipedia.org/wiki/DE-9IM">DE-9IM matrix pattern</ulink>.</para>

			<para>This is especially useful for testing compound checks of intersection, crosses, etc in one step.</para>
			<para>Do not call with a GeometryCollection as an argument</para>

			<note><para>This is the "allowable" version that returns a
			boolean, not an integer.  This is defined in OGC spec</para></note>

			<note><para>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 &amp;&amp;
				index call.</para></note>

			<para>Version 2: Takes geomA and geomB and returns the <xref linkend="DE-9IM" /></para>

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

			<note><para>Do not call with a GeometryCollection as an argument</para></note>

			<para>not in OGC spec, but implied. see s2.1.13.2</para>

			<para>Performed by the GEOS module</para>

			<para>&sfs_compliant; s2.1.1.2 // s2.1.13.3</para>
			<para>&sqlmm_compliant; SQL-MM 3: 5.1.25</para>
			<para>Enhanced: 2.0.0 - added support for specifying boundary node rule (requires GEOS &gt;= 3.0).</para>

		</refsection>


		<refsection>
		<title>Examples</title>
		<programlisting>
--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 &amp;&amp; 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
		</programlisting>
	</refsection>

	<!-- Optionally add a "See Also" section -->
	<refsection>
		<title>See Also</title>

		<para><xref linkend="ST_Crosses" />, <xref linkend="DE-9IM" />, <xref linkend="ST_Disjoint" />, <xref linkend="ST_Intersects" />, <xref linkend="ST_Touches" /></para>
	</refsection>
</refentry>

<refentry id="ST_RelateMatch">
	<refnamediv>
		<refname>ST_RelateMatch</refname>

		<refpurpose>Returns true if intersectionMattrixPattern1 implies intersectionMatrixPattern2</refpurpose>
	</refnamediv>

	<refsynopsisdiv>
		<funcsynopsis>
		  <funcprototype>
			<funcdef>boolean <function>ST_RelateMatch</function></funcdef>
			<paramdef><type>text </type> <parameter>intersectionMatrix</parameter></paramdef>
			<paramdef><type>text </type> <parameter>intersectionMatrixPattern</parameter></paramdef>
		  </funcprototype>
		</funcsynopsis>
	</refsynopsisdiv>

	<refsection>
		<title>Description</title>

		<para> Takes intersectionMatrix and intersectionMatrixPattern and Returns true if the intersectionMatrix satisfies
		the intersectionMatrixPattern. For more information refer to <xref linkend="DE-9IM" />.	</para>

		<para>Availability: 2.0.0 - requires GEOS &gt;= 3.3.0. </para>
	</refsection>


	<refsection>
		<title>Examples</title>
		<programlisting>
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);

		</programlisting>
	</refsection>

	<!-- Optionally add a "See Also" section -->
	<refsection>
		<title>See Also</title>
		<para><xref linkend="DE-9IM" />, <xref linkend="ST_Relate" /></para>
	</refsection>
</refentry>

<refentry id="ST_ShortestLine">
	  <refnamediv>
		<refname>ST_ShortestLine</refname>

		<refpurpose>Returns the 2-dimensional shortest line between two geometries</refpurpose>
	  </refnamediv>

	  <refsynopsisdiv>
		<funcsynopsis>
		  <funcprototype>
			<funcdef>geometry <function>ST_ShortestLine</function></funcdef>

			<paramdef><type>geometry </type>
			<parameter>g1</parameter></paramdef>

			<paramdef><type>geometry </type>
			<parameter>g2</parameter></paramdef>
		  </funcprototype>
		</funcsynopsis>
	  </refsynopsisdiv>

	  <refsection>
		<title>Description</title>

		<para>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.
		</para>

		<para>Availability: 1.5.0</para>
	  </refsection>

	  <refsection>
		<title>Examples</title>
			<informaltable>
				  <tgroup cols="2">
					<tbody>
					  <row>
						<entry><para><informalfigure>
							<mediaobject>
							  <imageobject>
								<imagedata fileref="images/st_shortestline01.png" />
							  </imageobject>
							  <caption><para>Shortest line between point and linestring</para></caption>
							</mediaobject>
						  </informalfigure>
				<programlisting>
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)
				</programlisting>
						  </para></entry>

						<entry><para><informalfigure>
							<mediaobject>
							  <imageobject>
								<imagedata fileref="images/st_shortestline02.png" />
							  </imageobject>
							  <caption><para>shortest line between polygon and polygon</para></caption>
							</mediaobject>
						  </informalfigure>
				<programlisting>
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)
				</programlisting>
						</para></entry>
					  </row>
		</tbody>
	</tgroup>
</informaltable>

	  </refsection>

	  <refsection>
		<title>See Also</title>

		<para><xref linkend="ST_ClosestPoint"/>, <xref linkend="ST_Distance"/>, <xref linkend="ST_LongestLine"/>, <xref linkend="ST_MaxDistance"/></para>
	  </refsection>
	</refentry>

	<refentry id="ST_Touches">
	  <refnamediv>
		<refname>ST_Touches</refname>

		<refpurpose>Returns <varname>TRUE</varname> if the geometries have at least one point in common,
		but their interiors do not intersect.</refpurpose>
	  </refnamediv>

	  <refsynopsisdiv>
		<funcsynopsis>
		  <funcprototype>
			<funcdef>boolean <function>ST_Touches</function></funcdef>

			<paramdef><type>geometry </type>
			<parameter>g1</parameter></paramdef>

			<paramdef><type>geometry </type>
			<parameter>g2</parameter></paramdef>
		  </funcprototype>
		</funcsynopsis>
	  </refsynopsisdiv>

	  <refsection>
		<title>Description</title>

		<para>Returns <varname>TRUE</varname> if the only points in common between
		<parameter>g1</parameter> and <parameter>g2</parameter> lie in the union of the
		boundaries of <parameter>g1</parameter> and <parameter>g2</parameter>.
		The <function>ST_Touches</function> relation applies
		to all Area/Area, Line/Line, Line/Area, Point/Area and Point/Line pairs of relationships,
		but <emphasis>not</emphasis> to the Point/Point pair.</para>

		<para>In mathematical terms, this predicate is expressed as:</para>

		<informalfigure>
		  <mediaobject>
			<imageobject>
			  <imagedata fileref="images/st_touches-math.gif" />
			</imageobject>
		  </mediaobject>
		</informalfigure>

		<para>The allowable DE-9IM Intersection Matrices for the two geometries are:</para>

		<itemizedlist>
		  <listitem>
			<para><markup>FT*******</markup></para>
		  </listitem>

		  <listitem>
			<para><markup>F**T*****</markup></para>
		  </listitem>

		  <listitem>
			<para><markup>F***T****</markup></para>
		  </listitem>
		</itemizedlist>

		<important>
		  <para>Do not call with a <varname>GEOMETRYCOLLECTION</varname> as an argument</para>
		</important>

		<note>
		  <para>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 <function>_ST_Touches</function> instead.</para>
		</note>

		<para>&sfs_compliant; s2.1.1.2 // s2.1.13.3</para>
		<para>&sqlmm_compliant; SQL-MM 3: 5.1.28</para>
	  </refsection>

	  <refsection>
		<title>Examples</title>

		<para>The <function>ST_Touches</function> predicate returns <varname>TRUE</varname> in all the following illustrations.</para>
		<informaltable>
		  <tgroup cols="3">
			<tbody>
			  <row>
				<entry><para><informalfigure>
					<mediaobject>
					  <imageobject>
						<imagedata fileref="images/st_touches01.png" />
					  </imageobject>

					  <caption><para><varname>POLYGON</varname> / <varname>POLYGON</varname></para></caption>
					</mediaobject>
				  </informalfigure></para></entry>

				<entry><para><informalfigure>
					<mediaobject>
					  <imageobject>
						<imagedata fileref="images/st_touches02.png" />
					  </imageobject>

					  <caption><para><varname>POLYGON</varname> / <varname>POLYGON</varname></para></caption>
					</mediaobject>
				  </informalfigure></para></entry>

				<entry><para><informalfigure>
					<mediaobject>
					  <imageobject>
						<imagedata fileref="images/st_touches03.png" />
					  </imageobject>

					  <caption><para><varname>POLYGON</varname> / <varname>LINESTRING</varname></para></caption>
					</mediaobject>
				  </informalfigure></para></entry>
			  </row>
			  <row>
				<entry><para><informalfigure>
					<mediaobject>
					  <imageobject>
						<imagedata fileref="images/st_touches04.png" />
					  </imageobject>

					  <caption><para><varname>LINESTRING</varname> / <varname>LINESTRING</varname></para></caption>
					</mediaobject>
				  </informalfigure></para></entry>

				<entry><para><informalfigure>
					<mediaobject>
					  <imageobject>
						<imagedata fileref="images/st_touches05.png" />
					  </imageobject>

					  <caption><para><varname>LINESTRING</varname> / <varname>LINESTRING</varname></para></caption>
					</mediaobject>
				  </informalfigure></para></entry>

				<entry><para><informalfigure>
					<mediaobject>
					  <imageobject>
						<imagedata fileref="images/st_touches06.png" />
					  </imageobject>

					  <caption><para><varname>POLYGON</varname> / <varname>POINT</varname></para></caption>
					</mediaobject>
				  </informalfigure></para></entry>
			  </row>
			</tbody>
		  </tgroup>
		</informaltable>

		<programlisting>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)</programlisting>
	  </refsection>
	</refentry>

	<refentry id="ST_Within">
	  <refnamediv>
		<refname>ST_Within</refname>

		<refpurpose>Returns true if the geometry A is completely inside geometry B</refpurpose>
	  </refnamediv>

	  <refsynopsisdiv>
		<funcsynopsis>
		  <funcprototype>
			<funcdef>boolean <function>ST_Within</function></funcdef>

			<paramdef><type>geometry </type>
			<parameter>A</parameter></paramdef>

			<paramdef><type>geometry </type>
			<parameter>B</parameter></paramdef>
		  </funcprototype>
		</funcsynopsis>
	  </refsynopsisdiv>

	  <refsection>
		<title>Description</title>

		<para>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.</para>

		<para>Performed by the GEOS module</para>

		<para>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.</para>

		<important>
		  <para>Do not call with a <varname>GEOMETRYCOLLECTION</varname> as an argument</para>
		</important>

		<important>
		  <para>Do not use this function with invalid geometries. You will get unexpected results.</para>
		</important>

		<para>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.</para>

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

		<para>&sfs_compliant; s2.1.1.2 // s2.1.13.3
		  - a.Relate(b, 'T*F**F***')
		</para>
		<para>&sqlmm_compliant; SQL-MM 3: 5.1.30</para>
	  </refsection>

	  <refsection>
		<title>Examples</title>
		  <programlisting>
--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)
		</programlisting>

		<para><inlinemediaobject>
		<imageobject>
		  <imagedata fileref="images/st_within01.png" />
		</imageobject>
	  </inlinemediaobject> </para>
	  </refsection>

	  <refsection>
		<title>See Also</title>
		<para><xref linkend="ST_Contains"/>, <xref linkend="ST_Equals"/>, <xref linkend="ST_IsValid"/></para>
	  </refsection>
	</refentry>


</sect1>
