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Postgres FD Implementation
Commit 791090bd authored by Tom Lane's avatar Tom Lane
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Doc: update section 9.11 for new function table layout. 

This also makes an attempt to flesh out the docs for some of the more
severely underdocumented geometric operators and functions.

This effort exposed that the point <^ point (point_below) and
point >^ point (point_above) operators are misnamed; they should be
<<| and |>>, because they act like the other operators named that
way and not like the other operators named <^ and >^.  But I just
documented them that way; fixing it is matter for another patch.

The haphazard datatype coverage of many of the operators is also
now depressingly obvious.

Discussion: https://postgr.es/m/158110996889.1089.4224139874633222837@wrigleys.postgresql.org
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doc/src/sgml/func.sgml
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...@@ -9446,499 +9446,1111 @@ CREATE TYPE rainbow AS ENUM ('red', 'orange', 'yellow', 'green', 'blue', 'purple ...@@ -9446,499 +9446,1111 @@ CREATE TYPE rainbow AS ENUM ('red', 'orange', 'yellow', 'green', 'blue', 'purple
linkend="functions-geometry-conv-table"/>. linkend="functions-geometry-conv-table"/>.
</para> </para>
<table id="functions-geometry-op-table">
<title>Geometric Operators</title>
<tgroup cols="1">
<thead>
<row>
<entry role="functableentry">
Operator<?br?>Description<?br?>Example(s)
</entry>
</row>
</thead>
<tbody>
<row>
<entry role="functableentry">
<replaceable>geometric_type</replaceable> <literal>+</literal> <type>point</type>
<returnvalue><replaceable>geometric_type</replaceable></returnvalue>
<?br?>
Adds the coordinates of the second <type>point</type> to those of each
point of the first argument, thus performing translation.
Available for <type>point</type>, <type>box</type>, <type>path</type>,
<type>circle</type>.
<?br?>
<literal>box '(1,1),(0,0)' + point '(2,0)'</literal>
<returnvalue>(3,1),(2,0)</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<type>path</type> <literal>+</literal> <type>path</type>
<returnvalue>path</returnvalue>
<?br?>
Concatenates two open paths (returns NULL if either path is closed).
<?br?>
<literal>path '[(0,0),(1,1)]' + path '[(2,2),(3,3),(4,4)]'</literal>
<returnvalue>[(0,0),(1,1),(2,2),(3,3),(4,4)]</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<replaceable>geometric_type</replaceable> <literal>-</literal> <type>point</type>
<returnvalue><replaceable>geometric_type</replaceable></returnvalue>
<?br?>
Subtracts the coordinates of the second <type>point</type> from those
of each point of the first argument, thus performing translation.
Available for <type>point</type>, <type>box</type>, <type>path</type>,
<type>circle</type>.
<?br?>
<literal>box '(1,1),(0,0)' - point '(2,0)'</literal>
<returnvalue>(-1,1),(-2,0)</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<replaceable>geometric_type</replaceable> <literal>*</literal> <type>point</type>
<returnvalue><replaceable>geometric_type</replaceable></returnvalue>
<?br?>
Multiplies each point of the first argument by the second
<type>point</type><footnote><para>For this purpose, the
product of two points
(<replaceable>x1</replaceable>,<replaceable>y1</replaceable>) and
(<replaceable>x2</replaceable>,<replaceable>y2</replaceable>) is
defined as
(<replaceable>x1</replaceable>*<replaceable>x2</replaceable> -
<replaceable>y1</replaceable>*<replaceable>y2</replaceable>,
<replaceable>x1</replaceable>*<replaceable>y2</replaceable> +
<replaceable>y1</replaceable>*<replaceable>x2</replaceable>).</para></footnote>.
Interpreting the <type>point</type> as a vector, this is equivalent to
scaling the object's size and distance from the origin by the length
of the vector, and rotating it counterclockwise around the origin by
the vector's angle from the <replaceable>x</replaceable> axis.
Available for <type>point</type>, <type>box</type>, <type>path</type>,
<type>circle</type>.
<?br?>
<literal>path '((0,0),(1,0),(1,1))' * point '(3.0,0)'</literal>
<returnvalue>((0,0),(3,0),(3,3))</returnvalue>
<?br?>
<literal>path '((0,0),(1,0),(1,1))' * point(cosd(45), sind(45))</literal>
<returnvalue>((0,0),&zwsp;(0.7071067811865475,0.7071067811865475),&zwsp;(0,1.414213562373095))</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<replaceable>geometric_type</replaceable> <literal>/</literal> <type>point</type>
<returnvalue><replaceable>geometric_type</replaceable></returnvalue>
<?br?>
Divides each point of the first argument by the
second <type>point</type><footnote><para>For this purpose, the
quotient of two points
(<replaceable>x1</replaceable>,<replaceable>y1</replaceable>) and
(<replaceable>x2</replaceable>,<replaceable>y2</replaceable>) is
defined as
((<replaceable>x1</replaceable>*<replaceable>x2</replaceable> +
<replaceable>y1</replaceable>*<replaceable>y2</replaceable>) /
<replaceable>L</replaceable>,
(<replaceable>y1</replaceable>*<replaceable>x2</replaceable> -
<replaceable>x1</replaceable>*<replaceable>y2</replaceable>) /
<replaceable>L</replaceable>),
where <replaceable>L</replaceable> =
<replaceable>x2</replaceable>*<replaceable>x2</replaceable> +
<replaceable>y2</replaceable>*<replaceable>y2</replaceable>.</para></footnote>.
Interpreting the <type>point</type> as a vector, this is equivalent to
scaling the object's size and distance from the origin down by the
length of the vector, and rotating it clockwise around the origin by
the vector's angle from the <replaceable>x</replaceable> axis.
Available for <type>point</type>, <type>box</type>, <type>path</type>,
<type>circle</type>.
<?br?>
<literal>path '((0,0),(1,0),(1,1))' / point '(2.0,0)'</literal>
<returnvalue>((0,0),(0.5,0),(0.5,0.5))</returnvalue>
<?br?>
<literal>path '((0,0),(1,0),(1,1))' / point(cosd(45), sind(45))</literal>
<returnvalue>((0,0),&zwsp;(0.7071067811865476,-0.7071067811865476),&zwsp;(1.4142135623730951,0))</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<literal>@-@</literal> <replaceable>geometric_type</replaceable>
<returnvalue>double precision</returnvalue>
<?br?>
Computes the total length.
Available for <type>lseg</type>, <type>path</type>.
<?br?>
<literal>@-@ path '[(0,0),(1,0),(1,1)]'</literal>
<returnvalue>2</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<literal>@@</literal> <replaceable>geometric_type</replaceable>
<returnvalue>point</returnvalue>
<?br?>
Computes the center point.
Available for <type>box</type>, <type>lseg</type>, <type>path</type>,
<type>polygon</type>, <type>circle</type>.
<?br?>
<literal>@@ box '(2,2),(0,0)'</literal>
<returnvalue>(1,1)</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<literal>#</literal> <replaceable>geometric_type</replaceable>
<returnvalue>integer</returnvalue>
<?br?>
Returns the number of points.
Available for <type>path</type>, <type>polygon</type>.
<?br?>
<literal># path '((1,0),(0,1),(-1,0))'</literal>
<returnvalue>3</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<replaceable>geometric_type</replaceable> <literal>#</literal> <replaceable>geometric_type</replaceable>
<returnvalue>point</returnvalue>
<?br?>
Computes the point of intersection, or NULL if there is none.
Available for <type>lseg</type>, <type>line</type>.
<?br?>
<literal>lseg '[(0,0),(1,1)]' # lseg '[(1,0),(0,1)]'</literal>
<returnvalue>(0.5,0.5)</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<type>box</type> <literal>#</literal> <type>box</type>
<returnvalue>box</returnvalue>
<?br?>
Computes the intersection of two boxes, or NULL if there is none.
<?br?>
<literal>box '(2,2),(-1,-1)' # box '(1,1),(-2,-2)'</literal>
<returnvalue>(1,1),(-1,-1)</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<replaceable>geometric_type</replaceable> <literal>##</literal> <replaceable>geometric_type</replaceable>
<returnvalue>point</returnvalue>
<?br?>
Computes the closest point to the first object on the second object.
Available for these pairs of types:
(<type>point</type>, <type>box</type>),
(<type>point</type>, <type>lseg</type>),
(<type>point</type>, <type>line</type>),
(<type>lseg</type>, <type>box</type>),
(<type>lseg</type>, <type>lseg</type>),
(<type>lseg</type>, <type>line</type>),
(<type>line</type>, <type>box</type>),
(<type>line</type>, <type>lseg</type>).
<?br?>
<literal>point '(0,0)' ## lseg '[(2,0),(0,2)]'</literal>
<returnvalue>(1,1)</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<replaceable>geometric_type</replaceable> <literal>&lt;-&gt;</literal> <replaceable>geometric_type</replaceable>
<returnvalue>double precision</returnvalue>
<?br?>
Computes the distance between the objects.
Available for all seven geometric types, for all combinations
of <type>point</type> with another geometric type, and for
these additional pairs of types:
(<type>box</type>, <type>lseg</type>),
(<type>box</type>, <type>line</type>),
(<type>lseg</type>, <type>line</type>),
(<type>polygon</type>, <type>circle</type>)
(and the commutator cases).
<?br?>
<literal>circle '&lt;(0,0),1&gt;' &lt;-&gt; circle '&lt;(5,0),1&gt;'</literal>
<returnvalue>3</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<replaceable>geometric_type</replaceable> <literal>@&gt;</literal> <replaceable>geometric_type</replaceable>
<returnvalue>boolean</returnvalue>
<?br?>
Does first object contain second?
Available for these pairs of types:
(<literal>box</literal>, <literal>point</literal>),
(<literal>box</literal>, <literal>box</literal>),
(<literal>path</literal>, <literal>point</literal>),
(<literal>polygon</literal>, <literal>point</literal>),
(<literal>polygon</literal>, <literal>polygon</literal>),
(<literal>circle</literal>, <literal>point</literal>),
(<literal>circle</literal>, <literal>circle</literal>).
<?br?>
<literal>circle '&lt;(0,0),2&gt;' @&gt; point '(1,1)'</literal>
<returnvalue>t</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<replaceable>geometric_type</replaceable> <literal>&lt;@</literal> <replaceable>geometric_type</replaceable>
<returnvalue>boolean</returnvalue>
<?br?>
Is first object contained in or on second?
Available for these pairs of types:
(<literal>point</literal>, <literal>box</literal>),
(<literal>point</literal>, <literal>lseg</literal>),
(<literal>point</literal>, <literal>line</literal>),
(<literal>point</literal>, <literal>path</literal>),
(<literal>point</literal>, <literal>polygon</literal>),
(<literal>point</literal>, <literal>circle</literal>),
(<literal>box</literal>, <literal>box</literal>),
(<literal>lseg</literal>, <literal>box</literal>),
(<literal>lseg</literal>, <literal>line</literal>),
(<literal>polygon</literal>, <literal>polygon</literal>),
(<literal>circle</literal>, <literal>circle</literal>).
<?br?>
<literal>point '(1,1)' &lt;@ circle '&lt;(0,0),2&gt;'</literal>
<returnvalue>t</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<replaceable>geometric_type</replaceable> <literal>&amp;&amp;</literal> <replaceable>geometric_type</replaceable>
<returnvalue>boolean</returnvalue>
<?br?>
Do these objects overlap? (One point in common makes this true.)
Available for <type>box</type>, <type>polygon</type>,
<type>circle</type>.
<?br?>
<literal>box '(1,1),(0,0)' &amp;&amp; box '(2,2),(0,0)'</literal>
<returnvalue>t</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<replaceable>geometric_type</replaceable> <literal>&lt;&lt;</literal> <replaceable>geometric_type</replaceable>
<returnvalue>boolean</returnvalue>
<?br?>
Is first object strictly left of second?
Available for <type>point</type>, <type>box</type>,
<type>polygon</type>, <type>circle</type>.
<?br?>
<literal>circle '&lt;(0,0),1&gt;' &lt;&lt; circle '&lt;(5,0),1&gt;'</literal>
<returnvalue>t</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<replaceable>geometric_type</replaceable> <literal>&gt;&gt;</literal> <replaceable>geometric_type</replaceable>
<returnvalue>boolean</returnvalue>
<?br?>
Is first object strictly right of second?
Available for <type>point</type>, <type>box</type>,
<type>polygon</type>, <type>circle</type>.
<?br?>
<literal>circle '&lt;(5,0),1&gt;' &gt;&gt; circle '&lt;(0,0),1&gt;'</literal>
<returnvalue>t</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<replaceable>geometric_type</replaceable> <literal>&amp;&lt;</literal> <replaceable>geometric_type</replaceable>
<returnvalue>boolean</returnvalue>
<?br?>
Does first object not extend to the right of second?
Available for <type>box</type>, <type>polygon</type>,
<type>circle</type>.
<?br?>
<literal>box '(1,1),(0,0)' &amp;&lt; box '(2,2),(0,0)'</literal>
<returnvalue>t</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<replaceable>geometric_type</replaceable> <literal>&amp;&gt;</literal> <replaceable>geometric_type</replaceable>
<returnvalue>boolean</returnvalue>
<?br?>
Does first object not extend to the left of second?
Available for <type>box</type>, <type>polygon</type>,
<type>circle</type>.
<?br?>
<literal>box '(3,3),(0,0)' &amp;&gt; box '(2,2),(0,0)'</literal>
<returnvalue>t</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<replaceable>geometric_type</replaceable> <literal>&lt;&lt;|</literal> <replaceable>geometric_type</replaceable>
<returnvalue>boolean</returnvalue>
<?br?>
Is first object strictly below second?
Available for <type>box</type>, <type>polygon</type>,
<type>circle</type>.
<?br?>
<literal>box '(3,3),(0,0)' &lt;&lt;| box '(5,5),(3,4)'</literal>
<returnvalue>t</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<replaceable>geometric_type</replaceable> <literal>|&gt;&gt;</literal> <replaceable>geometric_type</replaceable>
<returnvalue>boolean</returnvalue>
<?br?>
Is first object strictly above second?
Available for <type>box</type>, <type>polygon</type>,
<type>circle</type>.
<?br?>
<literal>box '(5,5),(3,4)' |&gt;&gt; box '(3,3),(0,0)'</literal>
<returnvalue>t</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<replaceable>geometric_type</replaceable> <literal>&amp;&lt;|</literal> <replaceable>geometric_type</replaceable>
<returnvalue>boolean</returnvalue>
<?br?>
Does first object not extend above second?
Available for <type>box</type>, <type>polygon</type>,
<type>circle</type>.
<?br?>
<literal>box '(1,1),(0,0)' &amp;&lt;| box '(2,2),(0,0)'</literal>
<returnvalue>t</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<replaceable>geometric_type</replaceable> <literal>|&amp;&gt;</literal> <replaceable>geometric_type</replaceable>
<returnvalue>boolean</returnvalue>
<?br?>
Does first object not extend below second?
Available for <type>box</type>, <type>polygon</type>,
<type>circle</type>.
<?br?>
<literal>box '(3,3),(0,0)' |&amp;&gt; box '(2,2),(0,0)'</literal>
<returnvalue>t</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<type>box</type> <literal>&lt;^</literal> <type>box</type>
<returnvalue>boolean</returnvalue>
<?br?>
Is first object below second (allows edges to touch)?
<?br?>
<literal>box '((1,1),(0,0))' &lt;^ box '((2,2),(1,1))'</literal>
<returnvalue>t</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<type>point</type> <literal>&lt;^</literal> <type>point</type>
<returnvalue>boolean</returnvalue>
<?br?>
Is first object strictly below second?
(This operator is misnamed; it should be <literal>&lt;&lt;|</literal>.)
<?br?>
<literal>point '(1,0)' &lt;^ point '(1,1)'</literal>
<returnvalue>t</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<type>box</type> <literal>&gt;^</literal> <type>box</type>
<returnvalue>boolean</returnvalue>
<?br?>
Is first object above second (allows edges to touch)?
<?br?>
<literal>box '((2,2),(1,1))' &gt;^ box '((1,1),(0,0))'</literal>
<returnvalue>t</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<type>point</type> <literal>&gt;^</literal> <type>point</type>
<returnvalue>boolean</returnvalue>
<?br?>
Is first object strictly above second?
(This operator is misnamed; it should be <literal>|&gt;&gt;</literal>.)
<?br?>
<literal>point '(1,1)' &gt;^ point '(1,0)'</literal>
<returnvalue>t</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<replaceable>geometric_type</replaceable> <literal>?#</literal> <replaceable>geometric_type</replaceable>
<returnvalue>boolean</returnvalue>
<?br?>
Do these objects intersect?
Available for these pairs of types:
(<type>box</type>, <type>box</type>),
(<type>lseg</type>, <type>box</type>),
(<type>lseg</type>, <type>lseg</type>),
(<type>lseg</type>, <type>line</type>),
(<type>line</type>, <type>box</type>),
(<type>line</type>, <type>line</type>),
(<type>path</type>, <type>path</type>).
<?br?>
<literal>lseg '[(-1,0),(1,0)]' ?# box '(2,2),(-2,-2)'</literal>
<returnvalue>t</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<literal>?-</literal> <replaceable>geometric_type</replaceable>
<returnvalue>boolean</returnvalue>
<?br?>
Is line horizontal?
Available for <type>lseg</type>, <type>line</type>.
<?br?>
<literal>?- lseg '[(-1,0),(1,0)]'</literal>
<returnvalue>t</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<type>point</type> <literal>?-</literal> <type>point</type>
<returnvalue>boolean</returnvalue>
<?br?>
Are points horizontally aligned (that is, have same y coordinate)?
<?br?>
<literal>point '(1,0)' ?- point '(0,0)'</literal>
<returnvalue>t</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<literal>?|</literal> <replaceable>geometric_type</replaceable>
<returnvalue>boolean</returnvalue>
<?br?>
Is line vertical?
Available for <type>lseg</type>, <type>line</type>.
<?br?>
<literal>?| lseg '[(-1,0),(1,0)]'</literal>
<returnvalue>f</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<type>point</type> <literal>?|</literal> <type>point</type>
<returnvalue>boolean</returnvalue>
<?br?>
Are points vertically aligned (that is, have same x coordinate)?
<?br?>
<literal>point '(0,1)' ?| point '(0,0)'</literal>
<returnvalue>t</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<replaceable>geometric_type</replaceable> <literal>?-|</literal> <replaceable>geometric_type</replaceable>
<returnvalue>boolean</returnvalue>
<?br?>
Are lines perpendicular?
Available for <type>lseg</type>, <type>line</type>.
<?br?>
<literal>lseg '[(0,0),(0,1)]' ?-| lseg '[(0,0),(1,0)]'</literal>
<returnvalue>t</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<replaceable>geometric_type</replaceable> <literal>?||</literal> <replaceable>geometric_type</replaceable>
<returnvalue>boolean</returnvalue>
<?br?>
Are lines parallel?
Available for <type>lseg</type>, <type>line</type>.
<?br?>
<literal>lseg '[(-1,0),(1,0)]' ?|| lseg '[(-1,2),(1,2)]'</literal>
<returnvalue>t</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<replaceable>geometric_type</replaceable> <literal>~=</literal> <replaceable>geometric_type</replaceable>
<returnvalue>boolean</returnvalue>
<?br?>
Are these objects the same?
Available for <type>point</type>, <type>box</type>,
<type>polygon</type>, <type>circle</type>.
<?br?>
<literal>polygon '((0,0),(1,1))' ~= polygon '((1,1),(0,0))'</literal>
<returnvalue>t</returnvalue>
</entry>
</row>
</tbody>
</tgroup>
</table>
<caution> <caution>
<para> <para>
Note that the <quote>same as</quote> operator, <literal>~=</literal>, represents Note that the <quote>same as</quote> operator, <literal>~=</literal>,
the usual notion of equality for the <type>point</type>, represents the usual notion of equality for the <type>point</type>,
<type>box</type>, <type>polygon</type>, and <type>circle</type> types. <type>box</type>, <type>polygon</type>, and <type>circle</type> types.
Some of these types also have an <literal>=</literal> operator, but Some of the geometric types also have an <literal>=</literal> operator, but
<literal>=</literal> compares <literal>=</literal> compares for equal <emphasis>areas</emphasis> only.
for equal <emphasis>areas</emphasis> only. The other scalar comparison operators The other scalar comparison operators (<literal>&lt;=</literal> and so
(<literal>&lt;=</literal> and so on) likewise compare areas for these types. on), where available for these types, likewise compare areas.
</para> </para>
</caution> </caution>
<table id="functions-geometry-op-table"> <note>
<title>Geometric Operators</title> <para>
<tgroup cols="3"> Before <productname>PostgreSQL</productname> 8.2, the containment
<thead> operators <literal>@&gt;</literal> and <literal>&lt;@</literal> were respectively
<row> called <literal>~</literal> and <literal>@</literal>. These names are still
<entry>Operator</entry> available, but are deprecated and will eventually be removed.
<entry>Description</entry> </para>
<entry>Example</entry> </note>
</row>
</thead> <table id="functions-geometry-func-table">
<tbody> <title>Geometric Functions</title>
<row> <tgroup cols="1">
<entry> <literal>+</literal> </entry> <thead>
<entry>Translation</entry> <row>
<entry><literal>box '((0,0),(1,1))' + point '(2.0,0)'</literal></entry> <entry role="functableentry">
</row> Function<?br?>Description<?br?>Example(s)
<row> </entry>
<entry> <literal>-</literal> </entry> </row>
<entry>Translation</entry> </thead>
<entry><literal>box '((0,0),(1,1))' - point '(2.0,0)'</literal></entry>
</row> <tbody>
<row> <row>
<entry> <literal>*</literal> </entry> <entry role="functableentry">
<entry>Scaling/rotation</entry> <indexterm>
<entry><literal>box '((0,0),(1,1))' * point '(2.0,0)'</literal></entry> <primary>area</primary>
</row> </indexterm>
<row> <function>area</function> ( <replaceable>geometric_type</replaceable> )
<entry> <literal>/</literal> </entry> <returnvalue>double precision</returnvalue>
<entry>Scaling/rotation</entry> <?br?>
<entry><literal>box '((0,0),(2,2))' / point '(2.0,0)'</literal></entry> Computes area.
</row> Available for <type>box</type>, <type>path</type>, <type>circle</type>.
<row> A <type>path</type> input must be closed, else NULL is returned.
<entry> <literal>#</literal> </entry> Also, if the <type>path</type> is self-intersecting, the result may be
<entry>Point or box of intersection</entry> meaningless.
<entry><literal>box '((1,-1),(-1,1))' # box '((1,1),(-2,-2))'</literal></entry> <?br?>
</row> <literal>area(box '(2,2),(0,0)')</literal>
<row> <returnvalue>4</returnvalue>
<entry> <literal>#</literal> </entry> </entry>
<entry>Number of points in path or polygon</entry> </row>
<entry><literal># path '((1,0),(0,1),(-1,0))'</literal></entry>
</row> <row>
<row> <entry role="functableentry">
<entry> <literal>@-@</literal> </entry> <indexterm>
<entry>Length or circumference</entry> <primary>center</primary>
<entry><literal>@-@ path '((0,0),(1,0))'</literal></entry> </indexterm>
</row> <function>center</function> ( <replaceable>geometric_type</replaceable> )
<row> <returnvalue>point</returnvalue>
<entry> <literal>@@</literal> </entry> <?br?>
<entry>Center</entry> Computes center point.
<entry><literal>@@ circle '((0,0),10)'</literal></entry> Available for <type>box</type>, <type>circle</type>.
</row> <?br?>
<row> <literal>center(box '(1,2),(0,0)')</literal>
<entry> <literal>##</literal> </entry> <returnvalue>(0.5,1)</returnvalue>
<entry>Closest point to first operand on second operand</entry> </entry>
<entry><literal>point '(0,0)' ## lseg '((2,0),(0,2))'</literal></entry> </row>
</row>
<row> <row>
<entry> <literal>&lt;-&gt;</literal> </entry> <entry role="functableentry">
<entry>Distance between</entry> <indexterm>
<entry><literal>circle '((0,0),1)' &lt;-&gt; circle '((5,0),1)'</literal></entry> <primary>diagonal</primary>
</row> </indexterm>
<row> <function>diagonal</function> ( <type>box</type> )
<entry> <literal>&amp;&amp;</literal> </entry> <returnvalue>lseg</returnvalue>
<entry>Overlaps? (One point in common makes this true.)</entry> <?br?>
<entry><literal>box '((0,0),(1,1))' &amp;&amp; box '((0,0),(2,2))'</literal></entry> Extracts box's diagonal as a line segment
</row> (same as <function>lseg(box)</function>).
<row> <?br?>
<entry> <literal>&lt;&lt;</literal> </entry> <literal>diagonal(box '(1,2),(0,0)')</literal>
<entry>Is strictly left of?</entry> <returnvalue>[(1,2),(0,0)]</returnvalue>
<entry><literal>circle '((0,0),1)' &lt;&lt; circle '((5,0),1)'</literal></entry> </entry>
</row> </row>
<row>
<entry> <literal>&gt;&gt;</literal> </entry> <row>
<entry>Is strictly right of?</entry> <entry role="functableentry">
<entry><literal>circle '((5,0),1)' &gt;&gt; circle '((0,0),1)'</literal></entry> <indexterm>
</row> <primary>diameter</primary>
<row> </indexterm>
<entry> <literal>&amp;&lt;</literal> </entry> <function>diameter</function> ( <type>circle</type> )
<entry>Does not extend to the right of?</entry> <returnvalue>double precision</returnvalue>
<entry><literal>box '((0,0),(1,1))' &amp;&lt; box '((0,0),(2,2))'</literal></entry> <?br?>
</row> Computes diameter of circle.
<row> <?br?>
<entry> <literal>&amp;&gt;</literal> </entry> <literal>diameter(circle '&lt;(0,0),2&gt;')</literal>
<entry>Does not extend to the left of?</entry> <returnvalue>4</returnvalue>
<entry><literal>box '((0,0),(3,3))' &amp;&gt; box '((0,0),(2,2))'</literal></entry> </entry>
</row> </row>
<row>
<entry> <literal>&lt;&lt;|</literal> </entry> <row>
<entry>Is strictly below?</entry> <entry role="functableentry">
<entry><literal>box '((0,0),(3,3))' &lt;&lt;| box '((3,4),(5,5))'</literal></entry> <indexterm>
</row> <primary>height</primary>
<row> </indexterm>
<entry> <literal>|&gt;&gt;</literal> </entry> <function>height</function> ( <type>box</type> )
<entry>Is strictly above?</entry> <returnvalue>double precision</returnvalue>
<entry><literal>box '((3,4),(5,5))' |&gt;&gt; box '((0,0),(3,3))'</literal></entry> <?br?>
</row> Computes vertical size of box.
<row> <?br?>
<entry> <literal>&amp;&lt;|</literal> </entry> <literal>height(box '(1,2),(0,0)')</literal>
<entry>Does not extend above?</entry> <returnvalue>2</returnvalue>
<entry><literal>box '((0,0),(1,1))' &amp;&lt;| box '((0,0),(2,2))'</literal></entry> </entry>
</row> </row>
<row>
<entry> <literal>|&amp;&gt;</literal> </entry> <row>
<entry>Does not extend below?</entry> <entry role="functableentry">
<entry><literal>box '((0,0),(3,3))' |&amp;&gt; box '((0,0),(2,2))'</literal></entry> <indexterm>
</row> <primary>isclosed</primary>
<row> </indexterm>
<entry> <literal>&lt;^</literal> </entry> <function>isclosed</function> ( <type>path</type> )
<entry>Is below (allows touching)?</entry> <returnvalue>boolean</returnvalue>
<entry><literal>circle '((0,0),1)' &lt;^ circle '((0,5),1)'</literal></entry> <?br?>
</row> Is path closed?
<row> <?br?>
<entry> <literal>&gt;^</literal> </entry> <literal>isclosed(path '((0,0),(1,1),(2,0))')</literal>
<entry>Is above (allows touching)?</entry> <returnvalue>t</returnvalue>
<entry><literal>circle '((0,5),1)' &gt;^ circle '((0,0),1)'</literal></entry> </entry>
</row> </row>
<row>
<entry> <literal>?#</literal> </entry> <row>
<entry>Intersects?</entry> <entry role="functableentry">
<entry><literal>lseg '((-1,0),(1,0))' ?# box '((-2,-2),(2,2))'</literal></entry> <indexterm>
</row> <primary>isopen</primary>
<row> </indexterm>
<entry> <literal>?-</literal> </entry> <function>isopen</function> ( <type>path</type> )
<entry>Is horizontal?</entry> <returnvalue>boolean</returnvalue>
<entry><literal>?- lseg '((-1,0),(1,0))'</literal></entry> <?br?>
</row> Is path open?
<row> <?br?>
<entry> <literal>?-</literal> </entry> <literal>isopen(path '[(0,0),(1,1),(2,0)]')</literal>
<entry>Are horizontally aligned?</entry> <returnvalue>t</returnvalue>
<entry><literal>point '(1,0)' ?- point '(0,0)'</literal></entry> </entry>
</row> </row>
<row>
<entry> <literal>?|</literal> </entry> <row>
<entry>Is vertical?</entry> <entry role="functableentry">
<entry><literal>?| lseg '((-1,0),(1,0))'</literal></entry> <indexterm>
</row> <primary>length</primary>
<row> </indexterm>
<entry> <literal>?|</literal> </entry> <function>length</function> ( <replaceable>geometric_type</replaceable> )
<entry>Are vertically aligned?</entry> <returnvalue>double precision</returnvalue>
<entry><literal>point '(0,1)' ?| point '(0,0)'</literal></entry> <?br?>
</row> Computes the total length.
<row> Available for <type>lseg</type>, <type>path</type>.
<entry> <literal>?-|</literal> </entry> <?br?>
<entry>Is perpendicular?</entry> <literal>length(path '((-1,0),(1,0))')</literal>
<entry><literal>lseg '((0,0),(0,1))' ?-| lseg '((0,0),(1,0))'</literal></entry> <returnvalue>4</returnvalue>
</row> </entry>
<row> </row>
<entry> <literal>?||</literal> </entry>
<entry>Are parallel?</entry> <row>
<entry><literal>lseg '((-1,0),(1,0))' ?|| lseg '((-1,2),(1,2))'</literal></entry> <entry role="functableentry">
</row> <indexterm>
<row> <primary>npoints</primary>
<entry> <literal>@&gt;</literal> </entry> </indexterm>
<entry>Contains?</entry> <function>npoints</function> ( <replaceable>geometric_type</replaceable> )
<entry><literal>circle '((0,0),2)' @&gt; point '(1,1)'</literal></entry> <returnvalue>integer</returnvalue>
</row> <?br?>
<row> Returns the number of points.
<entry> <literal>&lt;@</literal> </entry> Available for <type>path</type>, <type>polygon</type>.
<entry>Contained in or on?</entry> <?br?>
<entry><literal>point '(1,1)' &lt;@ circle '((0,0),2)'</literal></entry> <literal>npoints(path '[(0,0),(1,1),(2,0)]')</literal>
</row> <returnvalue>3</returnvalue>
<row> </entry>
<entry> <literal>~=</literal> </entry> </row>
<entry>Same as?</entry>
<entry><literal>polygon '((0,0),(1,1))' ~= polygon '((1,1),(0,0))'</literal></entry> <row>
</row> <entry role="functableentry">
</tbody> <indexterm>
</tgroup> <primary>pclose</primary>
</indexterm>
<function>pclose</function> ( <type>path</type> )
<returnvalue>path</returnvalue>
<?br?>
Converts path to closed form.
<?br?>
<literal>pclose(path '[(0,0),(1,1),(2,0)]')</literal>
<returnvalue>((0,0),(1,1),(2,0))</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<indexterm>
<primary>popen</primary>
</indexterm>
<function>popen</function> ( <type>path</type> )
<returnvalue>path</returnvalue>
<?br?>
Converts path to open form.
<?br?>
<literal>popen(path '((0,0),(1,1),(2,0))')</literal>
<returnvalue>[(0,0),(1,1),(2,0)]</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<indexterm>
<primary>radius</primary>
</indexterm>
<function>radius</function> ( <type>circle</type> )
<returnvalue>double precision</returnvalue>
<?br?>
Computes radius of circle.
<?br?>
<literal>radius(circle '&lt;(0,0),2&gt;')</literal>
<returnvalue>2</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<indexterm>
<primary>slope</primary>
</indexterm>
<function>slope</function> ( <type>point</type>, <type>point</type> )
<returnvalue>double precision</returnvalue>
<?br?>
Computes slope of a line drawn through the two points.
<?br?>
<literal>slope(point '(0,0)', point '(2,1)')</literal>
<returnvalue>0.5</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<indexterm>
<primary>width</primary>
</indexterm>
<function>width</function> ( <type>box</type> )
<returnvalue>double precision</returnvalue>
<?br?>
Computes horizontal size of box.
<?br?>
<literal>width(box '(1,2),(0,0)')</literal>
<returnvalue>1</returnvalue>
</entry>
</row>
</tbody>
</tgroup>
</table> </table>
<note> <table id="functions-geometry-conv-table">
<para> <title>Geometric Type Conversion Functions</title>
Before <productname>PostgreSQL</productname> 8.2, the containment <tgroup cols="1">
operators <literal>@&gt;</literal> and <literal>&lt;@</literal> were respectively <thead>
called <literal>~</literal> and <literal>@</literal>. These names are still <row>
available, but are deprecated and will eventually be removed. <entry role="functableentry">
</para> Function<?br?>Description<?br?>Example(s)
</note> </entry>
</row>
</thead>
<tbody>
<row>
<entry role="functableentry">
<indexterm>
<primary>box</primary>
</indexterm>
<function>box</function> ( <type>circle</type> )
<returnvalue>box</returnvalue>
<?br?>
Computes box inscribed within the circle.
<?br?>
<literal>box(circle '&lt;(0,0),2&gt;')</literal>
<returnvalue>(1.414213562373095,1.414213562373095),&zwsp;(-1.414213562373095,-1.414213562373095)</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<function>box</function> ( <type>point</type> )
<returnvalue>box</returnvalue>
<?br?>
Converts point to empty box.
<?br?>
<literal>box(point '(1,0)')</literal>
<returnvalue>(1,0),(1,0)</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<function>box</function> ( <type>point</type>, <type>point</type> )
<returnvalue>box</returnvalue>
<?br?>
Converts any two corner points to box.
<?br?>
<literal>box(point '(0,1)', point '(1,0)')</literal>
<returnvalue>(1,1),(0,0)</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<function>box</function> ( <type>polygon</type> )
<returnvalue>box</returnvalue>
<?br?>
Computes bounding box of polygon.
<?br?>
<literal>box(polygon '((0,0),(1,1),(2,0))')</literal>
<returnvalue>(2,1),(0,0)</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<indexterm>
<primary>bound_box</primary>
</indexterm>
<function>bound_box</function> ( <type>box</type>, <type>box</type> )
<returnvalue>box</returnvalue>
<?br?>
Computes bounding box of two boxes.
<?br?>
<literal>bound_box(box '(1,1),(0,0)', box '(4,4),(3,3)')</literal>
<returnvalue>(4,4),(0,0)</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<indexterm>
<primary>circle</primary>
</indexterm>
<function>circle</function> ( <type>box</type> )
<returnvalue>circle</returnvalue>
<?br?>
Computes smallest circle enclosing box.
<?br?>
<literal>circle(box '(1,1),(0,0)')</literal>
<returnvalue>&lt;(0.5,0.5),0.7071067811865476&gt;</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<function>circle</function> ( <type>point</type>, <type>double precision</type> )
<returnvalue>circle</returnvalue>
<?br?>
Constructs circle from center and radius.
<?br?>
<literal>circle(point '(0,0)', 2.0)</literal>
<returnvalue>&lt;(0,0),2&gt;</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<function>circle</function> ( <type>polygon</type> )
<returnvalue>circle</returnvalue>
<?br?>
Converts polygon to circle. The circle's center is the mean of the
positions of the polygon's points, and the radius is the average
distance of the polygon's points from that center.
<?br?>
<literal>circle(polygon '((0,0),(1,3),(2,0))')</literal>
<returnvalue>&lt;(1,1),1.6094757082487299&gt;</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<indexterm>
<primary>line</primary>
</indexterm>
<function>line</function> ( <type>point</type>, <type>point</type> )
<returnvalue>line</returnvalue>
<?br?>
Converts two points to the line through them.
<?br?>
<literal>line(point '(-1,0)', point '(1,0)')</literal>
<returnvalue>{0,-1,0}</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<indexterm>
<primary>lseg</primary>
</indexterm>
<function>lseg</function> ( <type>box</type> )
<returnvalue>lseg</returnvalue>
<?br?>
Extracts box's diagonal as a line segment.
<?br?>
<literal>lseg(box '(1,0),(-1,0)')</literal>
<returnvalue>[(1,0),(-1,0)]</returnvalue>
</entry>
</row>
<indexterm> <row>
<primary>area</primary> <entry role="functableentry">
</indexterm> <function>lseg</function> ( <type>point</type>, <type>point</type> )
<indexterm> <returnvalue>lseg</returnvalue>
<primary>center</primary> <?br?>
</indexterm> Constructs line segment from two endpoints.
<indexterm> <?br?>
<primary>diameter</primary> <literal>lseg(point '(-1,0)', point '(1,0)')</literal>
</indexterm> <returnvalue>[(-1,0),(1,0)]</returnvalue>
<indexterm> </entry>
<primary>height</primary> </row>
</indexterm>
<indexterm>
<primary>isclosed</primary>
</indexterm>
<indexterm>
<primary>isopen</primary>
</indexterm>
<indexterm>
<primary>length</primary>
</indexterm>
<indexterm>
<primary>npoints</primary>
</indexterm>
<indexterm>
<primary>pclose</primary>
</indexterm>
<indexterm>
<primary>popen</primary>
</indexterm>
<indexterm>
<primary>radius</primary>
</indexterm>
<indexterm>
<primary>width</primary>
</indexterm>
<table id="functions-geometry-func-table"> <row>
<title>Geometric Functions</title> <entry role="functableentry">
<tgroup cols="4"> <indexterm>
<thead> <primary>path</primary>
<row> </indexterm>
<entry>Function</entry> <function>path</function> ( <type>polygon</type> )
<entry>Return Type</entry> <returnvalue>path</returnvalue>
<entry>Description</entry> <?br?>
<entry>Example</entry> Converts polygon to a closed path with the same list of points.
</row> <?br?>
</thead> <literal>path(polygon '((0,0),(1,1),(2,0))')</literal>
<tbody> <returnvalue>((0,0),(1,1),(2,0))</returnvalue>
<row> </entry>
<entry><literal><function>area(<replaceable>object</replaceable>)</function></literal></entry> </row>
<entry><type>double precision</type></entry>
<entry>area</entry>
<entry><literal>area(box '((0,0),(1,1))')</literal></entry>
</row>
<row>
<entry><literal><function>center(<replaceable>object</replaceable>)</function></literal></entry>
<entry><type>point</type></entry>
<entry>center</entry>
<entry><literal>center(box '((0,0),(1,2))')</literal></entry>
</row>
<row>
<entry><literal><function>diameter(<type>circle</type>)</function></literal></entry>
<entry><type>double precision</type></entry>
<entry>diameter of circle</entry>
<entry><literal>diameter(circle '((0,0),2.0)')</literal></entry>
</row>
<row>
<entry><literal><function>height(<type>box</type>)</function></literal></entry>
<entry><type>double precision</type></entry>
<entry>vertical size of box</entry>
<entry><literal>height(box '((0,0),(1,1))')</literal></entry>
</row>
<row>
<entry><literal><function>isclosed(<type>path</type>)</function></literal></entry>
<entry><type>boolean</type></entry>
<entry>a closed path?</entry>
<entry><literal>isclosed(path '((0,0),(1,1),(2,0))')</literal></entry>
</row>
<row>
<entry><literal><function>isopen(<type>path</type>)</function></literal></entry>
<entry><type>boolean</type></entry>
<entry>an open path?</entry>
<entry><literal>isopen(path '[(0,0),(1,1),(2,0)]')</literal></entry>
</row>
<row>
<entry><literal><function>length(<replaceable>object</replaceable>)</function></literal></entry>
<entry><type>double precision</type></entry>
<entry>length</entry>
<entry><literal>length(path '((-1,0),(1,0))')</literal></entry>
</row>
<row>
<entry><literal><function>npoints(<type>path</type>)</function></literal></entry>
<entry><type>int</type></entry>
<entry>number of points</entry>
<entry><literal>npoints(path '[(0,0),(1,1),(2,0)]')</literal></entry>
</row>
<row>
<entry><literal><function>npoints(<type>polygon</type>)</function></literal></entry>
<entry><type>int</type></entry>
<entry>number of points</entry>
<entry><literal>npoints(polygon '((1,1),(0,0))')</literal></entry>
</row>
<row>
<entry><literal><function>pclose(<type>path</type>)</function></literal></entry>
<entry><type>path</type></entry>
<entry>convert path to closed</entry>
<entry><literal>pclose(path '[(0,0),(1,1),(2,0)]')</literal></entry>
</row>
<row>
<entry><literal><function>popen(<type>path</type>)</function></literal></entry>
<entry><type>path</type></entry>
<entry>convert path to open</entry>
<entry><literal>popen(path '((0,0),(1,1),(2,0))')</literal></entry>
</row>
<row>
<entry><literal><function>radius(<type>circle</type>)</function></literal></entry>
<entry><type>double precision</type></entry>
<entry>radius of circle</entry>
<entry><literal>radius(circle '((0,0),2.0)')</literal></entry>
</row>
<row>
<entry><literal><function>width(<type>box</type>)</function></literal></entry>
<entry><type>double precision</type></entry>
<entry>horizontal size of box</entry>
<entry><literal>width(box '((0,0),(1,1))')</literal></entry>
</row>
</tbody>
</tgroup>
</table>
<table id="functions-geometry-conv-table"> <row>
<title>Geometric Type Conversion Functions</title> <entry role="functableentry">
<tgroup cols="4"> <indexterm>
<thead> <primary>point</primary>
<row> </indexterm>
<entry>Function</entry> <function>point</function> ( <type>double precision</type>, <type>double precision</type> )
<entry>Return Type</entry> <returnvalue>point</returnvalue>
<entry>Description</entry> <?br?>
<entry>Example</entry> Constructs point from its coordinates.
</row> <?br?>
</thead> <literal>point(23.4, -44.5)</literal>
<tbody> <returnvalue>(23.4,-44.5)</returnvalue>
<row> </entry>
<entry> </row>
<indexterm>
<primary>box</primary> <row>
</indexterm> <entry role="functableentry">
<literal><function>box(<type>circle</type>)</function></literal> <function>point</function> ( <type>box</type> )
</entry> <returnvalue>point</returnvalue>
<entry><type>box</type></entry> <?br?>
<entry>circle to box</entry> Computes center of box.
<entry><literal>box(circle '((0,0),2.0)')</literal></entry> <?br?>
</row> <literal>point(box '(1,0),(-1,0)')</literal>
<row> <returnvalue>(0,0)</returnvalue>
<entry><literal><function>box(<type>point</type>)</function></literal></entry> </entry>
<entry><type>box</type></entry> </row>
<entry>point to empty box</entry>
<entry><literal>box(point '(0,0)')</literal></entry> <row>
</row> <entry role="functableentry">
<row> <function>point</function> ( <type>circle</type> )
<entry><literal><function>box(<type>point</type>, <type>point</type>)</function></literal></entry> <returnvalue>point</returnvalue>
<entry><type>box</type></entry> <?br?>
<entry>points to box</entry> Computes center of circle.
<entry><literal>box(point '(0,0)', point '(1,1)')</literal></entry> <?br?>
</row> <literal>point(circle '&lt;(0,0),2&gt;')</literal>
<row> <returnvalue>(0,0)</returnvalue>
<entry><literal><function>box(<type>polygon</type>)</function></literal></entry> </entry>
<entry><type>box</type></entry> </row>
<entry>polygon to box</entry>
<entry><literal>box(polygon '((0,0),(1,1),(2,0))')</literal></entry> <row>
</row> <entry role="functableentry">
<row> <function>point</function> ( <type>lseg</type> )
<entry><literal><function>bound_box(<type>box</type>, <type>box</type>)</function></literal></entry> <returnvalue>point</returnvalue>
<entry><type>box</type></entry> <?br?>
<entry>boxes to bounding box</entry> Computes center of line segment.
<entry><literal>bound_box(box '((0,0),(1,1))', box '((3,3),(4,4))')</literal></entry> <?br?>
</row> <literal>point(lseg '[(-1,0),(1,0)]')</literal>
<row> <returnvalue>(0,0)</returnvalue>
<entry> </entry>
<indexterm> </row>
<primary>circle</primary>
</indexterm> <row>
<literal><function>circle(<type>box</type>)</function></literal> <entry role="functableentry">
</entry> <function>point</function> ( <type>polygon</type> )
<entry><type>circle</type></entry> <returnvalue>point</returnvalue>
<entry>box to circle</entry> <?br?>
<entry><literal>circle(box '((0,0),(1,1))')</literal></entry> Computes center of polygon (the mean of the
</row> positions of the polygon's points).
<row> <?br?>
<entry><literal><function>circle(<type>point</type>, <type>double precision</type>)</function></literal></entry> <literal>point(polygon '((0,0),(1,1),(2,0))')</literal>
<entry><type>circle</type></entry> <returnvalue>(1,0.3333333333333333)</returnvalue>
<entry>center and radius to circle</entry> </entry>
<entry><literal>circle(point '(0,0)', 2.0)</literal></entry> </row>
</row>
<row> <row>
<entry><literal><function>circle(<type>polygon</type>)</function></literal></entry> <entry role="functableentry">
<entry><type>circle</type></entry> <indexterm>
<entry>polygon to circle</entry> <primary>polygon</primary>
<entry><literal>circle(polygon '((0,0),(1,1),(2,0))')</literal></entry> </indexterm>
</row> <function>polygon</function> ( <type>box</type> )
<row> <returnvalue>polygon</returnvalue>
<entry><literal><function>line(<type>point</type>, <type>point</type>)</function></literal></entry> <?br?>
<entry><type>line</type></entry> Converts box to a 4-point polygon.
<entry>points to line</entry> <?br?>
<entry><literal>line(point '(-1,0)', point '(1,0)')</literal></entry> <literal>polygon(box '(1,1),(0,0)')</literal>
</row> <returnvalue>((0,0),(0,1),(1,1),(1,0))</returnvalue>
<row> </entry>
<entry> </row>
<indexterm>
<primary>lseg</primary> <row>
</indexterm> <entry role="functableentry">
<literal><function>lseg(<type>box</type>)</function></literal> <function>polygon</function> ( <type>circle</type> )
</entry> <returnvalue>polygon</returnvalue>
<entry><type>lseg</type></entry> <?br?>
<entry>box diagonal to line segment</entry> Converts circle to a 12-point polygon.
<entry><literal>lseg(box '((-1,0),(1,0))')</literal></entry> <?br?>
</row> <literal>polygon(circle '&lt;(0,0),2&gt;')</literal>
<row> <returnvalue>((-2,0),&zwsp;(-1.7320508075688774,0.9999999999999999),&zwsp;(-1.0000000000000002,1.7320508075688772),&zwsp;(-1.2246063538223773e-16,2),&zwsp;(0.9999999999999996,1.7320508075688774),&zwsp;(1.732050807568877,1.0000000000000007),&zwsp;(2,2.4492127076447545e-16),&zwsp;(1.7320508075688776,-0.9999999999999994),&zwsp;(1.0000000000000009,-1.7320508075688767),&zwsp;(3.673819061467132e-16,-2),&zwsp;(-0.9999999999999987,-1.732050807568878),&zwsp;(-1.7320508075688767,-1.0000000000000009))</returnvalue>
<entry><literal><function>lseg(<type>point</type>, <type>point</type>)</function></literal></entry> </entry>
<entry><type>lseg</type></entry> </row>
<entry>points to line segment</entry>
<entry><literal>lseg(point '(-1,0)', point '(1,0)')</literal></entry> <row>
</row> <entry role="functableentry">
<row> <function>polygon</function> ( <type>integer</type>, <type>circle</type> )
<entry> <returnvalue>polygon</returnvalue>
<indexterm> <?br?>
<primary>path</primary> Converts circle to an <replaceable>n</replaceable>-point polygon.
</indexterm> <?br?>
<literal><function>path(<type>polygon</type>)</function></literal> <literal>polygon(4, circle '&lt;(3,0),1&gt;')</literal>
</entry> <returnvalue>((2,0),&zwsp;(3,1),&zwsp;(4,1.2246063538223773e-16),&zwsp;(3,-1))</returnvalue>
<entry><type>path</type></entry> </entry>
<entry>polygon to path</entry> </row>
<entry><literal>path(polygon '((0,0),(1,1),(2,0))')</literal></entry>
</row> <row>
<row> <entry role="functableentry">
<entry> <function>polygon</function> ( <type>path</type> )
<indexterm> <returnvalue>polygon</returnvalue>
<primary>point</primary> <?br?>
</indexterm> Converts closed path to a polygon with the same list of points.
<literal><function>point</function>(<type>double <?br?>
precision</type>, <type>double precision</type>)</literal> <literal>polygon(path '((0,0),(1,1),(2,0))')</literal>
</entry> <returnvalue>((0,0),(1,1),(2,0))</returnvalue>
<entry><type>point</type></entry> </entry>
<entry>construct point</entry> </row>
<entry><literal>point(23.4, -44.5)</literal></entry>
</row> </tbody>
<row> </tgroup>
<entry><literal><function>point(<type>box</type>)</function></literal></entry>
<entry><type>point</type></entry>
<entry>center of box</entry>
<entry><literal>point(box '((-1,0),(1,0))')</literal></entry>
</row>
<row>
<entry><literal><function>point(<type>circle</type>)</function></literal></entry>
<entry><type>point</type></entry>
<entry>center of circle</entry>
<entry><literal>point(circle '((0,0),2.0)')</literal></entry>
</row>
<row>
<entry><literal><function>point(<type>lseg</type>)</function></literal></entry>
<entry><type>point</type></entry>
<entry>center of line segment</entry>
<entry><literal>point(lseg '((-1,0),(1,0))')</literal></entry>
</row>
<row>
<entry><literal><function>point(<type>polygon</type>)</function></literal></entry>
<entry><type>point</type></entry>
<entry>center of polygon</entry>
<entry><literal>point(polygon '((0,0),(1,1),(2,0))')</literal></entry>
</row>
<row>
<entry>
<indexterm>
<primary>polygon</primary>
</indexterm>
<literal><function>polygon(<type>box</type>)</function></literal>
</entry>
<entry><type>polygon</type></entry>
<entry>box to 4-point polygon</entry>
<entry><literal>polygon(box '((0,0),(1,1))')</literal></entry>
</row>
<row>
<entry><literal><function>polygon(<type>circle</type>)</function></literal></entry>
<entry><type>polygon</type></entry>
<entry>circle to 12-point polygon</entry>
<entry><literal>polygon(circle '((0,0),2.0)')</literal></entry>
</row>
<row>
<entry><literal><function>polygon(<replaceable class="parameter">npts</replaceable>, <type>circle</type>)</function></literal></entry>
<entry><type>polygon</type></entry>
<entry>circle to <replaceable class="parameter">npts</replaceable>-point polygon</entry>
<entry><literal>polygon(12, circle '((0,0),2.0)')</literal></entry>
</row>
<row>
<entry><literal><function>polygon(<type>path</type>)</function></literal></entry>
<entry><type>polygon</type></entry>
<entry>path to polygon</entry>
<entry><literal>polygon(path '((0,0),(1,1),(2,0))')</literal></entry>
</row>
</tbody>
</tgroup>
</table> </table>
<para> <para>
...@@ -9951,22 +10563,6 @@ CREATE TYPE rainbow AS ENUM ('red', 'orange', 'yellow', 'green', 'blue', 'purple ...@@ -9951,22 +10563,6 @@ CREATE TYPE rainbow AS ENUM ('red', 'orange', 'yellow', 'green', 'blue', 'purple
as an array of two <type>point</type> values. as an array of two <type>point</type> values.
</para> </para>
<para>
The <function>area</function> function works for the types
<type>box</type>, <type>circle</type>, and <type>path</type>.
The <function>area</function> function only works on the
<type>path</type> data type if the points in the
<type>path</type> are non-intersecting. For example, the
<type>path</type>
<literal>'((0,0),(0,1),(2,1),(2,2),(1,2),(1,0),(0,0))'::PATH</literal>
will not work; however, the following visually identical
<type>path</type>
<literal>'((0,0),(0,1),(1,1),(1,2),(2,2),(2,1),(1,1),(1,0),(0,0))'::PATH</literal>
will work. If the concept of an intersecting versus
non-intersecting <type>path</type> is confusing, draw both of the
above <type>path</type>s side by side on a piece of graph paper.
</para>
</sect1> </sect1>
......
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