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<title>9.10.Geometric Functions and Operators</title>
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<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"><div class="sect1" lang="en">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="functions-geometry"></a>9.10.Geometric Functions and Operators</h2></div></div></div>
<p> The geometric types <code class="type">point</code>, <code class="type">box</code>,
<code class="type">lseg</code>, <code class="type">line</code>, <code class="type">path</code>,
<code class="type">polygon</code>, and <code class="type">circle</code> have a large set of
native support functions and operators, shown in <a href="functions-geometry.html#functions-geometry-op-table" title="Table9.28.Geometric Operators">Table9.28, “Geometric Operators”</a>, <a href="functions-geometry.html#functions-geometry-func-table" title="Table9.29.Geometric Functions">Table9.29, “Geometric Functions”</a>, and <a href="functions-geometry.html#functions-geometry-conv-table" title="Table9.30.Geometric Type Conversion Functions">Table9.30, “Geometric Type Conversion Functions”</a>.
</p>
<div class="caution" style="margin-left: 0.5in; margin-right: 0.5in;">
<h3 class="title">Caution</h3>
<p> Note that the “<span class="quote">same as</span>” operator, <code class="literal">~=</code>, represents
the usual notion of equality for the <code class="type">point</code>,
<code class="type">box</code>, <code class="type">polygon</code>, and <code class="type">circle</code> types.
Some of these types also have an <code class="literal">=</code> operator, but
<code class="literal">=</code> compares
for equal <span class="emphasis"><em>areas</em></span> only. The other scalar comparison operators
(<code class="literal"><=</code> and so on) likewise compare areas for these types.
</p>
</div>
<div class="table">
<a name="functions-geometry-op-table"></a><p class="title"><b>Table9.28.Geometric Operators</b></p>
<div class="table-contents"><table summary="Geometric Operators" border="1">
<colgroup>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>Operator</th>
<th>Description</th>
<th>Example</th>
</tr></thead>
<tbody>
<tr>
<td> <code class="literal">+</code> </td>
<td>Translation</td>
<td><code class="literal">box '((0,0),(1,1))' + point '(2.0,0)'</code></td>
</tr>
<tr>
<td> <code class="literal">-</code> </td>
<td>Translation</td>
<td><code class="literal">box '((0,0),(1,1))' - point '(2.0,0)'</code></td>
</tr>
<tr>
<td> <code class="literal">*</code> </td>
<td>Scaling/rotation</td>
<td><code class="literal">box '((0,0),(1,1))' * point '(2.0,0)'</code></td>
</tr>
<tr>
<td> <code class="literal">/</code> </td>
<td>Scaling/rotation</td>
<td><code class="literal">box '((0,0),(2,2))' / point '(2.0,0)'</code></td>
</tr>
<tr>
<td> <code class="literal">#</code> </td>
<td>Point or box of intersection</td>
<td><code class="literal">'((1,-1),(-1,1))' # '((1,1),(-1,-1))'</code></td>
</tr>
<tr>
<td> <code class="literal">#</code> </td>
<td>Number of points in path or polygon</td>
<td><code class="literal"># '((1,0),(0,1),(-1,0))'</code></td>
</tr>
<tr>
<td> <code class="literal">@-@</code> </td>
<td>Length or circumference</td>
<td><code class="literal">@-@ path '((0,0),(1,0))'</code></td>
</tr>
<tr>
<td> <code class="literal">@@</code> </td>
<td>Center</td>
<td><code class="literal">@@ circle '((0,0),10)'</code></td>
</tr>
<tr>
<td> <code class="literal">##</code> </td>
<td>Closest point to first operand on second operand</td>
<td><code class="literal">point '(0,0)' ## lseg '((2,0),(0,2))'</code></td>
</tr>
<tr>
<td> <code class="literal"><-></code> </td>
<td>Distance between</td>
<td><code class="literal">circle '((0,0),1)' <-> circle '((5,0),1)'</code></td>
</tr>
<tr>
<td> <code class="literal">&&</code> </td>
<td>Overlaps?</td>
<td><code class="literal">box '((0,0),(1,1))' && box '((0,0),(2,2))'</code></td>
</tr>
<tr>
<td> <code class="literal"><<</code> </td>
<td>Is strictly left of?</td>
<td><code class="literal">circle '((0,0),1)' << circle '((5,0),1)'</code></td>
</tr>
<tr>
<td> <code class="literal">>></code> </td>
<td>Is strictly right of?</td>
<td><code class="literal">circle '((5,0),1)' >> circle '((0,0),1)'</code></td>
</tr>
<tr>
<td> <code class="literal">&<</code> </td>
<td>Does not extend to the right of?</td>
<td><code class="literal">box '((0,0),(1,1))' &< box '((0,0),(2,2))'</code></td>
</tr>
<tr>
<td> <code class="literal">&></code> </td>
<td>Does not extend to the left of?</td>
<td><code class="literal">box '((0,0),(3,3))' &> box '((0,0),(2,2))'</code></td>
</tr>
<tr>
<td> <code class="literal"><<|</code> </td>
<td>Is strictly below?</td>
<td><code class="literal">box '((0,0),(3,3))' <<| box '((3,4),(5,5))'</code></td>
</tr>
<tr>
<td> <code class="literal">|>></code> </td>
<td>Is strictly above?</td>
<td><code class="literal">box '((3,4),(5,5))' |>> box '((0,0),(3,3))'</code></td>
</tr>
<tr>
<td> <code class="literal">&<|</code> </td>
<td>Does not extend above?</td>
<td><code class="literal">box '((0,0),(1,1))' &<| box '((0,0),(2,2))'</code></td>
</tr>
<tr>
<td> <code class="literal">|&></code> </td>
<td>Does not extend below?</td>
<td><code class="literal">box '((0,0),(3,3))' |&> box '((0,0),(2,2))'</code></td>
</tr>
<tr>
<td> <code class="literal"><^</code> </td>
<td>Is below (allows touching)?</td>
<td><code class="literal">circle '((0,0),1)' <^ circle '((0,5),1)'</code></td>
</tr>
<tr>
<td> <code class="literal">>^</code> </td>
<td>Is above (allows touching)?</td>
<td><code class="literal">circle '((0,5),1)' >^ circle '((0,0),1)'</code></td>
</tr>
<tr>
<td> <code class="literal">?#</code> </td>
<td>Intersects?</td>
<td><code class="literal">lseg '((-1,0),(1,0))' ?# box '((-2,-2),(2,2))'</code></td>
</tr>
<tr>
<td> <code class="literal">?-</code> </td>
<td>Is horizontal?</td>
<td><code class="literal">?- lseg '((-1,0),(1,0))'</code></td>
</tr>
<tr>
<td> <code class="literal">?-</code> </td>
<td>Are horizontally aligned?</td>
<td><code class="literal">point '(1,0)' ?- point '(0,0)'</code></td>
</tr>
<tr>
<td> <code class="literal">?|</code> </td>
<td>Is vertical?</td>
<td><code class="literal">?| lseg '((-1,0),(1,0))'</code></td>
</tr>
<tr>
<td> <code class="literal">?|</code> </td>
<td>Are vertically aligned?</td>
<td><code class="literal">point '(0,1)' ?| point '(0,0)'</code></td>
</tr>
<tr>
<td> <code class="literal">?-|</code> </td>
<td>Is perpendicular?</td>
<td><code class="literal">lseg '((0,0),(0,1))' ?-| lseg '((0,0),(1,0))'</code></td>
</tr>
<tr>
<td> <code class="literal">?||</code> </td>
<td>Are parallel?</td>
<td><code class="literal">lseg '((-1,0),(1,0))' ?|| lseg '((-1,2),(1,2))'</code></td>
</tr>
<tr>
<td> <code class="literal">~</code> </td>
<td>Contains?</td>
<td><code class="literal">circle '((0,0),2)' ~ point '(1,1)'</code></td>
</tr>
<tr>
<td> <code class="literal">@</code> </td>
<td>Contained in or on?</td>
<td><code class="literal">point '(1,1)' @ circle '((0,0),2)'</code></td>
</tr>
<tr>
<td> <code class="literal">~=</code> </td>
<td>Same as?</td>
<td><code class="literal">polygon '((0,0),(1,1))' ~= polygon '((1,1),(0,0))'</code></td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><a name="id614805"></a><a name="id614812"></a><a name="id614818"></a><a name="id614824"></a><a name="id614831"></a><a name="id614837"></a><a name="id614843"></a><a name="id614850"></a><a name="id614856"></a><a name="id614862"></a><a name="id614868"></a><a name="id614875"></a><div class="table">
<a name="functions-geometry-func-table"></a><p class="title"><b>Table9.29.Geometric Functions</b></p>
<div class="table-contents"><table summary="Geometric Functions" border="1">
<colgroup>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>Function</th>
<th>Return Type</th>
<th>Description</th>
<th>Example</th>
</tr></thead>
<tbody>
<tr>
<td><code class="literal"><code class="function">area</code>(<em class="replaceable"><code>object</code></em>)</code></td>
<td><code class="type">double precision</code></td>
<td>area</td>
<td><code class="literal">area(box '((0,0),(1,1))')</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">center</code>(<em class="replaceable"><code>object</code></em>)</code></td>
<td><code class="type">point</code></td>
<td>center</td>
<td><code class="literal">center(box '((0,0),(1,2))')</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">diameter</code>(<code class="type">circle</code>)</code></td>
<td><code class="type">double precision</code></td>
<td>diameter of circle</td>
<td><code class="literal">diameter(circle '((0,0),2.0)')</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">height</code>(<code class="type">box</code>)</code></td>
<td><code class="type">double precision</code></td>
<td>vertical size of box</td>
<td><code class="literal">height(box '((0,0),(1,1))')</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">isclosed</code>(<code class="type">path</code>)</code></td>
<td><code class="type">boolean</code></td>
<td>a closed path?</td>
<td><code class="literal">isclosed(path '((0,0),(1,1),(2,0))')</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">isopen</code>(<code class="type">path</code>)</code></td>
<td><code class="type">boolean</code></td>
<td>an open path?</td>
<td><code class="literal">isopen(path '[(0,0),(1,1),(2,0)]')</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">length</code>(<em class="replaceable"><code>object</code></em>)</code></td>
<td><code class="type">double precision</code></td>
<td>length</td>
<td><code class="literal">length(path '((-1,0),(1,0))')</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">npoints</code>(<code class="type">path</code>)</code></td>
<td><code class="type">int</code></td>
<td>number of points</td>
<td><code class="literal">npoints(path '[(0,0),(1,1),(2,0)]')</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">npoints</code>(<code class="type">polygon</code>)</code></td>
<td><code class="type">int</code></td>
<td>number of points</td>
<td><code class="literal">npoints(polygon '((1,1),(0,0))')</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">pclose</code>(<code class="type">path</code>)</code></td>
<td><code class="type">path</code></td>
<td>convert path to closed</td>
<td><code class="literal">pclose(path '[(0,0),(1,1),(2,0)]')</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">popen</code>(<code class="type">path</code>)</code></td>
<td><code class="type">path</code></td>
<td>convert path to open</td>
<td><code class="literal">popen(path '((0,0),(1,1),(2,0))')</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">radius</code>(<code class="type">circle</code>)</code></td>
<td><code class="type">double precision</code></td>
<td>radius of circle</td>
<td><code class="literal">radius(circle '((0,0),2.0)')</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">width</code>(<code class="type">box</code>)</code></td>
<td><code class="type">double precision</code></td>
<td>horizontal size of box</td>
<td><code class="literal">width(box '((0,0),(1,1))')</code></td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="functions-geometry-conv-table"></a><p class="title"><b>Table9.30.Geometric Type Conversion Functions</b></p>
<div class="table-contents"><table summary="Geometric Type Conversion Functions" border="1">
<colgroup>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>Function</th>
<th>Return Type</th>
<th>Description</th>
<th>Example</th>
</tr></thead>
<tbody>
<tr>
<td><code class="literal"><code class="function">box</code>(<code class="type">circle</code>)</code></td>
<td><code class="type">box</code></td>
<td>circle to box</td>
<td><code class="literal">box(circle '((0,0),2.0)')</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">box</code>(<code class="type">point</code>, <code class="type">point</code>)</code></td>
<td><code class="type">box</code></td>
<td>points to box</td>
<td><code class="literal">box(point '(0,0)', point '(1,1)')</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">box</code>(<code class="type">polygon</code>)</code></td>
<td><code class="type">box</code></td>
<td>polygon to box</td>
<td><code class="literal">box(polygon '((0,0),(1,1),(2,0))')</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">circle</code>(<code class="type">box</code>)</code></td>
<td><code class="type">circle</code></td>
<td>box to circle</td>
<td><code class="literal">circle(box '((0,0),(1,1))')</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">circle</code>(<code class="type">point</code>, <code class="type">double precision</code>)</code></td>
<td><code class="type">circle</code></td>
<td>center and radius to circle</td>
<td><code class="literal">circle(point '(0,0)', 2.0)</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">circle</code>(<code class="type">polygon</code>)</code></td>
<td><code class="type">circle</code></td>
<td>polygon to circle</td>
<td><code class="literal">circle(polygon '((0,0),(1,1),(2,0))')</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">lseg</code>(<code class="type">box</code>)</code></td>
<td><code class="type">lseg</code></td>
<td>box diagonal to line segment</td>
<td><code class="literal">lseg(box '((-1,0),(1,0))')</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">lseg</code>(<code class="type">point</code>, <code class="type">point</code>)</code></td>
<td><code class="type">lseg</code></td>
<td>points to line segment</td>
<td><code class="literal">lseg(point '(-1,0)', point '(1,0)')</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">path</code>(<code class="type">polygon</code>)</code></td>
<td><code class="type">point</code></td>
<td>polygon to path</td>
<td><code class="literal">path(polygon '((0,0),(1,1),(2,0))')</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">point</code>(<code class="type">double
precision</code>, <code class="type">double precision</code>)</code></td>
<td><code class="type">point</code></td>
<td>construct point</td>
<td><code class="literal">point(23.4, -44.5)</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">point</code>(<code class="type">box</code>)</code></td>
<td><code class="type">point</code></td>
<td>center of box</td>
<td><code class="literal">point(box '((-1,0),(1,0))')</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">point</code>(<code class="type">circle</code>)</code></td>
<td><code class="type">point</code></td>
<td>center of circle</td>
<td><code class="literal">point(circle '((0,0),2.0)')</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">point</code>(<code class="type">lseg</code>)</code></td>
<td><code class="type">point</code></td>
<td>center of line segment</td>
<td><code class="literal">point(lseg '((-1,0),(1,0))')</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">point</code>(<code class="type">polygon</code>)</code></td>
<td><code class="type">point</code></td>
<td>center of polygon</td>
<td><code class="literal">point(polygon '((0,0),(1,1),(2,0))')</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">polygon</code>(<code class="type">box</code>)</code></td>
<td><code class="type">polygon</code></td>
<td>box to 4-point polygon</td>
<td><code class="literal">polygon(box '((0,0),(1,1))')</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">polygon</code>(<code class="type">circle</code>)</code></td>
<td><code class="type">polygon</code></td>
<td>circle to 12-point polygon</td>
<td><code class="literal">polygon(circle '((0,0),2.0)')</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">polygon</code>(<em class="replaceable"><code>npts</code></em>, <code class="type">circle</code>)</code></td>
<td><code class="type">polygon</code></td>
<td>circle to <em class="replaceable"><code>npts</code></em>-point polygon</td>
<td><code class="literal">polygon(12, circle '((0,0),2.0)')</code></td>
</tr>
<tr>
<td><code class="literal"><code class="function">polygon</code>(<code class="type">path</code>)</code></td>
<td><code class="type">polygon</code></td>
<td>path to polygon</td>
<td><code class="literal">polygon(path '((0,0),(1,1),(2,0))')</code></td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><p> It is possible to access the two component numbers of a <code class="type">point</code>
as though it were an array with indices 0 and 1. For example, if
<code class="literal">t.p</code> is a <code class="type">point</code> column then
<code class="literal">SELECT p[0] FROM t</code> retrieves the X coordinate and
<code class="literal">UPDATE t SET p[1] = ...</code> changes the Y coordinate.
In the same way, a value of type <code class="type">box</code> or <code class="type">lseg</code> may be treated
as an array of two <code class="type">point</code> values.
</p>
<p> The <code class="function">area</code> function works for the types
<code class="type">box</code>, <code class="type">circle</code>, and <code class="type">path</code>.
The <code class="function">area</code> function only works on the
<code class="type">path</code> data type if the points in the
<code class="type">path</code> are non-intersecting. For example, the
<code class="type">path</code>
<code class="literal">'((0,0),(0,1),(2,1),(2,2),(1,2),(1,0),(0,0))'::PATH</code>
won't work, however, the following visually identical
<code class="type">path</code>
<code class="literal">'((0,0),(0,1),(1,1),(1,2),(2,2),(2,1),(1,1),(1,0),(0,0))'::PATH</code>
will work. If the concept of an intersecting versus
non-intersecting <code class="type">path</code> is confusing, draw both of the
above <code class="type">path</code>s side by side on a piece of graph paper.
</p>
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