<?xml version="1.0" encoding="UTF-8"?>
  <sect1 id="Operators">
	<title>Operators</title>

	    <sect2 id="operators-bbox">
      <title>Bounding Box Operators</title>

		<refentry id="geometry_overlaps">
		  <refnamediv>
			<refname>&amp;&amp;</refname>

			<refpurpose>Returns <varname>TRUE</varname> if A's 2D bounding box intersects B's 2D bounding box.</refpurpose>
		  </refnamediv>

		  <refsynopsisdiv>
			<funcsynopsis>
			  <funcprototype>
				<!-- TODO: Ideally, it would be nice if this could be reordered to
				"boolean (geometry A && geometry B)" instead of
				"boolean &&( geometry A, geometry B)" -->
				<funcdef>boolean <function>&amp;&amp;</function></funcdef>

				<paramdef>
				  <type>geometry </type>

				  <parameter>A</parameter>
				</paramdef>

				<paramdef>
				  <type>geometry </type>

				  <parameter>B</parameter>
				</paramdef>
			  </funcprototype>
			  <funcprototype>
				<funcdef>boolean <function>&amp;&amp;</function></funcdef>

				<paramdef>
				  <type>geography </type>

				  <parameter>A</parameter>
				</paramdef>

				<paramdef>
				  <type>geography </type>

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

        <refsection>
            <title>Description</title>

            <para>The <varname>&amp;&amp;</varname> operator returns <varname>TRUE</varname> if the 2D bounding box of geometry A intersects the 2D bounding box of geometry B.</para>

            <note><para>This operand will make use of any indexes that may be available on the
                geometries.</para></note>

            <para>Enhanced: 2.0.0 support for Polyhedral surfaces was introduced.</para>
            <para>Availability: 1.5.0 support for geography was introduced.</para>
            <para>&curve_support;</para>
            <para>&P_support;</para>
        </refsection>

		<refsection>
			<title>Examples</title>

			<programlisting>SELECT tbl1.column1, tbl2.column1, tbl1.column2 &amp;&amp; tbl2.column2 AS overlaps
FROM ( VALUES
	(1, 'LINESTRING(0 0, 3 3)'::geometry),
	(2, 'LINESTRING(0 1, 0 5)'::geometry)) AS tbl1,
( VALUES
	(3, 'LINESTRING(1 2, 4 6)'::geometry)) AS tbl2;

 column1 | column1 | overlaps
---------+---------+----------
	   1 |       3 | t
	   2 |       3 | f
(2 rows)</programlisting>
<!-- TODO Add geography examples -->
		  </refsection>

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

			<para>
                <xref linkend="ST_Intersects" />,
                <xref linkend="ST_Extent" />,
				<xref linkend="ST_Geometry_Overabove" />,
				<xref linkend="ST_Geometry_Overright" />,
				<xref linkend="ST_Geometry_Overbelow" />,
				<xref linkend="ST_Geometry_Overleft" />,
				<xref linkend="ST_Geometry_Contain" />,
				<xref linkend="ST_Geometry_Contained" />
            </para>
		  </refsection>
		</refentry>

		<refentry id="overlaps_geometry_box2df">
		  <refnamediv>
			<refname>&amp;&amp;(geometry,box2df)</refname>

			<refpurpose>Returns <varname>TRUE</varname> if a geometry's (cached) 2D bounding box intersects a 2D float precision bounding box (BOX2DF).</refpurpose>
		  </refnamediv>

		  <refsynopsisdiv>
			<funcsynopsis>
			  <funcprototype>
				<funcdef>boolean <function>&amp;&amp;</function></funcdef>

				<paramdef>
				  <type>geometry </type>

				  <parameter>A</parameter>
				</paramdef>

				<paramdef>
				  <type>box2df</type>

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

		  <refsection>
			<title>Description</title>

			<para>The <varname>&amp;&amp;</varname> operator returns <varname>TRUE</varname> if the cached 2D bounding box of geometry A intersects the 2D bounding box B, using float precision. This means that if B is a (double precision) box2d, it will be internally converted to a float precision 2D bounding box (BOX2DF)</para>

			<note><para>This operand is intended to be used internally by BRIN indexes, more
				than by users.</para></note>

			<para>Availability: 2.3.0 support for Block Range INdexes (BRIN) was introduced. Requires PostgreSQL 9.5+.</para>
			<para>&curve_support;</para>
			<para>&P_support;</para>
		  </refsection>

		  <refsection>
			<title>Examples</title>

			<programlisting>SELECT ST_Point(1,1) &amp;&amp; ST_MakeBox2D(ST_Point(0,0), ST_Point(2,2)) AS overlaps;

 overlaps
----------
 t
(1 row)</programlisting>
		  </refsection>

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

			<para>
				<xref linkend="overlaps_box2df_geometry" />,
				<xref linkend="overlaps_box2df_box2df" />,
				<xref linkend="contains_geometry_box2df" />,
				<xref linkend="contains_box2df_geometry" />,
				<xref linkend="contains_box2df_box2df" />,
				<xref linkend="is_contained_geometry_box2df" />,
				<xref linkend="is_contained_box2df_geometry" />,
				<xref linkend="is_contained_box2df_box2df" /></para>
		  </refsection>
		</refentry>

		<refentry id="overlaps_box2df_geometry">
		  <refnamediv>
			<refname>&amp;&amp;(box2df,geometry)</refname>

			<refpurpose>Returns <varname>TRUE</varname> if a 2D float precision bounding box (BOX2DF) intersects a geometry's (cached) 2D bounding box.</refpurpose>
		  </refnamediv>

		  <refsynopsisdiv>
			<funcsynopsis>
			  <funcprototype>
				<funcdef>boolean <function>&amp;&amp;</function></funcdef>

				<paramdef>
				  <type>box2df </type>

				  <parameter>A</parameter>
				</paramdef>

				<paramdef>
				  <type>geometry </type>

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

		  <refsection>
			<title>Description</title>

			<para>The <varname>&amp;&amp;</varname> operator returns <varname>TRUE</varname> if the 2D bounding box A intersects the cached 2D bounding box of geometry B, using float precision. This means that if A is a (double precision) box2d, it will be internally converted to a float precision 2D bounding box (BOX2DF)</para>

			<note><para>This operand is intended to be used internally by BRIN indexes, more
				than by users.</para></note>

			<para>Availability: 2.3.0 support for Block Range INdexes (BRIN) was introduced. Requires PostgreSQL 9.5+.</para>
			<para>&curve_support;</para>
			<para>&P_support;</para>
		  </refsection>

		  <refsection>
			<title>Examples</title>

			<programlisting>SELECT ST_MakeBox2D(ST_Point(0,0), ST_Point(2,2)) &amp;&amp; ST_Point(1,1) AS overlaps;

 overlaps
----------
 t
(1 row)</programlisting>
		  </refsection>

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

			<para>
				<xref linkend="overlaps_geometry_box2df" />,
				<xref linkend="overlaps_box2df_box2df" />,
				<xref linkend="contains_geometry_box2df" />,
				<xref linkend="contains_box2df_geometry" />,
				<xref linkend="contains_box2df_box2df" />,
				<xref linkend="is_contained_geometry_box2df" />,
				<xref linkend="is_contained_box2df_geometry" />,
				<xref linkend="is_contained_box2df_box2df" /></para>
		  </refsection>
		</refentry>

		<refentry id="overlaps_box2df_box2df">
		  <refnamediv>
			<refname>&amp;&amp;(box2df,box2df)</refname>

			<refpurpose>Returns <varname>TRUE</varname> if two 2D float precision bounding boxes (BOX2DF) intersect each other.</refpurpose>
		  </refnamediv>

		  <refsynopsisdiv>
			<funcsynopsis>
			  <funcprototype>
				<funcdef>boolean <function>&amp;&amp;</function></funcdef>

				<paramdef>
				  <type>box2df </type>

				  <parameter>A</parameter>
				</paramdef>

				<paramdef>
				  <type>box2df </type>

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

		  <refsection>
			<title>Description</title>

			<para>The <varname>&amp;&amp;</varname> operator returns <varname>TRUE</varname> if two 2D bounding boxes A and B intersect each other, using float precision. This means that if A (or B) is a (double precision) box2d, it will be internally converted to a float precision 2D bounding box (BOX2DF)</para>

			<note><para>This operator is intended to be used internally by BRIN indexes, more
				than by users.</para></note>

			<para>Availability: 2.3.0 support for Block Range INdexes (BRIN) was introduced. Requires PostgreSQL 9.5+.</para>
			<para>&curve_support;</para>
			<para>&P_support;</para>
		  </refsection>

		  <refsection>
			<title>Examples</title>

			<programlisting>SELECT ST_MakeBox2D(ST_Point(0,0), ST_Point(2,2)) &amp;&amp; ST_MakeBox2D(ST_Point(1,1), ST_Point(3,3)) AS overlaps;

 overlaps
----------
 t
(1 row)</programlisting>
		  </refsection>

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

			<para>
				<xref linkend="overlaps_geometry_box2df" />,
				<xref linkend="overlaps_box2df_geometry" />,
				<xref linkend="contains_geometry_box2df" />,
				<xref linkend="contains_box2df_geometry" />,
				<xref linkend="contains_box2df_box2df" />,
				<xref linkend="is_contained_geometry_box2df" />,
				<xref linkend="is_contained_box2df_geometry" />,
				<xref linkend="is_contained_box2df_box2df" /></para>
		  </refsection>
		</refentry>

		<refentry id="geometry_overlaps_nd">
		  <refnamediv>
			<refname>&amp;&amp;&amp;</refname>

			<refpurpose>Returns <varname>TRUE</varname> if A's n-D bounding box intersects B's n-D bounding box.</refpurpose>
		  </refnamediv>

		  <refsynopsisdiv>
		      <funcsynopsis>
		      <funcprototype>
				<funcdef>boolean <function>&amp;&amp;&amp;</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>The <varname>&amp;&amp;&amp;</varname> operator returns <varname>TRUE</varname> if the n-D bounding box of geometry A intersects the n-D bounding box of geometry B.</para>

			<note><para>This operand will make use of any indexes that may be available on the
				geometries.</para></note>

			<para>Availability: 2.0.0</para>
			<para>&curve_support;</para>
			<para>&P_support;</para>
			<para>&T_support;</para>
			<para>&Z_support;</para>
		  </refsection>

		  <refsection>
			<title>Examples: 3D LineStrings</title>

			<programlisting>SELECT tbl1.column1, tbl2.column1, tbl1.column2 &amp;&amp;&amp; tbl2.column2 AS overlaps_3d,
			            tbl1.column2 &amp;&amp; tbl2.column2 AS overlaps_2d
FROM ( VALUES
	(1, 'LINESTRING Z(0 0 1, 3 3 2)'::geometry),
	(2, 'LINESTRING Z(1 2 0, 0 5 -1)'::geometry)) AS tbl1,
( VALUES
	(3, 'LINESTRING Z(1 2 1, 4 6 1)'::geometry)) AS tbl2;

 column1 | column1 | overlaps_3d | overlaps_2d
---------+---------+-------------+-------------
       1 |       3 | t           | t
       2 |       3 | f           | t
</programlisting>

		  </refsection>
		  <refsection>
			<title>Examples: 3M LineStrings</title>

			<programlisting>SELECT tbl1.column1, tbl2.column1, tbl1.column2 &amp;&amp;&amp; tbl2.column2 AS overlaps_3zm,
			            tbl1.column2 &amp;&amp; tbl2.column2 AS overlaps_2d
FROM ( VALUES
	(1, 'LINESTRING M(0 0 1, 3 3 2)'::geometry),
	(2, 'LINESTRING M(1 2 0, 0 5 -1)'::geometry)) AS tbl1,
( VALUES
	(3, 'LINESTRING M(1 2 1, 4 6 1)'::geometry)) AS tbl2;

 column1 | column1 | overlaps_3zm | overlaps_2d
---------+---------+-------------+-------------
       1 |       3 | t           | t
       2 |       3 | f           | t
</programlisting>

		  </refsection>

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

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

		<refentry id="overlaps_nd_geometry_gidx">
		  <refnamediv>
			<refname>&amp;&amp;&amp;(geometry,gidx)</refname>

			<refpurpose>Returns <varname>TRUE</varname> if a geometry's (cached) n-D bounding box intersects a n-D float precision bounding box (GIDX).</refpurpose>
		  </refnamediv>

		  <refsynopsisdiv>
			<funcsynopsis>
			  <funcprototype>
				<funcdef>boolean <function>&amp;&amp;&amp;</function></funcdef>

				<paramdef>
				  <type>geometry </type>

				  <parameter>A</parameter>
				</paramdef>

				<paramdef>
				  <type>gidx </type>

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

		  <refsection>
			<title>Description</title>

			<para>The <varname>&amp;&amp;&amp;</varname> operator returns <varname>TRUE</varname> if the cached n-D bounding box of geometry A intersects the n-D bounding box B, using float precision. This means that if B is a (double precision) box3d, it will be internally converted to a float precision 3D bounding box (GIDX)</para>

			<note><para>This operator is intended to be used internally by BRIN indexes, more
				than by users.</para></note>

			<para>Availability: 2.3.0 support for Block Range INdexes (BRIN) was introduced. Requires PostgreSQL 9.5+.</para>
			<para>&curve_support;</para>
			<para>&P_support;</para>
			<para>&T_support;</para>
			<para>&Z_support;</para>
		  </refsection>

		  <refsection>
			<title>Examples</title>

			<programlisting>SELECT ST_MakePoint(1,1,1) &amp;&amp;&amp; ST_3DMakeBox(ST_MakePoint(0,0,0), ST_MakePoint(2,2,2)) AS overlaps;

 overlaps
----------
 t
(1 row)</programlisting>
		  </refsection>

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

			<para>
				<xref linkend="overlaps_nd_gidx_geometry" />,
				<xref linkend="overlaps_nd_gidx_gidx" /></para>
		  </refsection>
		</refentry>

		<refentry id="overlaps_nd_gidx_geometry">
		  <refnamediv>
			<refname>&amp;&amp;&amp;(gidx,geometry)</refname>

			<refpurpose>Returns <varname>TRUE</varname> if a n-D float precision bounding box (GIDX) intersects a geometry's (cached) n-D bounding box.</refpurpose>
		  </refnamediv>

		  <refsynopsisdiv>
			<funcsynopsis>
			  <funcprototype>
				<funcdef>boolean <function>&amp;&amp;&amp;</function></funcdef>

				<paramdef>
				  <type>gidx </type>

				  <parameter>A</parameter>
				</paramdef>

				<paramdef>
				  <type>geometry </type>

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

		  <refsection>
			<title>Description</title>

			<para>The <varname>&amp;&amp;&amp;</varname> operator returns <varname>TRUE</varname> if the n-D bounding box A intersects the cached n-D bounding box of geometry B, using float precision. This means that if A is a (double precision) box3d, it will be internally converted to a float precision 3D bounding box (GIDX)</para>

			<note><para>This operator is intended to be used internally by BRIN indexes, more
				than by users.</para></note>

			<para>Availability: 2.3.0 support for Block Range INdexes (BRIN) was introduced. Requires PostgreSQL 9.5+.</para>
			<para>&curve_support;</para>
			<para>&P_support;</para>
			<para>&T_support;</para>
			<para>&Z_support;</para>
		  </refsection>

		  <refsection>
			<title>Examples</title>

			<programlisting>SELECT ST_3DMakeBox(ST_MakePoint(0,0,0), ST_MakePoint(2,2,2)) &amp;&amp;&amp; ST_MakePoint(1,1,1) AS overlaps;

 overlaps
----------
 t
(1 row)</programlisting>
		  </refsection>

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

			<para>
				<xref linkend="overlaps_nd_geometry_gidx" />,
				<xref linkend="overlaps_nd_gidx_gidx" /></para>
		  </refsection>
		</refentry>

		<refentry id="overlaps_nd_gidx_gidx">
		  <refnamediv>
			<refname>&amp;&amp;&amp;(gidx,gidx)</refname>

			<refpurpose>Returns <varname>TRUE</varname> if two n-D float precision bounding boxes (GIDX) intersect each other.</refpurpose>
		  </refnamediv>

		  <refsynopsisdiv>
			<funcsynopsis>
			  <funcprototype>
				<funcdef>boolean <function>&amp;&amp;&amp;</function></funcdef>

				<paramdef>
				  <type>gidx </type>

				  <parameter>A</parameter>
				</paramdef>

				<paramdef>
				  <type>gidx </type>

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

		  <refsection>
			<title>Description</title>

			<para>The <varname>&amp;&amp;&amp;</varname> operator returns <varname>TRUE</varname> if two n-D bounding boxes A and B intersect each other, using float precision. This means that if A (or B) is a (double precision) box3d, it will be internally converted to a float precision 3D bounding box (GIDX)</para>

			<note><para>This operator is intended to be used internally by BRIN indexes, more
				than by users.</para></note>

			<para>Availability: 2.3.0 support for Block Range INdexes (BRIN) was introduced. Requires PostgreSQL 9.5+.</para>
			<para>&curve_support;</para>
			<para>&P_support;</para>
			<para>&T_support;</para>
			<para>&Z_support;</para>
		  </refsection>

		  <refsection>
			<title>Examples</title>

			<programlisting>SELECT ST_3DMakeBox(ST_MakePoint(0,0,0), ST_MakePoint(2,2,2)) &amp;&amp;&amp; ST_3DMakeBox(ST_MakePoint(1,1,1), ST_MakePoint(3,3,3)) AS overlaps;

 overlaps
----------
 t
(1 row)</programlisting>
		  </refsection>

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

			<para>
                                <xref linkend="overlaps_nd_geometry_gidx" />,
                                <xref linkend="overlaps_nd_gidx_geometry" /></para>
		  </refsection>
		</refentry>

		<refentry id="ST_Geometry_Overleft">
		  <refnamediv>
			<refname>&amp;&lt;</refname>

			<refpurpose>Returns <varname>TRUE</varname> if A's bounding box overlaps or is to the left of B's.</refpurpose>
		  </refnamediv>

		  <refsynopsisdiv>
			<funcsynopsis>
			  <funcprototype>
				<!-- TODO: Ideally, it would be nice if this could be reordered to
				"boolean (geometry A &< geometry B)" instead of
				"boolean &<( geometry A, geometry B)" -->
				<funcdef>boolean <function>&amp;&lt;</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>The <varname>&amp;&lt;</varname> operator returns <varname>TRUE</varname> if the bounding box of geometry A
			overlaps or is to the left of the bounding box of geometry B, or more accurately, overlaps or is NOT to the right
			of the bounding box of geometry B.</para>

			<note><para>This operand will make use of any indexes that may be available on the
				geometries.</para></note>
		  </refsection>

		  <refsection>
			<title>Examples</title>

			<programlisting>SELECT tbl1.column1, tbl2.column1, tbl1.column2 &amp;&lt; tbl2.column2 AS overleft
FROM
  ( VALUES
	(1, 'LINESTRING(1 2, 4 6)'::geometry)) AS tbl1,
  ( VALUES
	(2, 'LINESTRING(0 0, 3 3)'::geometry),
	(3, 'LINESTRING(0 1, 0 5)'::geometry),
	(4, 'LINESTRING(6 0, 6 1)'::geometry)) AS tbl2;

 column1 | column1 | overleft
---------+---------+----------
	   1 |       2 | f
	   1 |       3 | f
	   1 |       4 | t
(3 rows)</programlisting>
		  </refsection>

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

			<para>
				<xref linkend="geometry_overlaps" />,
				<xref linkend="ST_Geometry_Overabove" />,
				<xref linkend="ST_Geometry_Overright" />,
				<xref linkend="ST_Geometry_Overbelow" /></para>
		  </refsection>
		</refentry>

		<refentry id="ST_Geometry_Overbelow">
		  <refnamediv>
			<refname>&amp;&lt;|</refname>

			<refpurpose>Returns <varname>TRUE</varname> if A's bounding box overlaps or is below B's.</refpurpose>
		  </refnamediv>

		  <refsynopsisdiv>
			<funcsynopsis>
			  <funcprototype>
				<!-- TODO: Ideally, it would be nice if this could be reordered to
				"boolean (geometry A &<| geometry B)" instead of
				"boolean &<|( geometry A, geometry B)" -->
				<funcdef>boolean <function>&amp;&lt;|</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>The <varname>&amp;&lt;|</varname> operator returns <varname>TRUE</varname> if the bounding box of geometry A
			overlaps or is below of the bounding box of geometry B, or more accurately, overlaps or is NOT above the bounding
			box of geometry B.</para>

			<para>&curve_support;</para>
			<para>&P_support;</para>

			<note><para>This operand will make use of any indexes that may be available on the
				geometries.</para></note>
		  </refsection>

		  <refsection>
			<title>Examples</title>

			<programlisting>SELECT tbl1.column1, tbl2.column1, tbl1.column2 &amp;&lt;| tbl2.column2 AS overbelow
FROM
  ( VALUES
	(1, 'LINESTRING(6 0, 6 4)'::geometry)) AS tbl1,
  ( VALUES
	(2, 'LINESTRING(0 0, 3 3)'::geometry),
	(3, 'LINESTRING(0 1, 0 5)'::geometry),
	(4, 'LINESTRING(1 2, 4 6)'::geometry)) AS tbl2;

 column1 | column1 | overbelow
---------+---------+-----------
	   1 |       2 | f
	   1 |       3 | t
	   1 |       4 | t
(3 rows)</programlisting>
		  </refsection>

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

			<para>
				<xref linkend="geometry_overlaps" />,
				<xref linkend="ST_Geometry_Overabove" />,
				<xref linkend="ST_Geometry_Overright" />,
				<xref linkend="ST_Geometry_Overleft" /></para>
		  </refsection>
		</refentry>

		<refentry id="ST_Geometry_Overright">
		  <refnamediv>
			<refname>&amp;&gt;</refname>

			<refpurpose>Returns <varname>TRUE</varname> if A' bounding box overlaps or is to the right of B's.</refpurpose>
		  </refnamediv>

		  <refsynopsisdiv>
			<funcsynopsis>
			  <funcprototype>
				<!-- TODO: Ideally, it would be nice if this could be reordered to
				"boolean (geometry A &> geometry B)" instead of
				"boolean &>( geometry A, geometry B)" -->
				<funcdef>boolean <function>&amp;&gt;</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>The <varname>&amp;&gt;</varname> operator returns <varname>TRUE</varname> if the bounding box of geometry A
			overlaps or is to the right of the bounding box of geometry B, or more accurately, overlaps or is NOT to the left
			of the bounding box of geometry B.</para>

			<note><para>This operand will make use of any indexes that may be available on the
				geometries.</para></note>
		  </refsection>

		  <refsection>
			<title>Examples</title>

			<programlisting>SELECT tbl1.column1, tbl2.column1, tbl1.column2 &amp;&gt; tbl2.column2 AS overright
FROM
  ( VALUES
	(1, 'LINESTRING(1 2, 4 6)'::geometry)) AS tbl1,
  ( VALUES
	(2, 'LINESTRING(0 0, 3 3)'::geometry),
	(3, 'LINESTRING(0 1, 0 5)'::geometry),
	(4, 'LINESTRING(6 0, 6 1)'::geometry)) AS tbl2;

 column1 | column1 | overright
---------+---------+-----------
	   1 |       2 | t
	   1 |       3 | t
	   1 |       4 | f
(3 rows)</programlisting>
		  </refsection>

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

			<para>
				<xref linkend="geometry_overlaps" />,
				<xref linkend="ST_Geometry_Overabove" />,
				<xref linkend="ST_Geometry_Overbelow" />,
				<xref linkend="ST_Geometry_Overleft" /></para>
		  </refsection>
		</refentry>

		<refentry id="ST_Geometry_Left">
		  <refnamediv>
			<refname>&lt;&lt;</refname>

			<refpurpose>Returns <varname>TRUE</varname> if A's bounding box is strictly to the left of B's.</refpurpose>
		  </refnamediv>

		  <refsynopsisdiv>
			<funcsynopsis>
			  <funcprototype>
				<!-- TODO: Ideally, it would be nice if this could be reordered to
				"boolean (geometry A << geometry B)" instead of
				"boolean <<( geometry A, geometry B)" -->
				<funcdef>boolean <function>&lt;&lt;</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>The <varname>&lt;&lt;</varname> operator returns <varname>TRUE</varname> if the bounding box of geometry A
			is strictly to the left of the bounding box of geometry B.</para>

			<note><para>This operand will make use of any indexes that may be available on the
				geometries.</para></note>
		  </refsection>

		  <refsection>
			<title>Examples</title>

			<programlisting>SELECT tbl1.column1, tbl2.column1, tbl1.column2 &lt;&lt; tbl2.column2 AS left
FROM
  ( VALUES
	(1, 'LINESTRING (1 2, 1 5)'::geometry)) AS tbl1,
  ( VALUES
	(2, 'LINESTRING (0 0, 4 3)'::geometry),
	(3, 'LINESTRING (6 0, 6 5)'::geometry),
	(4, 'LINESTRING (2 2, 5 6)'::geometry)) AS tbl2;

 column1 | column1 | left
---------+---------+------
	   1 |       2 | f
	   1 |       3 | t
	   1 |       4 | t
(3 rows)</programlisting>
		  </refsection>

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

			<para><xref linkend="ST_Geometry_Right" />, <xref linkend="ST_Geometry_Above" />, <xref linkend="ST_Geometry_Below" /></para>
		  </refsection>
		</refentry>

		<refentry id="ST_Geometry_Below">
		  <refnamediv>
			<refname>&lt;&lt;|</refname>

			<refpurpose>Returns <varname>TRUE</varname> if A's bounding box is strictly below B's.</refpurpose>
		  </refnamediv>

		  <refsynopsisdiv>
			<funcsynopsis>
			  <funcprototype>
				<!-- TODO: Ideally, it would be nice if this could be reordered to
				"boolean (geometry A <<| geometry B)" instead of
				"boolean <<|( geometry A, geometry B)" -->
				<funcdef>boolean <function>&lt;&lt;|</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>The <varname>&lt;&lt;|</varname> operator returns <varname>TRUE</varname> if the bounding box of geometry A
			is strictly below the bounding box of geometry B.</para>

			<note><para>This operand will make use of any indexes that may be available on the
				geometries.</para></note>
		  </refsection>

		  <refsection>
			<title>Examples</title>

			<programlisting>SELECT tbl1.column1, tbl2.column1, tbl1.column2 &lt;&lt;| tbl2.column2 AS below
FROM
  ( VALUES
	(1, 'LINESTRING (0 0, 4 3)'::geometry)) AS tbl1,
  ( VALUES
	(2, 'LINESTRING (1 4, 1 7)'::geometry),
	(3, 'LINESTRING (6 1, 6 5)'::geometry),
	(4, 'LINESTRING (2 3, 5 6)'::geometry)) AS tbl2;

 column1 | column1 | below
---------+---------+-------
	   1 |       2 | t
	   1 |       3 | f
	   1 |       4 | f
(3 rows)</programlisting>
		  </refsection>

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

			<para><xref linkend="ST_Geometry_Left" />, <xref linkend="ST_Geometry_Right" />, <xref linkend="ST_Geometry_Above" /></para>
		  </refsection>
		</refentry>

		<refentry id="ST_Geometry_EQ">
		  <refnamediv>
			<refname>&#61;</refname>

			<refpurpose>Returns <varname>TRUE</varname> if the coordinates and coordinate order geometry/geography A
			are the same as the coordinates and coordinate order of geometry/geography B.</refpurpose>
		  </refnamediv>

		  <refsynopsisdiv>
			<funcsynopsis>
			  <funcprototype>
				<!-- TODO: Ideally, it would be nice if this could be reordered to
				"boolean (geometry A = geometry B)" instead of
				"boolean =( geometry A, geometry B)" -->
				<funcdef>boolean <function>&#61;</function></funcdef>

				<paramdef>
				  <type>geometry </type>

				  <parameter>A</parameter>
				</paramdef>

				<paramdef>
				  <type>geometry </type>

				  <parameter>B</parameter>
				</paramdef>
			  </funcprototype>

			  <funcprototype>
				<funcdef>boolean <function>&#61;</function></funcdef>

					<paramdef>
					  <type>geography </type>

					  <parameter>A</parameter>
					</paramdef>

					<paramdef>
					  <type>geography </type>

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

		  <refsection>
			<title>Description</title>

			<para>The <varname>&#61;</varname> operator returns <varname>TRUE</varname> if the coordinates and coordinate order geometry/geography A
			are the same as the coordinates and coordinate order of geometry/geography B.  PostgreSQL uses the =, &lt;, and &gt; operators defined for geometries to
			perform internal orderings and comparison of geometries (ie. in a GROUP BY or ORDER BY clause).</para>

			<note>
			  <para>Only geometry/geography that are exactly equal in all respects,
          with the same coordinates, in the same order, are considered
          equal by this operator. For "spatial equality", that ignores
          things like coordinate order, and can detect features that
          cover the same spatial area with different representations,
          use <xref linkend="ST_OrderingEquals" />
          or <xref linkend="ST_Equals" /></para>
			</note>

			<caution><para>This operand will NOT make use of any indexes that may be available on the
				geometries. For an index assisted exact equality test, combine &#61; with &amp;&amp;.</para></caution>


			<para>Changed: 2.4.0, in prior versions this was bounding box equality not a geometric equality. If you need bounding box equality, use <xref linkend="ST_Geometry_Same" /> instead.</para>

			<para>&curve_support;</para>
			<para>&P_support;</para>

		  </refsection>

		  <refsection>
			<title>Examples</title>

			<programlisting>SELECT 'LINESTRING(0 0, 0 1, 1 0)'::geometry = 'LINESTRING(1 1, 0 0)'::geometry;
 ?column?
----------
 f
(1 row)

SELECT ST_AsText(column1)
FROM ( VALUES
	('LINESTRING(0 0, 1 1)'::geometry),
	('LINESTRING(1 1, 0 0)'::geometry)) AS foo;
	  st_astext
---------------------
 LINESTRING(0 0,1 1)
 LINESTRING(1 1,0 0)
(2 rows)

-- Note: the GROUP BY uses the "=" to compare for geometry equivalency.
SELECT ST_AsText(column1)
FROM ( VALUES
	('LINESTRING(0 0, 1 1)'::geometry),
	('LINESTRING(1 1, 0 0)'::geometry)) AS foo
GROUP BY column1;
      st_astext
---------------------
 LINESTRING(0 0,1 1)
 LINESTRING(1 1,0 0)
(2 rows)

-- In versions prior to 2.0, this used to return true --
 SELECT ST_GeomFromText('POINT(1707296.37 4820536.77)') =
	ST_GeomFromText('POINT(1707296.27 4820536.87)') As pt_intersect;

--pt_intersect --
f
</programlisting>
		  </refsection>

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

			<para><xref linkend="ST_Equals" />, <xref linkend="ST_OrderingEquals" />, <xref linkend="ST_Geometry_Same" />
			<!--, <xref linkend="ST_Geometry_LT" />, <xref linkend="ST_Geometry_GT" /> --></para>
		  </refsection>
		</refentry>

		<refentry id="ST_Geometry_Right">
		  <refnamediv>
			<refname>&gt;&gt;</refname>

			<refpurpose>Returns <varname>TRUE</varname> if A's bounding box is strictly to the right of B's.</refpurpose>
		  </refnamediv>

		  <refsynopsisdiv>
			<funcsynopsis>
			  <funcprototype>
				<!-- TODO: Ideally, it would be nice if this could be reordered to
				"boolean (geometry A >> geometry B)" instead of
				"boolean >>( geometry A, geometry B)" -->
				<funcdef>boolean <function>&gt;&gt;</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>The <varname>&gt;&gt;</varname> operator returns <varname>TRUE</varname> if the bounding box of geometry A
			is strictly to the right of the bounding box of geometry B.</para>

			<note><para>This operand will make use of any indexes that may be available on the
				geometries.</para></note>
		  </refsection>

		  <refsection>
			<title>Examples</title>

			<programlisting>SELECT tbl1.column1, tbl2.column1, tbl1.column2 &gt;&gt; tbl2.column2 AS right
FROM
  ( VALUES
	(1, 'LINESTRING (2 3, 5 6)'::geometry)) AS tbl1,
  ( VALUES
	(2, 'LINESTRING (1 4, 1 7)'::geometry),
	(3, 'LINESTRING (6 1, 6 5)'::geometry),
	(4, 'LINESTRING (0 0, 4 3)'::geometry)) AS tbl2;

 column1 | column1 | right
---------+---------+-------
	   1 |       2 | t
	   1 |       3 | f
	   1 |       4 | f
(3 rows)</programlisting>
		  </refsection>

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

			<para><xref linkend="ST_Geometry_Left" />, <xref linkend="ST_Geometry_Above" />, <xref linkend="ST_Geometry_Below" /></para>
		  </refsection>
		</refentry>

		<refentry id="ST_Geometry_Contained">
		  <refnamediv>
			<refname>@</refname>

			<refpurpose>Returns <varname>TRUE</varname> if A's bounding box is contained by B's.</refpurpose>
		  </refnamediv>

		  <refsynopsisdiv>
			<funcsynopsis>
			  <funcprototype>
				<!-- TODO: Ideally, it would be nice if this could be reordered to
				"boolean (geometry A @ geometry B)" instead of
				"boolean @( geometry A, geometry B)" -->
				<funcdef>boolean <function>@</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>The <varname>@</varname> operator returns <varname>TRUE</varname> if the bounding box of geometry A is completely
			contained by the bounding box of geometry B.</para>

			<note>
			  <para>This operand will make use of any indexes that may be available on the
			  geometries.</para>
			</note>
		  </refsection>

		  <refsection>
			<title>Examples</title>

			<programlisting>SELECT tbl1.column1, tbl2.column1, tbl1.column2 @ tbl2.column2 AS contained
FROM
  ( VALUES
	(1, 'LINESTRING (1 1, 3 3)'::geometry)) AS tbl1,
  ( VALUES
	(2, 'LINESTRING (0 0, 4 4)'::geometry),
	(3, 'LINESTRING (2 2, 4 4)'::geometry),
	(4, 'LINESTRING (1 1, 3 3)'::geometry)) AS tbl2;

 column1 | column1 | contained
---------+---------+-----------
	   1 |       2 | t
	   1 |       3 | f
	   1 |       4 | t
(3 rows)</programlisting>
		  </refsection>

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

			<para><xref linkend="ST_Geometry_Contain" />, <xref linkend="geometry_overlaps" /></para>
		  </refsection>
		</refentry>

		<refentry id="is_contained_geometry_box2df">
		  <refnamediv>
			<refname>@(geometry,box2df)</refname>

			<refpurpose>Returns <varname>TRUE</varname> if a geometry's 2D bounding box is contained into a 2D float precision bounding box (BOX2DF).</refpurpose>
		  </refnamediv>

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

				<paramdef>
				  <type>geometry </type>

				  <parameter>A</parameter>
				</paramdef>

				<paramdef>
				  <type>box2df </type>

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

		  <refsection>
			<title>Description</title>

			<para>The <varname>@</varname> operator returns <varname>TRUE</varname> if the A geometry's 2D bounding box is contained the 2D bounding box B, using float precision. This means that if B is a (double precision) box2d, it will be internally converted to a float precision 2D bounding box (BOX2DF)</para>

			<note><para>This operand is intended to be used internally by BRIN indexes, more
				than by users.</para></note>

			<para>Availability: 2.3.0 support for Block Range INdexes (BRIN) was introduced. Requires PostgreSQL 9.5+.</para>
			<para>&curve_support;</para>
			<para>&P_support;</para>
		  </refsection>

		  <refsection>
			<title>Examples</title>

			<programlisting>SELECT ST_Buffer(ST_GeomFromText('POINT(2 2)'), 1) @ ST_MakeBox2D(ST_Point(0,0), ST_Point(5,5)) AS is_contained;

 is_contained
--------------
 t
(1 row)</programlisting>
		  </refsection>

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

			<para>
				<xref linkend="overlaps_geometry_box2df" />,
				<xref linkend="overlaps_box2df_geometry" />,
				<xref linkend="overlaps_box2df_box2df" />,
				<xref linkend="contains_geometry_box2df" />,
				<xref linkend="contains_box2df_geometry" />,
				<xref linkend="contains_box2df_box2df" />,
				<xref linkend="is_contained_box2df_geometry" />,
				<xref linkend="is_contained_box2df_box2df" /></para>
		  </refsection>
		</refentry>

		<refentry id="is_contained_box2df_geometry">
		  <refnamediv>
			<refname>@(box2df,geometry)</refname>

			<refpurpose>Returns <varname>TRUE</varname> if a 2D float precision bounding box (BOX2DF) is contained into a geometry's 2D bounding box.</refpurpose>
		  </refnamediv>

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

				<paramdef>
				  <type>box2df </type>

				  <parameter>A</parameter>
				</paramdef>

				<paramdef>
				  <type>geometry </type>

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

		  <refsection>
			<title>Description</title>

			<para>The <varname>@</varname> operator returns <varname>TRUE</varname> if the 2D bounding box A is contained into the B geometry's 2D bounding box, using float precision. This means that if B is a (double precision) box2d, it will be internally converted to a float precision 2D bounding box (BOX2DF)</para>

			<note><para>This operand is intended to be used internally by BRIN indexes, more
				than by users.</para></note>

			<para>Availability: 2.3.0 support for Block Range INdexes (BRIN) was introduced. Requires PostgreSQL 9.5+.</para>
			<para>&curve_support;</para>
			<para>&P_support;</para>
		  </refsection>

		  <refsection>
			<title>Examples</title>

			<programlisting>SELECT ST_MakeBox2D(ST_Point(2,2), ST_Point(3,3)) @ ST_Buffer(ST_GeomFromText('POINT(1 1)'), 10) AS is_contained;

 is_contained
--------------
 t
(1 row)</programlisting>
		  </refsection>

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

			<para>
				<xref linkend="overlaps_geometry_box2df" />,
				<xref linkend="overlaps_box2df_geometry" />,
				<xref linkend="overlaps_box2df_box2df" />,
				<xref linkend="contains_geometry_box2df" />,
				<xref linkend="contains_box2df_geometry" />,
				<xref linkend="contains_box2df_box2df" />,
				<xref linkend="is_contained_geometry_box2df" />,
				<xref linkend="is_contained_box2df_box2df" /></para>
		  </refsection>
		</refentry>

		<refentry id="is_contained_box2df_box2df">
		  <refnamediv>
			<refname>@(box2df,box2df)</refname>

			<refpurpose>Returns <varname>TRUE</varname> if a 2D float precision bounding box (BOX2DF) is contained into another 2D float precision bounding box.</refpurpose>
		  </refnamediv>

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

				<paramdef>
				  <type>box2df </type>

				  <parameter>A</parameter>
				</paramdef>

				<paramdef>
				  <type>box2df </type>

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

		  <refsection>
			<title>Description</title>

			<para>The <varname>@</varname> operator returns <varname>TRUE</varname> if the 2D bounding box A is contained into the 2D bounding box B, using float precision. This means that if A (or B) is a (double precision) box2d, it will be internally converted to a float precision 2D bounding box (BOX2DF)</para>

			<note><para>This operand is intended to be used internally by BRIN indexes, more
				than by users.</para></note>

			<para>Availability: 2.3.0 support for Block Range INdexes (BRIN) was introduced. Requires PostgreSQL 9.5+.</para>
			<para>&curve_support;</para>
			<para>&P_support;</para>
		  </refsection>

		  <refsection>
			<title>Examples</title>

			<programlisting>SELECT ST_MakeBox2D(ST_Point(2,2), ST_Point(3,3)) @ ST_MakeBox2D(ST_Point(0,0), ST_Point(5,5)) AS is_contained;

 is_contained
--------------
 t
(1 row)</programlisting>
		  </refsection>

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

			<para>
				<xref linkend="overlaps_geometry_box2df" />,
				<xref linkend="overlaps_box2df_geometry" />,
				<xref linkend="overlaps_box2df_box2df" />,
				<xref linkend="contains_geometry_box2df" />,
				<xref linkend="contains_box2df_geometry" />,
				<xref linkend="contains_box2df_box2df" />,
				<xref linkend="is_contained_geometry_box2df" />,
				<xref linkend="is_contained_box2df_geometry" /></para>
		  </refsection>
		</refentry>

		<refentry id="ST_Geometry_Overabove">
		  <refnamediv>
			<refname>|&amp;&gt;</refname>

			<refpurpose>Returns <varname>TRUE</varname> if A's bounding box overlaps or is above B's.</refpurpose>
		  </refnamediv>

		  <refsynopsisdiv>
			<funcsynopsis>
			  <funcprototype>
				<!-- TODO: Ideally, it would be nice if this could be reordered to
				"boolean (geometry A |&> geometry B)" instead of
				"boolean |&>( geometry A, geometry B)" -->
				<funcdef>boolean <function>|&amp;&gt;</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>The <varname>|&amp;&gt;</varname> operator returns <varname>TRUE</varname> if the bounding box of geometry A
			overlaps or is above the bounding box of geometry B, or more accurately, overlaps or is NOT below
			the bounding box of geometry B.</para>

			<note><para>This operand will make use of any indexes that may be available on the
			  geometries.</para></note>
		  </refsection>

		  <refsection>
			<title>Examples</title>

			<programlisting>SELECT tbl1.column1, tbl2.column1, tbl1.column2 |&amp;&gt; tbl2.column2 AS overabove
FROM
  ( VALUES
	(1, 'LINESTRING(6 0, 6 4)'::geometry)) AS tbl1,
  ( VALUES
	(2, 'LINESTRING(0 0, 3 3)'::geometry),
	(3, 'LINESTRING(0 1, 0 5)'::geometry),
	(4, 'LINESTRING(1 2, 4 6)'::geometry)) AS tbl2;

 column1 | column1 | overabove
---------+---------+-----------
	   1 |       2 | t
	   1 |       3 | f
	   1 |       4 | f
(3 rows)</programlisting>
		  </refsection>

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

			<para>
				<xref linkend="geometry_overlaps" />,
				<xref linkend="ST_Geometry_Overright" />,
				<xref linkend="ST_Geometry_Overbelow" />,
				<xref linkend="ST_Geometry_Overleft" /></para>
		  </refsection>
		</refentry>

		<refentry id="ST_Geometry_Above">
		  <refnamediv>
			<refname>|&gt;&gt;</refname>

			<refpurpose>Returns <varname>TRUE</varname> if A's bounding box is strictly above B's.</refpurpose>
		  </refnamediv>

		  <refsynopsisdiv>
			<funcsynopsis>
			  <funcprototype>
				<!-- TODO: Ideally, it would be nice if this could be reordered to
				"boolean (geometry A |>> geometry B)" instead of
				"boolean |>>( geometry A, geometry B)" -->
				<funcdef>boolean <function>|&gt;&gt;</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>The <varname>|&gt;&gt;</varname> operator returns <varname>TRUE</varname> if the bounding box of geometry A
			is strictly above the bounding box of geometry B.</para>

			<note><para>This operand will make use of any indexes that may be available on the
			  geometries.</para></note>
		  </refsection>

		  <refsection>
			<title>Examples</title>

			<programlisting>SELECT tbl1.column1, tbl2.column1, tbl1.column2 |&gt;&gt; tbl2.column2 AS above
FROM
  ( VALUES
	(1, 'LINESTRING (1 4, 1 7)'::geometry)) AS tbl1,
  ( VALUES
	(2, 'LINESTRING (0 0, 4 2)'::geometry),
	(3, 'LINESTRING (6 1, 6 5)'::geometry),
	(4, 'LINESTRING (2 3, 5 6)'::geometry)) AS tbl2;

 column1 | column1 | above
---------+---------+-------
	   1 |       2 | t
	   1 |       3 | f
	   1 |       4 | f
(3 rows)</programlisting>
		  </refsection>

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

			<para><xref linkend="ST_Geometry_Left" />, <xref linkend="ST_Geometry_Right" />, <xref linkend="ST_Geometry_Below" /></para>
		  </refsection>
		</refentry>

		<refentry id="ST_Geometry_Contain">
		  <refnamediv>
			<refname>~</refname>

			<refpurpose>Returns <varname>TRUE</varname> if A's bounding box contains B's.</refpurpose>
		  </refnamediv>

		  <refsynopsisdiv>
			<funcsynopsis>
			  <funcprototype>
				<!-- TODO: Ideally, it would be nice if this could be reordered to
				"boolean (geometry A ~ geometry B)" instead of
				"boolean ~( geometry A, geometry B)" -->
				<funcdef>boolean <function>~</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>The <varname>~</varname> operator returns <varname>TRUE</varname> if the bounding box of geometry A completely
			contains the bounding box of geometry B.</para>

			<note><para>This operand will make use of any indexes that may be available on the
			  geometries.</para></note>
		  </refsection>

		  <refsection>
			<title>Examples</title>

			<programlisting>SELECT tbl1.column1, tbl2.column1, tbl1.column2 ~ tbl2.column2 AS contains
FROM
  ( VALUES
	(1, 'LINESTRING (0 0, 3 3)'::geometry)) AS tbl1,
  ( VALUES
	(2, 'LINESTRING (0 0, 4 4)'::geometry),
	(3, 'LINESTRING (1 1, 2 2)'::geometry),
	(4, 'LINESTRING (0 0, 3 3)'::geometry)) AS tbl2;

 column1 | column1 | contains
---------+---------+----------
	   1 |       2 | f
	   1 |       3 | t
	   1 |       4 | t
(3 rows)</programlisting>
		  </refsection>

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

			<para><xref linkend="ST_Geometry_Contained" />, <xref linkend="geometry_overlaps" /></para>
		  </refsection>
		</refentry>

		<refentry id="contains_geometry_box2df">
		  <refnamediv>
			<refname>~(geometry,box2df)</refname>

			<refpurpose>Returns <varname>TRUE</varname> if a geometry's 2D bonding box contains a 2D float precision bounding box (GIDX).</refpurpose>
		  </refnamediv>

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

				<paramdef>
				  <type>geometry </type>

				  <parameter>A</parameter>
				</paramdef>

				<paramdef>
				  <type>box2df </type>

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

		  <refsection>
			<title>Description</title>

			<para>The <varname>~</varname> operator returns <varname>TRUE</varname> if the 2D bounding box of a geometry A contains the 2D bounding box B, using float precision. This means that if B is a (double precision) box2d, it will be internally converted to a float precision 2D bounding box (BOX2DF)</para>

			<note><para>This operand is intended to be used internally by BRIN indexes, more
				than by users.</para></note>

			<para>Availability: 2.3.0 support for Block Range INdexes (BRIN) was introduced. Requires PostgreSQL 9.5+.</para>
			<para>&curve_support;</para>
			<para>&P_support;</para>
		  </refsection>

		  <refsection>
			<title>Examples</title>

			<programlisting>SELECT ST_Buffer(ST_GeomFromText('POINT(1 1)'), 10) ~ ST_MakeBox2D(ST_Point(0,0), ST_Point(2,2)) AS contains;

 contains
----------
 t
(1 row)</programlisting>
		  </refsection>

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

			<para>
				<xref linkend="overlaps_geometry_box2df" />,
				<xref linkend="overlaps_box2df_geometry" />,
				<xref linkend="overlaps_box2df_box2df" />,
				<xref linkend="contains_box2df_geometry" />,
				<xref linkend="contains_box2df_box2df" />,
				<xref linkend="is_contained_geometry_box2df" />,
				<xref linkend="is_contained_box2df_geometry" />,
				<xref linkend="is_contained_box2df_box2df" /></para>
		  </refsection>
		</refentry>

		<refentry id="contains_box2df_geometry">
		  <refnamediv>
			<refname>~(box2df,geometry)</refname>

			<refpurpose>Returns <varname>TRUE</varname> if a 2D float precision bounding box (BOX2DF) contains a geometry's 2D bonding box.</refpurpose>
		  </refnamediv>

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

				<paramdef>
				  <type>box2df </type>

				  <parameter>A</parameter>
				</paramdef>

				<paramdef>
				  <type>geometry </type>

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

		  <refsection>
			<title>Description</title>

			<para>The <varname>~</varname> operator returns <varname>TRUE</varname> if the 2D bounding box A contains the B geometry's bounding box, using float precision. This means that if A is a (double precision) box2d, it will be internally converted to a float precision 2D bounding box (BOX2DF)</para>

			<note><para>This operand is intended to be used internally by BRIN indexes, more
				than by users.</para></note>

			<para>Availability: 2.3.0 support for Block Range INdexes (BRIN) was introduced. Requires PostgreSQL 9.5+.</para>
			<para>&curve_support;</para>
			<para>&P_support;</para>
		  </refsection>

		  <refsection>
			<title>Examples</title>

			<programlisting>SELECT ST_MakeBox2D(ST_Point(0,0), ST_Point(5,5)) ~ ST_Buffer(ST_GeomFromText('POINT(2 2)'), 1) AS contains;

 contains
----------
 t
(1 row)</programlisting>
		  </refsection>

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

			<para>
				<xref linkend="overlaps_geometry_box2df" />,
				<xref linkend="overlaps_box2df_geometry" />,
				<xref linkend="overlaps_box2df_box2df" />,
				<xref linkend="contains_geometry_box2df" />,
				<xref linkend="contains_box2df_box2df" />,
				<xref linkend="is_contained_geometry_box2df" />,
				<xref linkend="is_contained_box2df_geometry" />,
				<xref linkend="is_contained_box2df_box2df" /></para>
		  </refsection>
		</refentry>

		<refentry id="contains_box2df_box2df">
		  <refnamediv>
			<refname>~(box2df,box2df)</refname>

			<refpurpose>Returns <varname>TRUE</varname> if a 2D float precision bounding box (BOX2DF) contains another 2D float precision bounding box (BOX2DF).</refpurpose>
		  </refnamediv>

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

				<paramdef>
				  <type>box2df </type>

				  <parameter>A</parameter>
				</paramdef>

				<paramdef>
				  <type>box2df </type>

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

		  <refsection>
			<title>Description</title>

			<para>The <varname>~</varname> operator returns <varname>TRUE</varname> if the 2D bounding box A contains the 2D bounding box B, using float precision. This means that if A is a (double precision) box2d, it will be internally converted to a float precision 2D bounding box (BOX2DF)</para>

			<note><para>This operand is intended to be used internally by BRIN indexes, more
				than by users.</para></note>

			<para>Availability: 2.3.0 support for Block Range INdexes (BRIN) was introduced. Requires PostgreSQL 9.5+.</para>
			<para>&curve_support;</para>
			<para>&P_support;</para>
		  </refsection>

		  <refsection>
			<title>Examples</title>

			<programlisting>SELECT ST_MakeBox2D(ST_Point(0,0), ST_Point(5,5)) ~ ST_MakeBox2D(ST_Point(2,2), ST_Point(3,3)) AS contains;

 contains
----------
 t
(1 row)</programlisting>
		  </refsection>

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

			<para>
				<xref linkend="overlaps_geometry_box2df" />,
				<xref linkend="overlaps_box2df_geometry" />,
				<xref linkend="overlaps_box2df_box2df" />,
				<xref linkend="contains_geometry_box2df" />,
				<xref linkend="contains_box2df_geometry" />,
				<xref linkend="is_contained_geometry_box2df" />,
				<xref linkend="is_contained_box2df_geometry" />,
				<xref linkend="is_contained_box2df_box2df" /></para>
		  </refsection>
		</refentry>

		<refentry id="ST_Geometry_Same">
		  <refnamediv>
			<refname>~=</refname>

			<refpurpose>Returns <varname>TRUE</varname> if A's bounding box is the same as B's.</refpurpose>
		  </refnamediv>

		  <refsynopsisdiv>
			<funcsynopsis>
			  <funcprototype>
				<!-- TODO: Ideally, it would be nice if this could be reordered to
				"boolean (geometry A ~= geometry B)" instead of
				"boolean ~=( geometry A, geometry B)" -->
				<funcdef>boolean <function>~=</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>The <varname>~=</varname> operator returns <varname>TRUE</varname> if the bounding box of geometry/geography A
			is the same as the bounding box of geometry/geography B.</para>

			<note><para>This operand will make use of any indexes that may be available on the
			  geometries.</para></note>

			 <para>Availability: 1.5.0 changed behavior</para>
			 <para>&P_support;</para>

			<warning>
			  <para>This operator has changed behavior in PostGIS 1.5
			  from testing for actual geometric equality to only
			  checking for bounding box equality. To complicate things
			  it also depends on if you have done a hard or soft upgrade
			  which behavior your database has. To find out which behavior
			  your database has you can run the query below.
				To check for true equality use <xref linkend="ST_OrderingEquals" /> or <xref
			  linkend="ST_Equals" />.</para>
			  </warning>
		  </refsection>

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

select 'LINESTRING(0 0, 1 1)'::geometry ~= 'LINESTRING(0 1, 1 0)'::geometry as equality;
 equality   |
-----------------+
          t    |
			</programlisting>
		  </refsection>
		  <refsection>
			<title>See Also</title>
			<para><xref linkend="ST_Equals" />, <xref linkend="ST_OrderingEquals" />, <xref linkend="ST_Geometry_EQ" /></para>
		  </refsection>
		</refentry>

    </sect2>
	<!-- ==============================================================================  -->

		<sect2 id="operators-distance">
		<title>Distance Operators</title>


		<refentry id="geometry_distance_knn">
		  <refnamediv>
			<refname>&lt;-&gt;</refname>

			<refpurpose>
Returns the 2D distance between A and B.
			</refpurpose>
		  </refnamediv>

		  <refsynopsisdiv>
			<funcsynopsis>
			  <funcprototype>
				<funcdef>double precision <function>&lt;-&gt;</function></funcdef>

				<paramdef>
				  <type>geometry </type>

				  <parameter>A</parameter>
				</paramdef>

				<paramdef>
				  <type>geometry </type>

				  <parameter>B</parameter>
				</paramdef>
			  </funcprototype>

			   <funcprototype>
				<funcdef>double precision <function>&lt;-&gt;</function></funcdef>

				<paramdef>
				  <type>geography </type>

				  <parameter>A</parameter>
				</paramdef>

				<paramdef>
				  <type>geography </type>

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

		  <refsection>
			<title>Description</title>

			<para>
The <varname>&lt;-&gt;</varname> operator returns the 2D distance between
two geometries.  Used in the "ORDER BY" clause provides index-assisted
nearest-neighbor result sets.  For PostgreSQL below 9.5 only gives
centroid distance of bounding boxes and for PostgreSQL 9.5+, does true
KNN distance search giving true distance between geometries, and distance
sphere for geographies.
      </para>

			<note><para>This operand will make use of 2D GiST indexes that may be available on the geometries.  It is different from other operators that use spatial indexes in that the spatial index is only used when the operator is in the ORDER BY clause.</para></note>
			<note><para>Index only kicks in if one of the geometries is a constant (not in a subquery/cte).  e.g. 'SRID=3005;POINT(1011102 450541)'::geometry instead of a.geom</para></note>
			<para>Refer to <ulink url="https://postgis.net/workshops/postgis-intro/knn.html">PostGIS workshop: Nearest-Neighbor Searching</ulink> for a detailed example.</para>

			 <para>Enhanced: 2.2.0 -- True KNN ("K nearest neighbor") behavior for geometry and geography for PostgreSQL 9.5+. Note for geography KNN is based on sphere rather than spheroid.  For PostgreSQL 9.4 and below, geography support is new but only supports centroid box.</para>
			 <para>Changed: 2.2.0 -- For PostgreSQL 9.5 users, old Hybrid syntax may be slower, so you'll want to get rid of that hack if you are running your code only on PostGIS 2.2+ 9.5+.  See examples below.</para>
			 <para>Availability: 2.0.0 -- Weak KNN provides nearest neighbors based on geometry centroid distances instead of true distances. Exact results for points, inexact for all other types. Available for PostgreSQL 9.1+</para>


		  </refsection>

		  <refsection>
			<title>Examples</title>
<programlisting><![CDATA[SELECT ST_Distance(geom, 'SRID=3005;POINT(1011102 450541)'::geometry) as d,edabbr, vaabbr
FROM va2005
ORDER BY d limit 10;]]>

        d         | edabbr | vaabbr
------------------+--------+--------
                0 | ALQ    | 128
 5541.57712511724 | ALQ    | 129A
 5579.67450712005 | ALQ    | 001
  6083.4207708641 | ALQ    | 131
  7691.2205404848 | ALQ    | 003
 7900.75451037313 | ALQ    | 122
 8694.20710669982 | ALQ    | 129B
 9564.24289057111 | ALQ    | 130
  12089.665931705 | ALQ    | 127
 18472.5531479404 | ALQ    | 002
(10 rows)
</programlisting>
<para>
Then the KNN raw answer:
</para>
<programlisting><![CDATA[SELECT st_distance(geom, 'SRID=3005;POINT(1011102 450541)'::geometry) as d,edabbr, vaabbr
FROM va2005
ORDER BY geom <-> 'SRID=3005;POINT(1011102 450541)'::geometry limit 10;]]>

        d         | edabbr | vaabbr
------------------+--------+--------
                0 | ALQ    | 128
 5541.57712511724 | ALQ    | 129A
 5579.67450712005 | ALQ    | 001
  6083.4207708641 | ALQ    | 131
  7691.2205404848 | ALQ    | 003
 7900.75451037313 | ALQ    | 122
 8694.20710669982 | ALQ    | 129B
 9564.24289057111 | ALQ    | 130
  12089.665931705 | ALQ    | 127
 18472.5531479404 | ALQ    | 002
(10 rows)
</programlisting>
<para>
If you run "EXPLAIN ANALYZE" on the two queries you would see a performance improvement for the second.
</para>

<para>
For users running with PostgreSQL &lt; 9.5, use a hybrid query to find the true nearest neighbors. First a CTE query using the index-assisted KNN, then an exact query to get correct ordering:
</para>
<programlisting><![CDATA[WITH index_query AS (
  SELECT ST_Distance(geom, 'SRID=3005;POINT(1011102 450541)'::geometry) as d,edabbr, vaabbr
	FROM va2005
  ORDER BY geom <-> 'SRID=3005;POINT(1011102 450541)'::geometry LIMIT 100)
  SELECT *
	FROM index_query
  ORDER BY d limit 10;]]>

        d         | edabbr | vaabbr
------------------+--------+--------
                0 | ALQ    | 128
 5541.57712511724 | ALQ    | 129A
 5579.67450712005 | ALQ    | 001
  6083.4207708641 | ALQ    | 131
  7691.2205404848 | ALQ    | 003
 7900.75451037313 | ALQ    | 122
 8694.20710669982 | ALQ    | 129B
 9564.24289057111 | ALQ    | 130
  12089.665931705 | ALQ    | 127
 18472.5531479404 | ALQ    | 002
(10 rows)

			</programlisting>
		  </refsection>
		  <refsection>
			<title>See Also</title>
			<para><xref linkend="ST_DWithin" />, <xref linkend="ST_Distance" />, <xref linkend="geometry_distance_box" /></para>
		  </refsection>
		</refentry>

		<refentry id="geometry_distance_cpa">
		  <refnamediv>
			<refname>|=|</refname>

			<refpurpose>
Returns the distance between A and B trajectories at their closest point of approach.
			</refpurpose>
		  </refnamediv>

		  <refsynopsisdiv>
			<funcsynopsis>
			  <funcprototype>
				<funcdef>double precision <function>|=|</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>
The <varname>|=|</varname> operator returns the 3D distance between
two trajectories (See <xref linkend="ST_IsValidTrajectory" />).
This is the same as <xref linkend="ST_DistanceCPA" /> but as an operator
it can be used for doing nearest neighbor searches using an N-dimensional
index (requires PostgreSQL 9.5.0 or higher).
      </para>

			<note><para>This operand will make use of ND GiST indexes that may be available on the geometries.  It is different from other operators that use spatial indexes in that the spatial index is only used when the operator is in the ORDER BY clause.</para></note>
			<note><para>Index only kicks in if one of the geometries is a constant (not in a subquery/cte).  e.g. 'SRID=3005;LINESTRINGM(0 0 0,0 0 1)'::geometry instead of a.geom</para></note>

			 <para>Availability: 2.2.0. Index-supported only available for PostgreSQL 9.5+</para>

		  </refsection>

		  <refsection>
			<title>Examples</title>
<programlisting>
-- Save a literal query trajectory in a psql variable...
\set qt 'ST_AddMeasure(ST_MakeLine(ST_MakePointM(-350,300,0),ST_MakePointM(-410,490,0)),10,20)'
-- Run the query !
SELECT track_id, dist FROM (
  SELECT track_id, ST_DistanceCPA(tr,:qt) dist
  FROM trajectories
  ORDER BY tr |=| :qt
  LIMIT 5
) foo;
 track_id        dist
----------+-------------------
      395 | 0.576496831518066
      380 |  5.06797130410151
      390 |  7.72262293958322
      385 |   9.8004461358071
      405 |  10.9534397988433
(5 rows)
</programlisting>
		  </refsection>
		  <refsection>
			<title>See Also</title>
			<para>
<xref linkend="ST_DistanceCPA" />,
<xref linkend="ST_ClosestPointOfApproach" />,
<xref linkend="ST_IsValidTrajectory" />
      </para>
		  </refsection>
		</refentry>

		<refentry id="geometry_distance_box">
		  <refnamediv>
			<refname>&lt;#&gt;</refname>

			<refpurpose>
Returns the 2D distance between A and B bounding boxes.
			</refpurpose>
		  </refnamediv>

		  <refsynopsisdiv>
			<funcsynopsis>
			  <funcprototype>
				<funcdef>double precision <function>&lt;#&gt;</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>The <varname>&lt;#&gt;</varname> operator returns distance between two floating point bounding boxes, possibly reading them from a spatial index (PostgreSQL 9.1+ required).   Useful for doing nearest neighbor <emphasis role="strong">approximate</emphasis> distance ordering.</para>

			<note><para>This operand will make use of any indexes that may be available on the
			  geometries.  It is different from other operators that use spatial indexes in that the spatial index is only used when the operator
			  is in the ORDER BY clause.</para></note>
			<note><para>Index only kicks in if one of the geometries is a constant e.g. ORDER BY (ST_GeomFromText('POINT(1 2)') &lt;#&gt; geom)  instead of g1.geom &lt;#&gt;.</para></note>

			 <para>Availability: 2.0.0 -- KNN only available for PostgreSQL 9.1+</para>

		  </refsection>

		  <refsection>
			<title>Examples</title>
<programlisting><![CDATA[SELECT *
FROM (
SELECT b.tlid, b.mtfcc,
	b.geom <#> ST_GeomFromText('LINESTRING(746149 2948672,745954 2948576,
		745787 2948499,745740 2948468,745712 2948438,
		745690 2948384,745677 2948319)',2249) As b_dist,
		ST_Distance(b.geom, ST_GeomFromText('LINESTRING(746149 2948672,745954 2948576,
		745787 2948499,745740 2948468,745712 2948438,
		745690 2948384,745677 2948319)',2249)) As act_dist
    FROM bos_roads As b
    ORDER BY b_dist, b.tlid
    LIMIT 100) As foo
    ORDER BY act_dist, tlid LIMIT 10;]]>

   tlid    | mtfcc |      b_dist      |     act_dist
-----------+-------+------------------+------------------
  85732027 | S1400 |                0 |                0
  85732029 | S1400 |                0 |                0
  85732031 | S1400 |                0 |                0
  85734335 | S1400 |                0 |                0
  85736037 | S1400 |                0 |                0
 624683742 | S1400 |                0 | 128.528874268666
  85719343 | S1400 | 260.839270432962 | 260.839270432962
  85741826 | S1400 | 164.759294123275 | 260.839270432962
  85732032 | S1400 |           277.75 | 311.830282365264
  85735592 | S1400 |           222.25 | 311.830282365264
(10 rows)
</programlisting>
		  </refsection>
		  <refsection>
			<title>See Also</title>
			<para><xref linkend="ST_DWithin" />, <xref linkend="ST_Distance" />, <xref linkend="geometry_distance_knn" /></para>
		  </refsection>
		</refentry>

		<refentry id="geometry_distance_centroid_nd">
		  <refnamediv>
			<refname>&lt;&lt;-&gt;&gt;</refname>

			<refpurpose>
Returns the n-D distance between the centroids of A and B bounding
boxes.
			</refpurpose>
		  </refnamediv>

		  <refsynopsisdiv>
			<funcsynopsis>
			  <funcprototype>
				<funcdef>double precision <function>&lt;&lt;-&gt;&gt;</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>
The <varname>&lt;&lt;-&gt;&gt;</varname> operator returns the n-D (euclidean)
distance between the centroids of the bounding boxes of two geometries.
Useful for doing nearest neighbor
<emphasis role="strong">approximate</emphasis> distance ordering.
      </para>

			<note><para>
This operand will make use of n-D GiST indexes that may be available on
the geometries.  It is different from other operators that use spatial
indexes in that the spatial index is only used when the operator is in
the ORDER BY clause.
      </para></note>
			<note><para>
Index only kicks in if one of the geometries is a constant (not in a
subquery/cte).  e.g. 'SRID=3005;POINT(1011102 450541)'::geometry instead
of a.geom
      </para></note>

			 <para>Availability: 2.2.0 -- KNN only available for PostgreSQL 9.1+</para>


		  </refsection>

		  <refsection>
			<title>See Also</title>
			<para>
<xref linkend="geometry_distance_box_nd" />,
<xref linkend="geometry_distance_knn" />
      </para>
		  </refsection>
		</refentry>

		<refentry id="geometry_distance_box_nd">
		  <refnamediv>
			<refname>&lt;&lt;#&gt;&gt;</refname>

			<refpurpose>
Returns the n-D distance between A and B bounding boxes.
			</refpurpose>
		  </refnamediv>

		  <refsynopsisdiv>
			<funcsynopsis>
			  <funcprototype>
				<funcdef>double precision <function>&lt;&lt;#&gt;&gt;</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>The <varname>&lt;&lt;#&gt;&gt;</varname> operator returns distance between two floating point bounding boxes, possibly reading them from a spatial index (PostgreSQL 9.1+ required).   Useful for doing nearest neighbor <emphasis role="strong">approximate</emphasis> distance ordering.</para>

			<note><para>This operand will make use of any indexes that may be available on the
			  geometries.  It is different from other operators that use spatial indexes in that the spatial index is only used when the operator
			  is in the ORDER BY clause.</para></note>
			<note><para>
Index only kicks in if one of the geometries is a constant e.g. ORDER BY
(ST_GeomFromText('POINT(1 2)') &lt;&lt;#&gt;&gt; geom)  instead of g1.geom
&lt;&lt;#&gt;&gt;.
      </para></note>

			 <para>Availability: 2.2.0 -- KNN only available for PostgreSQL 9.1+</para>

		  </refsection>

		  <refsection>
			<title>See Also</title>
			<para>
<xref linkend="geometry_distance_centroid_nd" />,
<xref linkend="geometry_distance_box" />
      </para>
		  </refsection>
		</refentry>

    </sect2>

	</sect1>
