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><DIV
CLASS="SECT1"
><H1
CLASS="SECT1"
><A
NAME="FUNCTIONS-GEOMETRY"
>9.11. Geometric Functions and Operators</A
></H1
><P
>    The geometric types <TT
CLASS="TYPE"
>point</TT
>, <TT
CLASS="TYPE"
>box</TT
>,
    <TT
CLASS="TYPE"
>lseg</TT
>, <TT
CLASS="TYPE"
>line</TT
>, <TT
CLASS="TYPE"
>path</TT
>,
    <TT
CLASS="TYPE"
>polygon</TT
>, and <TT
CLASS="TYPE"
>circle</TT
> have a large set of
    native support functions and operators, shown in <A
HREF="functions-geometry.html#FUNCTIONS-GEOMETRY-OP-TABLE"
>Table 9-31</A
>, <A
HREF="functions-geometry.html#FUNCTIONS-GEOMETRY-FUNC-TABLE"
>Table 9-32</A
>, and <A
HREF="functions-geometry.html#FUNCTIONS-GEOMETRY-CONV-TABLE"
>Table 9-33</A
>.
   </P
><DIV
CLASS="CAUTION"
><P
></P
><TABLE
CLASS="CAUTION"
BORDER="1"
WIDTH="100%"
><TR
><TD
ALIGN="CENTER"
><B
>Caution</B
></TD
></TR
><TR
><TD
ALIGN="LEFT"
><P
>     Note that the <SPAN
CLASS="QUOTE"
>"same as"</SPAN
> operator, <TT
CLASS="LITERAL"
>~=</TT
>, represents
     the usual notion of equality for the <TT
CLASS="TYPE"
>point</TT
>,
     <TT
CLASS="TYPE"
>box</TT
>, <TT
CLASS="TYPE"
>polygon</TT
>, and <TT
CLASS="TYPE"
>circle</TT
> types.
     Some of these types also have an <TT
CLASS="LITERAL"
>=</TT
> operator, but
     <TT
CLASS="LITERAL"
>=</TT
> compares
     for equal <SPAN
CLASS="emphasis"
><I
CLASS="EMPHASIS"
>areas</I
></SPAN
> only.  The other scalar comparison operators
     (<TT
CLASS="LITERAL"
>&lt;=</TT
> and so on) likewise compare areas for these types.
    </P
></TD
></TR
></TABLE
></DIV
><DIV
CLASS="TABLE"
><A
NAME="FUNCTIONS-GEOMETRY-OP-TABLE"
></A
><P
><B
>Table 9-31. Geometric Operators</B
></P
><TABLE
BORDER="1"
CLASS="CALSTABLE"
><COL><COL><COL><THEAD
><TR
><TH
>Operator</TH
><TH
>Description</TH
><TH
>Example</TH
></TR
></THEAD
><TBODY
><TR
><TD
> <TT
CLASS="LITERAL"
>+</TT
> </TD
><TD
>Translation</TD
><TD
><TT
CLASS="LITERAL"
>box '((0,0),(1,1))' + point '(2.0,0)'</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>-</TT
> </TD
><TD
>Translation</TD
><TD
><TT
CLASS="LITERAL"
>box '((0,0),(1,1))' - point '(2.0,0)'</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>*</TT
> </TD
><TD
>Scaling/rotation</TD
><TD
><TT
CLASS="LITERAL"
>box '((0,0),(1,1))' * point '(2.0,0)'</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>/</TT
> </TD
><TD
>Scaling/rotation</TD
><TD
><TT
CLASS="LITERAL"
>box '((0,0),(2,2))' / point '(2.0,0)'</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>#</TT
> </TD
><TD
>Point or box of intersection</TD
><TD
><TT
CLASS="LITERAL"
>box '((1,-1),(-1,1))' # box '((1,1),(-2,-2))'</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>#</TT
> </TD
><TD
>Number of points in path or polygon</TD
><TD
><TT
CLASS="LITERAL"
># path '((1,0),(0,1),(-1,0))'</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>@-@</TT
> </TD
><TD
>Length or circumference</TD
><TD
><TT
CLASS="LITERAL"
>@-@ path '((0,0),(1,0))'</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>@@</TT
> </TD
><TD
>Center</TD
><TD
><TT
CLASS="LITERAL"
>@@ circle '((0,0),10)'</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>##</TT
> </TD
><TD
>Closest point to first operand on second operand</TD
><TD
><TT
CLASS="LITERAL"
>point '(0,0)' ## lseg '((2,0),(0,2))'</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>&lt;-&gt;</TT
> </TD
><TD
>Distance between</TD
><TD
><TT
CLASS="LITERAL"
>circle '((0,0),1)' &lt;-&gt; circle '((5,0),1)'</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>&amp;&amp;</TT
> </TD
><TD
>Overlaps?  (One point in common makes this true.)</TD
><TD
><TT
CLASS="LITERAL"
>box '((0,0),(1,1))' &amp;&amp; box '((0,0),(2,2))'</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>&lt;&lt;</TT
> </TD
><TD
>Is strictly left of?</TD
><TD
><TT
CLASS="LITERAL"
>circle '((0,0),1)' &lt;&lt; circle '((5,0),1)'</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>&gt;&gt;</TT
> </TD
><TD
>Is strictly right of?</TD
><TD
><TT
CLASS="LITERAL"
>circle '((5,0),1)' &gt;&gt; circle '((0,0),1)'</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>&amp;&lt;</TT
> </TD
><TD
>Does not extend to the right of?</TD
><TD
><TT
CLASS="LITERAL"
>box '((0,0),(1,1))' &amp;&lt; box '((0,0),(2,2))'</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>&amp;&gt;</TT
> </TD
><TD
>Does not extend to the left of?</TD
><TD
><TT
CLASS="LITERAL"
>box '((0,0),(3,3))' &amp;&gt; box '((0,0),(2,2))'</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>&lt;&lt;|</TT
> </TD
><TD
>Is strictly below?</TD
><TD
><TT
CLASS="LITERAL"
>box '((0,0),(3,3))' &lt;&lt;| box '((3,4),(5,5))'</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>|&gt;&gt;</TT
> </TD
><TD
>Is strictly above?</TD
><TD
><TT
CLASS="LITERAL"
>box '((3,4),(5,5))' |&gt;&gt; box '((0,0),(3,3))'</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>&amp;&lt;|</TT
> </TD
><TD
>Does not extend above?</TD
><TD
><TT
CLASS="LITERAL"
>box '((0,0),(1,1))' &amp;&lt;| box '((0,0),(2,2))'</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>|&amp;&gt;</TT
> </TD
><TD
>Does not extend below?</TD
><TD
><TT
CLASS="LITERAL"
>box '((0,0),(3,3))' |&amp;&gt; box '((0,0),(2,2))'</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>&lt;^</TT
> </TD
><TD
>Is below (allows touching)?</TD
><TD
><TT
CLASS="LITERAL"
>circle '((0,0),1)' &lt;^ circle '((0,5),1)'</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>&gt;^</TT
> </TD
><TD
>Is above (allows touching)?</TD
><TD
><TT
CLASS="LITERAL"
>circle '((0,5),1)' &gt;^ circle '((0,0),1)'</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>?#</TT
> </TD
><TD
>Intersects?</TD
><TD
><TT
CLASS="LITERAL"
>lseg '((-1,0),(1,0))' ?# box '((-2,-2),(2,2))'</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>?-</TT
> </TD
><TD
>Is horizontal?</TD
><TD
><TT
CLASS="LITERAL"
>?- lseg '((-1,0),(1,0))'</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>?-</TT
> </TD
><TD
>Are horizontally aligned?</TD
><TD
><TT
CLASS="LITERAL"
>point '(1,0)' ?- point '(0,0)'</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>?|</TT
> </TD
><TD
>Is vertical?</TD
><TD
><TT
CLASS="LITERAL"
>?| lseg '((-1,0),(1,0))'</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>?|</TT
> </TD
><TD
>Are vertically aligned?</TD
><TD
><TT
CLASS="LITERAL"
>point '(0,1)' ?| point '(0,0)'</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>?-|</TT
> </TD
><TD
>Is perpendicular?</TD
><TD
><TT
CLASS="LITERAL"
>lseg '((0,0),(0,1))' ?-| lseg '((0,0),(1,0))'</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>?||</TT
> </TD
><TD
>Are parallel?</TD
><TD
><TT
CLASS="LITERAL"
>lseg '((-1,0),(1,0))' ?|| lseg '((-1,2),(1,2))'</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>@&gt;</TT
> </TD
><TD
>Contains?</TD
><TD
><TT
CLASS="LITERAL"
>circle '((0,0),2)' @&gt; point '(1,1)'</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>&lt;@</TT
> </TD
><TD
>Contained in or on?</TD
><TD
><TT
CLASS="LITERAL"
>point '(1,1)' &lt;@ circle '((0,0),2)'</TT
></TD
></TR
><TR
><TD
> <TT
CLASS="LITERAL"
>~=</TT
> </TD
><TD
>Same as?</TD
><TD
><TT
CLASS="LITERAL"
>polygon '((0,0),(1,1))' ~= polygon '((1,1),(0,0))'</TT
></TD
></TR
></TBODY
></TABLE
></DIV
><DIV
CLASS="NOTE"
><BLOCKQUOTE
CLASS="NOTE"
><P
><B
>Note: </B
>     Before <SPAN
CLASS="PRODUCTNAME"
>PostgreSQL</SPAN
> 8.2, the containment
     operators <TT
CLASS="LITERAL"
>@&gt;</TT
> and <TT
CLASS="LITERAL"
>&lt;@</TT
> were respectively
     called <TT
CLASS="LITERAL"
>~</TT
> and <TT
CLASS="LITERAL"
>@</TT
>.  These names are still
     available, but are deprecated and will eventually be removed.
    </P
></BLOCKQUOTE
></DIV
><DIV
CLASS="TABLE"
><A
NAME="FUNCTIONS-GEOMETRY-FUNC-TABLE"
></A
><P
><B
>Table 9-32. Geometric Functions</B
></P
><TABLE
BORDER="1"
CLASS="CALSTABLE"
><COL><COL><COL><COL><THEAD
><TR
><TH
>Function</TH
><TH
>Return Type</TH
><TH
>Description</TH
><TH
>Example</TH
></TR
></THEAD
><TBODY
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>area(<TT
CLASS="REPLACEABLE"
><I
>object</I
></TT
>)</CODE
></TT
></TD
><TD
><TT
CLASS="TYPE"
>double precision</TT
></TD
><TD
>area</TD
><TD
><TT
CLASS="LITERAL"
>area(box '((0,0),(1,1))')</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>center(<TT
CLASS="REPLACEABLE"
><I
>object</I
></TT
>)</CODE
></TT
></TD
><TD
><TT
CLASS="TYPE"
>point</TT
></TD
><TD
>center</TD
><TD
><TT
CLASS="LITERAL"
>center(box '((0,0),(1,2))')</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>diameter(<TT
CLASS="TYPE"
>circle</TT
>)</CODE
></TT
></TD
><TD
><TT
CLASS="TYPE"
>double precision</TT
></TD
><TD
>diameter of circle</TD
><TD
><TT
CLASS="LITERAL"
>diameter(circle '((0,0),2.0)')</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>height(<TT
CLASS="TYPE"
>box</TT
>)</CODE
></TT
></TD
><TD
><TT
CLASS="TYPE"
>double precision</TT
></TD
><TD
>vertical size of box</TD
><TD
><TT
CLASS="LITERAL"
>height(box '((0,0),(1,1))')</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>isclosed(<TT
CLASS="TYPE"
>path</TT
>)</CODE
></TT
></TD
><TD
><TT
CLASS="TYPE"
>boolean</TT
></TD
><TD
>a closed path?</TD
><TD
><TT
CLASS="LITERAL"
>isclosed(path '((0,0),(1,1),(2,0))')</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>isopen(<TT
CLASS="TYPE"
>path</TT
>)</CODE
></TT
></TD
><TD
><TT
CLASS="TYPE"
>boolean</TT
></TD
><TD
>an open path?</TD
><TD
><TT
CLASS="LITERAL"
>isopen(path '[(0,0),(1,1),(2,0)]')</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>length(<TT
CLASS="REPLACEABLE"
><I
>object</I
></TT
>)</CODE
></TT
></TD
><TD
><TT
CLASS="TYPE"
>double precision</TT
></TD
><TD
>length</TD
><TD
><TT
CLASS="LITERAL"
>length(path '((-1,0),(1,0))')</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>npoints(<TT
CLASS="TYPE"
>path</TT
>)</CODE
></TT
></TD
><TD
><TT
CLASS="TYPE"
>int</TT
></TD
><TD
>number of points</TD
><TD
><TT
CLASS="LITERAL"
>npoints(path '[(0,0),(1,1),(2,0)]')</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>npoints(<TT
CLASS="TYPE"
>polygon</TT
>)</CODE
></TT
></TD
><TD
><TT
CLASS="TYPE"
>int</TT
></TD
><TD
>number of points</TD
><TD
><TT
CLASS="LITERAL"
>npoints(polygon '((1,1),(0,0))')</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>pclose(<TT
CLASS="TYPE"
>path</TT
>)</CODE
></TT
></TD
><TD
><TT
CLASS="TYPE"
>path</TT
></TD
><TD
>convert path to closed</TD
><TD
><TT
CLASS="LITERAL"
>pclose(path '[(0,0),(1,1),(2,0)]')</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>popen(<TT
CLASS="TYPE"
>path</TT
>)</CODE
></TT
></TD
><TD
><TT
CLASS="TYPE"
>path</TT
></TD
><TD
>convert path to open</TD
><TD
><TT
CLASS="LITERAL"
>popen(path '((0,0),(1,1),(2,0))')</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>radius(<TT
CLASS="TYPE"
>circle</TT
>)</CODE
></TT
></TD
><TD
><TT
CLASS="TYPE"
>double precision</TT
></TD
><TD
>radius of circle</TD
><TD
><TT
CLASS="LITERAL"
>radius(circle '((0,0),2.0)')</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>width(<TT
CLASS="TYPE"
>box</TT
>)</CODE
></TT
></TD
><TD
><TT
CLASS="TYPE"
>double precision</TT
></TD
><TD
>horizontal size of box</TD
><TD
><TT
CLASS="LITERAL"
>width(box '((0,0),(1,1))')</TT
></TD
></TR
></TBODY
></TABLE
></DIV
><DIV
CLASS="TABLE"
><A
NAME="FUNCTIONS-GEOMETRY-CONV-TABLE"
></A
><P
><B
>Table 9-33. Geometric Type Conversion Functions</B
></P
><TABLE
BORDER="1"
CLASS="CALSTABLE"
><COL><COL><COL><COL><THEAD
><TR
><TH
>Function</TH
><TH
>Return Type</TH
><TH
>Description</TH
><TH
>Example</TH
></TR
></THEAD
><TBODY
><TR
><TD
>         
         <TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>box(<TT
CLASS="TYPE"
>circle</TT
>)</CODE
></TT
>
        </TD
><TD
><TT
CLASS="TYPE"
>box</TT
></TD
><TD
>circle to box</TD
><TD
><TT
CLASS="LITERAL"
>box(circle '((0,0),2.0)')</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>box(<TT
CLASS="TYPE"
>point</TT
>, <TT
CLASS="TYPE"
>point</TT
>)</CODE
></TT
></TD
><TD
><TT
CLASS="TYPE"
>box</TT
></TD
><TD
>points to box</TD
><TD
><TT
CLASS="LITERAL"
>box(point '(0,0)', point '(1,1)')</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>box(<TT
CLASS="TYPE"
>polygon</TT
>)</CODE
></TT
></TD
><TD
><TT
CLASS="TYPE"
>box</TT
></TD
><TD
>polygon to box</TD
><TD
><TT
CLASS="LITERAL"
>box(polygon '((0,0),(1,1),(2,0))')</TT
></TD
></TR
><TR
><TD
>         
         <TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>circle(<TT
CLASS="TYPE"
>box</TT
>)</CODE
></TT
>
        </TD
><TD
><TT
CLASS="TYPE"
>circle</TT
></TD
><TD
>box to circle</TD
><TD
><TT
CLASS="LITERAL"
>circle(box '((0,0),(1,1))')</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>circle(<TT
CLASS="TYPE"
>point</TT
>, <TT
CLASS="TYPE"
>double precision</TT
>)</CODE
></TT
></TD
><TD
><TT
CLASS="TYPE"
>circle</TT
></TD
><TD
>center and radius to circle</TD
><TD
><TT
CLASS="LITERAL"
>circle(point '(0,0)', 2.0)</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>circle(<TT
CLASS="TYPE"
>polygon</TT
>)</CODE
></TT
></TD
><TD
><TT
CLASS="TYPE"
>circle</TT
></TD
><TD
>polygon to circle</TD
><TD
><TT
CLASS="LITERAL"
>circle(polygon '((0,0),(1,1),(2,0))')</TT
></TD
></TR
><TR
><TD
>         
         <TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>lseg(<TT
CLASS="TYPE"
>box</TT
>)</CODE
></TT
>
        </TD
><TD
><TT
CLASS="TYPE"
>lseg</TT
></TD
><TD
>box diagonal to line segment</TD
><TD
><TT
CLASS="LITERAL"
>lseg(box '((-1,0),(1,0))')</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>lseg(<TT
CLASS="TYPE"
>point</TT
>, <TT
CLASS="TYPE"
>point</TT
>)</CODE
></TT
></TD
><TD
><TT
CLASS="TYPE"
>lseg</TT
></TD
><TD
>points to line segment</TD
><TD
><TT
CLASS="LITERAL"
>lseg(point '(-1,0)', point '(1,0)')</TT
></TD
></TR
><TR
><TD
>         
         <TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>path(<TT
CLASS="TYPE"
>polygon</TT
>)</CODE
></TT
>
        </TD
><TD
><TT
CLASS="TYPE"
>path</TT
></TD
><TD
>polygon to path</TD
><TD
><TT
CLASS="LITERAL"
>path(polygon '((0,0),(1,1),(2,0))')</TT
></TD
></TR
><TR
><TD
>         
         <TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>point</CODE
>(<TT
CLASS="TYPE"
>double
         precision</TT
>, <TT
CLASS="TYPE"
>double precision</TT
>)</TT
>
        </TD
><TD
><TT
CLASS="TYPE"
>point</TT
></TD
><TD
>construct point</TD
><TD
><TT
CLASS="LITERAL"
>point(23.4, -44.5)</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>point(<TT
CLASS="TYPE"
>box</TT
>)</CODE
></TT
></TD
><TD
><TT
CLASS="TYPE"
>point</TT
></TD
><TD
>center of box</TD
><TD
><TT
CLASS="LITERAL"
>point(box '((-1,0),(1,0))')</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>point(<TT
CLASS="TYPE"
>circle</TT
>)</CODE
></TT
></TD
><TD
><TT
CLASS="TYPE"
>point</TT
></TD
><TD
>center of circle</TD
><TD
><TT
CLASS="LITERAL"
>point(circle '((0,0),2.0)')</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>point(<TT
CLASS="TYPE"
>lseg</TT
>)</CODE
></TT
></TD
><TD
><TT
CLASS="TYPE"
>point</TT
></TD
><TD
>center of line segment</TD
><TD
><TT
CLASS="LITERAL"
>point(lseg '((-1,0),(1,0))')</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>point(<TT
CLASS="TYPE"
>polygon</TT
>)</CODE
></TT
></TD
><TD
><TT
CLASS="TYPE"
>point</TT
></TD
><TD
>center of polygon</TD
><TD
><TT
CLASS="LITERAL"
>point(polygon '((0,0),(1,1),(2,0))')</TT
></TD
></TR
><TR
><TD
>         
         <TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>polygon(<TT
CLASS="TYPE"
>box</TT
>)</CODE
></TT
>
        </TD
><TD
><TT
CLASS="TYPE"
>polygon</TT
></TD
><TD
>box to 4-point polygon</TD
><TD
><TT
CLASS="LITERAL"
>polygon(box '((0,0),(1,1))')</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>polygon(<TT
CLASS="TYPE"
>circle</TT
>)</CODE
></TT
></TD
><TD
><TT
CLASS="TYPE"
>polygon</TT
></TD
><TD
>circle to 12-point polygon</TD
><TD
><TT
CLASS="LITERAL"
>polygon(circle '((0,0),2.0)')</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>polygon(<TT
CLASS="REPLACEABLE"
><I
>npts</I
></TT
>, <TT
CLASS="TYPE"
>circle</TT
>)</CODE
></TT
></TD
><TD
><TT
CLASS="TYPE"
>polygon</TT
></TD
><TD
>circle to <TT
CLASS="REPLACEABLE"
><I
>npts</I
></TT
>-point polygon</TD
><TD
><TT
CLASS="LITERAL"
>polygon(12, circle '((0,0),2.0)')</TT
></TD
></TR
><TR
><TD
><TT
CLASS="LITERAL"
><CODE
CLASS="FUNCTION"
>polygon(<TT
CLASS="TYPE"
>path</TT
>)</CODE
></TT
></TD
><TD
><TT
CLASS="TYPE"
>polygon</TT
></TD
><TD
>path to polygon</TD
><TD
><TT
CLASS="LITERAL"
>polygon(path '((0,0),(1,1),(2,0))')</TT
></TD
></TR
></TBODY
></TABLE
></DIV
><P
>     It is possible to access the two component numbers of a <TT
CLASS="TYPE"
>point</TT
>
     as though the point were an array with indexes 0 and 1.  For example, if
     <TT
CLASS="LITERAL"
>t.p</TT
> is a <TT
CLASS="TYPE"
>point</TT
> column then
     <TT
CLASS="LITERAL"
>SELECT p[0] FROM t</TT
> retrieves the X coordinate and
     <TT
CLASS="LITERAL"
>UPDATE t SET p[1] = ...</TT
> changes the Y coordinate.
     In the same way, a value of type <TT
CLASS="TYPE"
>box</TT
> or <TT
CLASS="TYPE"
>lseg</TT
> can be treated
     as an array of two <TT
CLASS="TYPE"
>point</TT
> values.
    </P
><P
>     The <CODE
CLASS="FUNCTION"
>area</CODE
> function works for the types
     <TT
CLASS="TYPE"
>box</TT
>, <TT
CLASS="TYPE"
>circle</TT
>, and <TT
CLASS="TYPE"
>path</TT
>.
     The <CODE
CLASS="FUNCTION"
>area</CODE
> function only works on the
     <TT
CLASS="TYPE"
>path</TT
> data type if the points in the
     <TT
CLASS="TYPE"
>path</TT
> are non-intersecting.  For example, the
     <TT
CLASS="TYPE"
>path</TT
>
     <TT
CLASS="LITERAL"
>'((0,0),(0,1),(2,1),(2,2),(1,2),(1,0),(0,0))'::PATH</TT
>
     will not work;  however, the following visually identical
     <TT
CLASS="TYPE"
>path</TT
>
     <TT
CLASS="LITERAL"
>'((0,0),(0,1),(1,1),(1,2),(2,2),(2,1),(1,1),(1,0),(0,0))'::PATH</TT
>
     will work.  If the concept of an intersecting versus
     non-intersecting <TT
CLASS="TYPE"
>path</TT
> is confusing, draw both of the
     above <TT
CLASS="TYPE"
>path</TT
>s side by side on a piece of graph paper.
    </P
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