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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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...@@ -9446,188 +9446,576 @@ CREATE TYPE rainbow AS ENUM ('red', 'orange', 'yellow', 'green', 'blue', 'purple ...@@ -9446,188 +9446,576 @@ CREATE TYPE rainbow AS ENUM ('red', 'orange', 'yellow', 'green', 'blue', 'purple
linkend="functions-geometry-conv-table"/>. linkend="functions-geometry-conv-table"/>.
</para> </para>
<caution>
<para>
Note that the <quote>same as</quote> operator, <literal>~=</literal>, represents
the usual notion of equality for the <type>point</type>,
<type>box</type>, <type>polygon</type>, and <type>circle</type> types.
Some of these types also have an <literal>=</literal> operator, but
<literal>=</literal> compares
for equal <emphasis>areas</emphasis> only. The other scalar comparison operators
(<literal>&lt;=</literal> and so on) likewise compare areas for these types.
</para>
</caution>
<table id="functions-geometry-op-table"> <table id="functions-geometry-op-table">
<title>Geometric Operators</title> <title>Geometric Operators</title>
<tgroup cols="3"> <tgroup cols="1">
<thead> <thead>
<row> <row>
<entry>Operator</entry> <entry role="functableentry">
<entry>Description</entry> Operator<?br?>Description<?br?>Example(s)
<entry>Example</entry> </entry>
</row> </row>
</thead> </thead>
<tbody> <tbody>
<row> <row>
<entry> <literal>+</literal> </entry> <entry role="functableentry">
<entry>Translation</entry> <replaceable>geometric_type</replaceable> <literal>+</literal> <type>point</type>
<entry><literal>box '((0,0),(1,1))' + point '(2.0,0)'</literal></entry> <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>
<row> <row>
<entry> <literal>-</literal> </entry> <entry role="functableentry">
<entry>Translation</entry> <type>path</type> <literal>+</literal> <type>path</type>
<entry><literal>box '((0,0),(1,1))' - point '(2.0,0)'</literal></entry> <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>
<row> <row>
<entry> <literal>*</literal> </entry> <entry role="functableentry">
<entry>Scaling/rotation</entry> <replaceable>geometric_type</replaceable> <literal>-</literal> <type>point</type>
<entry><literal>box '((0,0),(1,1))' * point '(2.0,0)'</literal></entry> <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>
<row> <row>
<entry> <literal>/</literal> </entry> <entry role="functableentry">
<entry>Scaling/rotation</entry> <replaceable>geometric_type</replaceable> <literal>*</literal> <type>point</type>
<entry><literal>box '((0,0),(2,2))' / point '(2.0,0)'</literal></entry> <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>
<row> <row>
<entry> <literal>#</literal> </entry> <entry role="functableentry">
<entry>Point or box of intersection</entry> <replaceable>geometric_type</replaceable> <literal>/</literal> <type>point</type>
<entry><literal>box '((1,-1),(-1,1))' # box '((1,1),(-2,-2))'</literal></entry> <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>
<row> <row>
<entry> <literal>#</literal> </entry> <entry role="functableentry">
<entry>Number of points in path or polygon</entry> <literal>@-@</literal> <replaceable>geometric_type</replaceable>
<entry><literal># path '((1,0),(0,1),(-1,0))'</literal></entry> <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>
<row> <row>
<entry> <literal>@-@</literal> </entry> <entry role="functableentry">
<entry>Length or circumference</entry> <literal>@@</literal> <replaceable>geometric_type</replaceable>
<entry><literal>@-@ path '((0,0),(1,0))'</literal></entry> <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>
<row> <row>
<entry> <literal>@@</literal> </entry> <entry role="functableentry">
<entry>Center</entry> <literal>#</literal> <replaceable>geometric_type</replaceable>
<entry><literal>@@ circle '((0,0),10)'</literal></entry> <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>
<row> <row>
<entry> <literal>##</literal> </entry> <entry role="functableentry">
<entry>Closest point to first operand on second operand</entry> <replaceable>geometric_type</replaceable> <literal>#</literal> <replaceable>geometric_type</replaceable>
<entry><literal>point '(0,0)' ## lseg '((2,0),(0,2))'</literal></entry> <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>
<row> <row>
<entry> <literal>&lt;-&gt;</literal> </entry> <entry role="functableentry">
<entry>Distance between</entry> <type>box</type> <literal>#</literal> <type>box</type>
<entry><literal>circle '((0,0),1)' &lt;-&gt; circle '((5,0),1)'</literal></entry> <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>
<row> <row>
<entry> <literal>&amp;&amp;</literal> </entry> <entry role="functableentry">
<entry>Overlaps? (One point in common makes this true.)</entry> <replaceable>geometric_type</replaceable> <literal>##</literal> <replaceable>geometric_type</replaceable>
<entry><literal>box '((0,0),(1,1))' &amp;&amp; box '((0,0),(2,2))'</literal></entry> <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>
<row> <row>
<entry> <literal>&lt;&lt;</literal> </entry> <entry role="functableentry">
<entry>Is strictly left of?</entry> <replaceable>geometric_type</replaceable> <literal>&lt;-&gt;</literal> <replaceable>geometric_type</replaceable>
<entry><literal>circle '((0,0),1)' &lt;&lt; circle '((5,0),1)'</literal></entry> <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>
<row> <row>
<entry> <literal>&gt;&gt;</literal> </entry> <entry role="functableentry">
<entry>Is strictly right of?</entry> <replaceable>geometric_type</replaceable> <literal>@&gt;</literal> <replaceable>geometric_type</replaceable>
<entry><literal>circle '((5,0),1)' &gt;&gt; circle '((0,0),1)'</literal></entry> <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>
<row> <row>
<entry> <literal>&amp;&lt;</literal> </entry> <entry role="functableentry">
<entry>Does not extend to the right of?</entry> <replaceable>geometric_type</replaceable> <literal>&lt;@</literal> <replaceable>geometric_type</replaceable>
<entry><literal>box '((0,0),(1,1))' &amp;&lt; box '((0,0),(2,2))'</literal></entry> <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>
<row> <row>
<entry> <literal>&amp;&gt;</literal> </entry> <entry role="functableentry">
<entry>Does not extend to the left of?</entry> <replaceable>geometric_type</replaceable> <literal>&amp;&amp;</literal> <replaceable>geometric_type</replaceable>
<entry><literal>box '((0,0),(3,3))' &amp;&gt; box '((0,0),(2,2))'</literal></entry> <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>
<row> <row>
<entry> <literal>&lt;&lt;|</literal> </entry> <entry role="functableentry">
<entry>Is strictly below?</entry> <replaceable>geometric_type</replaceable> <literal>&lt;&lt;</literal> <replaceable>geometric_type</replaceable>
<entry><literal>box '((0,0),(3,3))' &lt;&lt;| box '((3,4),(5,5))'</literal></entry> <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>
<row> <row>
<entry> <literal>|&gt;&gt;</literal> </entry> <entry role="functableentry">
<entry>Is strictly above?</entry> <replaceable>geometric_type</replaceable> <literal>&gt;&gt;</literal> <replaceable>geometric_type</replaceable>
<entry><literal>box '((3,4),(5,5))' |&gt;&gt; box '((0,0),(3,3))'</literal></entry> <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>
<row> <row>
<entry> <literal>&amp;&lt;|</literal> </entry> <entry role="functableentry">
<entry>Does not extend above?</entry> <replaceable>geometric_type</replaceable> <literal>&amp;&lt;</literal> <replaceable>geometric_type</replaceable>
<entry><literal>box '((0,0),(1,1))' &amp;&lt;| box '((0,0),(2,2))'</literal></entry> <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>
<row> <row>
<entry> <literal>|&amp;&gt;</literal> </entry> <entry role="functableentry">
<entry>Does not extend below?</entry> <replaceable>geometric_type</replaceable> <literal>&amp;&gt;</literal> <replaceable>geometric_type</replaceable>
<entry><literal>box '((0,0),(3,3))' |&amp;&gt; box '((0,0),(2,2))'</literal></entry> <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>
<row> <row>
<entry> <literal>&lt;^</literal> </entry> <entry role="functableentry">
<entry>Is below (allows touching)?</entry> <replaceable>geometric_type</replaceable> <literal>&lt;&lt;|</literal> <replaceable>geometric_type</replaceable>
<entry><literal>circle '((0,0),1)' &lt;^ circle '((0,5),1)'</literal></entry> <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>
<row> <row>
<entry> <literal>&gt;^</literal> </entry> <entry role="functableentry">
<entry>Is above (allows touching)?</entry> <replaceable>geometric_type</replaceable> <literal>|&gt;&gt;</literal> <replaceable>geometric_type</replaceable>
<entry><literal>circle '((0,5),1)' &gt;^ circle '((0,0),1)'</literal></entry> <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>
<row> <row>
<entry> <literal>?#</literal> </entry> <entry role="functableentry">
<entry>Intersects?</entry> <replaceable>geometric_type</replaceable> <literal>&amp;&lt;|</literal> <replaceable>geometric_type</replaceable>
<entry><literal>lseg '((-1,0),(1,0))' ?# box '((-2,-2),(2,2))'</literal></entry> <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>
<row> <row>
<entry> <literal>?-</literal> </entry> <entry role="functableentry">
<entry>Is horizontal?</entry> <replaceable>geometric_type</replaceable> <literal>|&amp;&gt;</literal> <replaceable>geometric_type</replaceable>
<entry><literal>?- lseg '((-1,0),(1,0))'</literal></entry> <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>
<row> <row>
<entry> <literal>?-</literal> </entry> <entry role="functableentry">
<entry>Are horizontally aligned?</entry> <type>box</type> <literal>&lt;^</literal> <type>box</type>
<entry><literal>point '(1,0)' ?- point '(0,0)'</literal></entry> <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>
<row> <row>
<entry> <literal>?|</literal> </entry> <entry role="functableentry">
<entry>Is vertical?</entry> <type>point</type> <literal>&lt;^</literal> <type>point</type>
<entry><literal>?| lseg '((-1,0),(1,0))'</literal></entry> <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>
<row> <row>
<entry> <literal>?|</literal> </entry> <entry role="functableentry">
<entry>Are vertically aligned?</entry> <type>box</type> <literal>&gt;^</literal> <type>box</type>
<entry><literal>point '(0,1)' ?| point '(0,0)'</literal></entry> <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>
<row> <row>
<entry> <literal>?-|</literal> </entry> <entry role="functableentry">
<entry>Is perpendicular?</entry> <type>point</type> <literal>&gt;^</literal> <type>point</type>
<entry><literal>lseg '((0,0),(0,1))' ?-| lseg '((0,0),(1,0))'</literal></entry> <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>
<row> <row>
<entry> <literal>?||</literal> </entry> <entry role="functableentry">
<entry>Are parallel?</entry> <replaceable>geometric_type</replaceable> <literal>?#</literal> <replaceable>geometric_type</replaceable>
<entry><literal>lseg '((-1,0),(1,0))' ?|| lseg '((-1,2),(1,2))'</literal></entry> <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>
<row> <row>
<entry> <literal>@&gt;</literal> </entry> <entry role="functableentry">
<entry>Contains?</entry> <literal>?-</literal> <replaceable>geometric_type</replaceable>
<entry><literal>circle '((0,0),2)' @&gt; point '(1,1)'</literal></entry> <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>
<row> <row>
<entry> <literal>&lt;@</literal> </entry> <entry role="functableentry">
<entry>Contained in or on?</entry> <type>point</type> <literal>?-</literal> <type>point</type>
<entry><literal>point '(1,1)' &lt;@ circle '((0,0),2)'</literal></entry> <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>
<row> <row>
<entry> <literal>~=</literal> </entry> <entry role="functableentry">
<entry>Same as?</entry> <replaceable>geometric_type</replaceable> <literal>?||</literal> <replaceable>geometric_type</replaceable>
<entry><literal>polygon '((0,0),(1,1))' ~= polygon '((1,1),(0,0))'</literal></entry> <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> </row>
</tbody> </tbody>
</tgroup> </tgroup>
</table> </table>
<caution>
<para>
Note that the <quote>same as</quote> operator, <literal>~=</literal>,
represents the usual notion of equality for the <type>point</type>,
<type>box</type>, <type>polygon</type>, and <type>circle</type> types.
Some of the geometric types also have an <literal>=</literal> operator, but
<literal>=</literal> compares for equal <emphasis>areas</emphasis> only.
The other scalar comparison operators (<literal>&lt;=</literal> and so
on), where available for these types, likewise compare areas.
</para>
</caution>
<note> <note>
<para> <para>
Before <productname>PostgreSQL</productname> 8.2, the containment Before <productname>PostgreSQL</productname> 8.2, the containment
...@@ -9637,132 +10025,234 @@ CREATE TYPE rainbow AS ENUM ('red', 'orange', 'yellow', 'green', 'blue', 'purple ...@@ -9637,132 +10025,234 @@ CREATE TYPE rainbow AS ENUM ('red', 'orange', 'yellow', 'green', 'blue', 'purple
</para> </para>
</note> </note>
<table id="functions-geometry-func-table">
<title>Geometric Functions</title>
<tgroup cols="1">
<thead>
<row>
<entry role="functableentry">
Function<?br?>Description<?br?>Example(s)
</entry>
</row>
</thead>
<tbody>
<row>
<entry role="functableentry">
<indexterm> <indexterm>
<primary>area</primary> <primary>area</primary>
</indexterm> </indexterm>
<function>area</function> ( <replaceable>geometric_type</replaceable> )
<returnvalue>double precision</returnvalue>
<?br?>
Computes area.
Available for <type>box</type>, <type>path</type>, <type>circle</type>.
A <type>path</type> input must be closed, else NULL is returned.
Also, if the <type>path</type> is self-intersecting, the result may be
meaningless.
<?br?>
<literal>area(box '(2,2),(0,0)')</literal>
<returnvalue>4</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<indexterm> <indexterm>
<primary>center</primary> <primary>center</primary>
</indexterm> </indexterm>
<function>center</function> ( <replaceable>geometric_type</replaceable> )
<returnvalue>point</returnvalue>
<?br?>
Computes center point.
Available for <type>box</type>, <type>circle</type>.
<?br?>
<literal>center(box '(1,2),(0,0)')</literal>
<returnvalue>(0.5,1)</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<indexterm>
<primary>diagonal</primary>
</indexterm>
<function>diagonal</function> ( <type>box</type> )
<returnvalue>lseg</returnvalue>
<?br?>
Extracts box's diagonal as a line segment
(same as <function>lseg(box)</function>).
<?br?>
<literal>diagonal(box '(1,2),(0,0)')</literal>
<returnvalue>[(1,2),(0,0)]</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<indexterm> <indexterm>
<primary>diameter</primary> <primary>diameter</primary>
</indexterm> </indexterm>
<function>diameter</function> ( <type>circle</type> )
<returnvalue>double precision</returnvalue>
<?br?>
Computes diameter of circle.
<?br?>
<literal>diameter(circle '&lt;(0,0),2&gt;')</literal>
<returnvalue>4</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<indexterm> <indexterm>
<primary>height</primary> <primary>height</primary>
</indexterm> </indexterm>
<function>height</function> ( <type>box</type> )
<returnvalue>double precision</returnvalue>
<?br?>
Computes vertical size of box.
<?br?>
<literal>height(box '(1,2),(0,0)')</literal>
<returnvalue>2</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<indexterm> <indexterm>
<primary>isclosed</primary> <primary>isclosed</primary>
</indexterm> </indexterm>
<function>isclosed</function> ( <type>path</type> )
<returnvalue>boolean</returnvalue>
<?br?>
Is path closed?
<?br?>
<literal>isclosed(path '((0,0),(1,1),(2,0))')</literal>
<returnvalue>t</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<indexterm> <indexterm>
<primary>isopen</primary> <primary>isopen</primary>
</indexterm> </indexterm>
<function>isopen</function> ( <type>path</type> )
<returnvalue>boolean</returnvalue>
<?br?>
Is path open?
<?br?>
<literal>isopen(path '[(0,0),(1,1),(2,0)]')</literal>
<returnvalue>t</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<indexterm> <indexterm>
<primary>length</primary> <primary>length</primary>
</indexterm> </indexterm>
<function>length</function> ( <replaceable>geometric_type</replaceable> )
<returnvalue>double precision</returnvalue>
<?br?>
Computes the total length.
Available for <type>lseg</type>, <type>path</type>.
<?br?>
<literal>length(path '((-1,0),(1,0))')</literal>
<returnvalue>4</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<indexterm> <indexterm>
<primary>npoints</primary> <primary>npoints</primary>
</indexterm> </indexterm>
<function>npoints</function> ( <replaceable>geometric_type</replaceable> )
<returnvalue>integer</returnvalue>
<?br?>
Returns the number of points.
Available for <type>path</type>, <type>polygon</type>.
<?br?>
<literal>npoints(path '[(0,0),(1,1),(2,0)]')</literal>
<returnvalue>3</returnvalue>
</entry>
</row>
<row>
<entry role="functableentry">
<indexterm> <indexterm>
<primary>pclose</primary> <primary>pclose</primary>
</indexterm> </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> <indexterm>
<primary>popen</primary> <primary>popen</primary>
</indexterm> </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> <indexterm>
<primary>radius</primary> <primary>radius</primary>
</indexterm> </indexterm>
<indexterm> <function>radius</function> ( <type>circle</type> )
<primary>width</primary> <returnvalue>double precision</returnvalue>
</indexterm> <?br?>
Computes radius of circle.
<table id="functions-geometry-func-table"> <?br?>
<title>Geometric Functions</title> <literal>radius(circle '&lt;(0,0),2&gt;')</literal>
<tgroup cols="4"> <returnvalue>2</returnvalue>
<thead> </entry>
<row>
<entry>Function</entry>
<entry>Return Type</entry>
<entry>Description</entry>
<entry>Example</entry>
</row>
</thead>
<tbody>
<row>
<entry><literal><function>area(<replaceable>object</replaceable>)</function></literal></entry>
<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>
<row> <row>
<entry><literal><function>radius(<type>circle</type>)</function></literal></entry> <entry role="functableentry">
<entry><type>double precision</type></entry> <indexterm>
<entry>radius of circle</entry> <primary>slope</primary>
<entry><literal>radius(circle '((0,0),2.0)')</literal></entry> </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>
<row> <row>
<entry><literal><function>width(<type>box</type>)</function></literal></entry> <entry role="functableentry">
<entry><type>double precision</type></entry> <indexterm>
<entry>horizontal size of box</entry> <primary>width</primary>
<entry><literal>width(box '((0,0),(1,1))')</literal></entry> </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> </row>
</tbody> </tbody>
</tgroup> </tgroup>
...@@ -9770,173 +10260,295 @@ CREATE TYPE rainbow AS ENUM ('red', 'orange', 'yellow', 'green', 'blue', 'purple ...@@ -9770,173 +10260,295 @@ CREATE TYPE rainbow AS ENUM ('red', 'orange', 'yellow', 'green', 'blue', 'purple
<table id="functions-geometry-conv-table"> <table id="functions-geometry-conv-table">
<title>Geometric Type Conversion Functions</title> <title>Geometric Type Conversion Functions</title>
<tgroup cols="4"> <tgroup cols="1">
<thead> <thead>
<row> <row>
<entry>Function</entry> <entry role="functableentry">
<entry>Return Type</entry> Function<?br?>Description<?br?>Example(s)
<entry>Description</entry> </entry>
<entry>Example</entry>
</row> </row>
</thead> </thead>
<tbody> <tbody>
<row> <row>
<entry> <entry role="functableentry">
<indexterm> <indexterm>
<primary>box</primary> <primary>box</primary>
</indexterm> </indexterm>
<literal><function>box(<type>circle</type>)</function></literal> <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> </entry>
<entry><type>box</type></entry>
<entry>circle to box</entry>
<entry><literal>box(circle '((0,0),2.0)')</literal></entry>
</row> </row>
<row> <row>
<entry><literal><function>box(<type>point</type>)</function></literal></entry> <entry role="functableentry">
<entry><type>box</type></entry> <function>box</function> ( <type>point</type> )
<entry>point to empty box</entry> <returnvalue>box</returnvalue>
<entry><literal>box(point '(0,0)')</literal></entry> <?br?>
Converts point to empty box.
<?br?>
<literal>box(point '(1,0)')</literal>
<returnvalue>(1,0),(1,0)</returnvalue>
</entry>
</row> </row>
<row> <row>
<entry><literal><function>box(<type>point</type>, <type>point</type>)</function></literal></entry> <entry role="functableentry">
<entry><type>box</type></entry> <function>box</function> ( <type>point</type>, <type>point</type> )
<entry>points to box</entry> <returnvalue>box</returnvalue>
<entry><literal>box(point '(0,0)', point '(1,1)')</literal></entry> <?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>
<row> <row>
<entry><literal><function>box(<type>polygon</type>)</function></literal></entry> <entry role="functableentry">
<entry><type>box</type></entry> <function>box</function> ( <type>polygon</type> )
<entry>polygon to box</entry> <returnvalue>box</returnvalue>
<entry><literal>box(polygon '((0,0),(1,1),(2,0))')</literal></entry> <?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>
<row> <row>
<entry><literal><function>bound_box(<type>box</type>, <type>box</type>)</function></literal></entry> <entry role="functableentry">
<entry><type>box</type></entry> <indexterm>
<entry>boxes to bounding box</entry> <primary>bound_box</primary>
<entry><literal>bound_box(box '((0,0),(1,1))', box '((3,3),(4,4))')</literal></entry> </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>
<row> <row>
<entry> <entry role="functableentry">
<indexterm> <indexterm>
<primary>circle</primary> <primary>circle</primary>
</indexterm> </indexterm>
<literal><function>circle(<type>box</type>)</function></literal> <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> </entry>
<entry><type>circle</type></entry>
<entry>box to circle</entry>
<entry><literal>circle(box '((0,0),(1,1))')</literal></entry>
</row> </row>
<row> <row>
<entry><literal><function>circle(<type>point</type>, <type>double precision</type>)</function></literal></entry> <entry role="functableentry">
<entry><type>circle</type></entry> <function>circle</function> ( <type>point</type>, <type>double precision</type> )
<entry>center and radius to circle</entry> <returnvalue>circle</returnvalue>
<entry><literal>circle(point '(0,0)', 2.0)</literal></entry> <?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>
<row> <row>
<entry><literal><function>circle(<type>polygon</type>)</function></literal></entry> <entry role="functableentry">
<entry><type>circle</type></entry> <function>circle</function> ( <type>polygon</type> )
<entry>polygon to circle</entry> <returnvalue>circle</returnvalue>
<entry><literal>circle(polygon '((0,0),(1,1),(2,0))')</literal></entry> <?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>
<row> <row>
<entry><literal><function>line(<type>point</type>, <type>point</type>)</function></literal></entry> <entry role="functableentry">
<entry><type>line</type></entry> <indexterm>
<entry>points to line</entry> <primary>line</primary>
<entry><literal>line(point '(-1,0)', point '(1,0)')</literal></entry> </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>
<row> <row>
<entry> <entry role="functableentry">
<indexterm> <indexterm>
<primary>lseg</primary> <primary>lseg</primary>
</indexterm> </indexterm>
<literal><function>lseg(<type>box</type>)</function></literal> <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> </entry>
<entry><type>lseg</type></entry>
<entry>box diagonal to line segment</entry>
<entry><literal>lseg(box '((-1,0),(1,0))')</literal></entry>
</row> </row>
<row> <row>
<entry><literal><function>lseg(<type>point</type>, <type>point</type>)</function></literal></entry> <entry role="functableentry">
<entry><type>lseg</type></entry> <function>lseg</function> ( <type>point</type>, <type>point</type> )
<entry>points to line segment</entry> <returnvalue>lseg</returnvalue>
<entry><literal>lseg(point '(-1,0)', point '(1,0)')</literal></entry> <?br?>
Constructs line segment from two endpoints.
<?br?>
<literal>lseg(point '(-1,0)', point '(1,0)')</literal>
<returnvalue>[(-1,0),(1,0)]</returnvalue>
</entry>
</row> </row>
<row> <row>
<entry> <entry role="functableentry">
<indexterm> <indexterm>
<primary>path</primary> <primary>path</primary>
</indexterm> </indexterm>
<literal><function>path(<type>polygon</type>)</function></literal> <function>path</function> ( <type>polygon</type> )
<returnvalue>path</returnvalue>
<?br?>
Converts polygon to a closed path with the same list of points.
<?br?>
<literal>path(polygon '((0,0),(1,1),(2,0))')</literal>
<returnvalue>((0,0),(1,1),(2,0))</returnvalue>
</entry> </entry>
<entry><type>path</type></entry>
<entry>polygon to path</entry>
<entry><literal>path(polygon '((0,0),(1,1),(2,0))')</literal></entry>
</row> </row>
<row> <row>
<entry> <entry role="functableentry">
<indexterm> <indexterm>
<primary>point</primary> <primary>point</primary>
</indexterm> </indexterm>
<literal><function>point</function>(<type>double <function>point</function> ( <type>double precision</type>, <type>double precision</type> )
precision</type>, <type>double precision</type>)</literal> <returnvalue>point</returnvalue>
<?br?>
Constructs point from its coordinates.
<?br?>
<literal>point(23.4, -44.5)</literal>
<returnvalue>(23.4,-44.5)</returnvalue>
</entry> </entry>
<entry><type>point</type></entry>
<entry>construct point</entry>
<entry><literal>point(23.4, -44.5)</literal></entry>
</row> </row>
<row> <row>
<entry><literal><function>point(<type>box</type>)</function></literal></entry> <entry role="functableentry">
<entry><type>point</type></entry> <function>point</function> ( <type>box</type> )
<entry>center of box</entry> <returnvalue>point</returnvalue>
<entry><literal>point(box '((-1,0),(1,0))')</literal></entry> <?br?>
Computes center of box.
<?br?>
<literal>point(box '(1,0),(-1,0)')</literal>
<returnvalue>(0,0)</returnvalue>
</entry>
</row> </row>
<row> <row>
<entry><literal><function>point(<type>circle</type>)</function></literal></entry> <entry role="functableentry">
<entry><type>point</type></entry> <function>point</function> ( <type>circle</type> )
<entry>center of circle</entry> <returnvalue>point</returnvalue>
<entry><literal>point(circle '((0,0),2.0)')</literal></entry> <?br?>
Computes center of circle.
<?br?>
<literal>point(circle '&lt;(0,0),2&gt;')</literal>
<returnvalue>(0,0)</returnvalue>
</entry>
</row> </row>
<row> <row>
<entry><literal><function>point(<type>lseg</type>)</function></literal></entry> <entry role="functableentry">
<entry><type>point</type></entry> <function>point</function> ( <type>lseg</type> )
<entry>center of line segment</entry> <returnvalue>point</returnvalue>
<entry><literal>point(lseg '((-1,0),(1,0))')</literal></entry> <?br?>
Computes center of line segment.
<?br?>
<literal>point(lseg '[(-1,0),(1,0)]')</literal>
<returnvalue>(0,0)</returnvalue>
</entry>
</row> </row>
<row> <row>
<entry><literal><function>point(<type>polygon</type>)</function></literal></entry> <entry role="functableentry">
<entry><type>point</type></entry> <function>point</function> ( <type>polygon</type> )
<entry>center of polygon</entry> <returnvalue>point</returnvalue>
<entry><literal>point(polygon '((0,0),(1,1),(2,0))')</literal></entry> <?br?>
Computes center of polygon (the mean of the
positions of the polygon's points).
<?br?>
<literal>point(polygon '((0,0),(1,1),(2,0))')</literal>
<returnvalue>(1,0.3333333333333333)</returnvalue>
</entry>
</row> </row>
<row> <row>
<entry> <entry role="functableentry">
<indexterm> <indexterm>
<primary>polygon</primary> <primary>polygon</primary>
</indexterm> </indexterm>
<literal><function>polygon(<type>box</type>)</function></literal> <function>polygon</function> ( <type>box</type> )
<returnvalue>polygon</returnvalue>
<?br?>
Converts box to a 4-point polygon.
<?br?>
<literal>polygon(box '(1,1),(0,0)')</literal>
<returnvalue>((0,0),(0,1),(1,1),(1,0))</returnvalue>
</entry> </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>
<row> <row>
<entry><literal><function>polygon(<type>circle</type>)</function></literal></entry> <entry role="functableentry">
<entry><type>polygon</type></entry> <function>polygon</function> ( <type>circle</type> )
<entry>circle to 12-point polygon</entry> <returnvalue>polygon</returnvalue>
<entry><literal>polygon(circle '((0,0),2.0)')</literal></entry> <?br?>
Converts circle to a 12-point polygon.
<?br?>
<literal>polygon(circle '&lt;(0,0),2&gt;')</literal>
<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>
</row> </row>
<row> <row>
<entry><literal><function>polygon(<replaceable class="parameter">npts</replaceable>, <type>circle</type>)</function></literal></entry> <entry role="functableentry">
<entry><type>polygon</type></entry> <function>polygon</function> ( <type>integer</type>, <type>circle</type> )
<entry>circle to <replaceable class="parameter">npts</replaceable>-point polygon</entry> <returnvalue>polygon</returnvalue>
<entry><literal>polygon(12, circle '((0,0),2.0)')</literal></entry> <?br?>
Converts circle to an <replaceable>n</replaceable>-point polygon.
<?br?>
<literal>polygon(4, circle '&lt;(3,0),1&gt;')</literal>
<returnvalue>((2,0),&zwsp;(3,1),&zwsp;(4,1.2246063538223773e-16),&zwsp;(3,-1))</returnvalue>
</entry>
</row> </row>
<row> <row>
<entry><literal><function>polygon(<type>path</type>)</function></literal></entry> <entry role="functableentry">
<entry><type>polygon</type></entry> <function>polygon</function> ( <type>path</type> )
<entry>path to polygon</entry> <returnvalue>polygon</returnvalue>
<entry><literal>polygon(path '((0,0),(1,1),(2,0))')</literal></entry> <?br?>
Converts closed path to a polygon with the same list of points.
<?br?>
<literal>polygon(path '((0,0),(1,1),(2,0))')</literal>
<returnvalue>((0,0),(1,1),(2,0))</returnvalue>
</entry>
</row> </row>
</tbody> </tbody>
</tgroup> </tgroup>
</table> </table>
...@@ -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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