PostgreSQL 7.4 Documentation
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# 9.9. Geometric Functions and Operators

The geometric types `point`, `box`, `lseg`, `line`, `path`, `polygon`, and `circle` have a large set of native support functions and operators, shown in Table 9-28, Table 9-29, and Table 9-30.

Table 9-28. Geometric Operators

Operator | Description | Example
--- | --- | ---
+ | Translation | box '((0,0),(1,1))' + point '(2.0,0)'
- | Translation | box '((0,0),(1,1))' - point '(2.0,0)'
* | Scaling/rotation | box '((0,0),(1,1))' * point '(2.0,0)'
/ | Scaling/rotation | box '((0,0),(2,2))' / point '(2.0,0)'
# | Point or box of intersection | '((1,-1),(-1,1))' # '((1,1),(-1,-1))'
# | Number of points in path or polygon | # '((1,0),(0,1),(-1,0))'
@-@ | Length or circumference | @-@ path '((0,0),(1,0))'
@@ | Center | @@ circle '((0,0),10)'
## | Closest point to first operand on second operand | point '(0,0)' ## lseg '((2,0),(0,2))'
<-> | Distance between | circle '((0,0),1)' <-> circle '((5,0),1)'
&& | Overlaps? | box '((0,0),(1,1))' && box '((0,0),(2,2))'
&< | Overlaps or is left of? | box '((0,0),(1,1))' &< box '((0,0),(2,2))'
&> | Overlaps or is right of? | box '((0,0),(3,3))' &> box '((0,0),(2,2))'
<< | Is left of? | circle '((0,0),1)' << circle '((5,0),1)'
>> | Is right of? | circle '((5,0),1)' >> circle '((0,0),1)'
<^ | Is below? | circle '((0,0),1)' <^ circle '((0,5),1)'
>^ | Is above? | circle '((0,5),1)' >^ circle '((0,0),1)'
?# | Intersects? | lseg '((-1,0),(1,0))' ?# box '((-2,-2),(2,2))'
?- | Is horizontal? | ?- lseg '((-1,0),(1,0))'
?- | Are horizontally aligned? | point '(1,0)' ?- point '(0,0)'
?| | Is vertical? | ?| lseg '((-1,0),(1,0))'
?| | Are vertically aligned? | point '(0,1)' ?| point '(0,0)'
?-| | Is perpendicular? | lseg '((0,0),(0,1))' ?-| lseg '((0,0),(1,0))'
?|| | Are parallel? | lseg '((-1,0),(1,0))' ?|| lseg '((-1,2),(1,2))'
~ | Contains? | circle '((0,0),2)' ~ point '(1,1)'
@ | Contained in or on? | point '(1,1)' @ circle '((0,0),2)'
~= | Same as? | polygon '((0,0),(1,1))' ~= polygon '((1,1),(0,0))'

Table 9-29. Geometric Functions

Function | Return Type | Description | Example
--- | --- | --- | ---
`area`(object) | `double precision` | area | area(box '((0,0),(1,1))')
`box_intersect`(`box`, `box`) | `box` | intersection box | box_intersect(box '((0,0),(1,1))',box '((0.5,0.5),(2,2))')
`center`(object) | `point` | center | center(box '((0,0),(1,2))')
`diameter`(`circle`) | `double precision` | diameter of circle | diameter(circle '((0,0),2.0)')
`height`(`box`) | `double precision` | vertical size of box | height(box '((0,0),(1,1))')
`isclosed`(`path`) | `boolean` | a closed path? | isclosed(path '((0,0),(1,1),(2,0))')
`isopen`(`path`) | `boolean` | an open path? | isopen(path '[(0,0),(1,1),(2,0)]')
`length`(object) | `double precision` | length | length(path '((-1,0),(1,0))')
`npoints`(`path`) | `integer` | number of points | npoints(path '[(0,0),(1,1),(2,0)]')
`npoints`(`polygon`) | `integer` | number of points | npoints(polygon '((1,1),(0,0))')
`pclose`(`path`) | `path` | convert path to closed | popen(path '[(0,0),(1,1),(2,0)]')
`popen`(`path`) | `path` | convert path to open | popen(path '((0,0),(1,1),(2,0))')
`radius`(`circle`) | `double precision` | radius of circle | radius(circle '((0,0),2.0)')
`width`(`box`) | `double precision` | horizontal size of box | width(box '((0,0),(1,1))')

Table 9-30. Geometric Type Conversion Functions

Function | Return Type | Description | Example
--- | --- | --- | ---
`box`(`circle`) | `box` | circle to box | box(circle '((0,0),2.0)')
`box`(`point`, `point`) | `box` | points to box | box(point '(0,0)', point '(1,1)')
`box`(`polygon`) | `box` | polygon to box | box(polygon '((0,0),(1,1),(2,0))')
`circle`(`box`) | `circle` | box to circle | circle(box '((0,0),(1,1))')
`circle`(`point`, `double precision`) | `circle` | point and radius to circle | circle(point '(0,0)', 2.0)
`lseg`(`box`) | `lseg` | box diagonal to line segment | lseg(box '((-1,0),(1,0))')
`lseg`(`point`, `point`) | `lseg` | points to line segment | lseg(point '(-1,0)', point '(1,0)')
`path`(`polygon`) | `point` | polygon to path | path(polygon '((0,0),(1,1),(2,0))')
`point`(`circle`) | `point` | center of circle | point(circle '((0,0),2.0)')
`point`(`lseg`, `lseg`) | `point` | intersection | point(lseg '((-1,0),(1,0))', lseg '((-2,-2),(2,2))')
`point`(`polygon`) | `point` | center of polygon | point(polygon '((0,0),(1,1),(2,0))')
`polygon`(`box`) | `polygon` | box to 4-point polygon | polygon(box '((0,0),(1,1))')
`polygon`(`circle`) | `polygon` | circle to 12-point polygon | polygon(circle '((0,0),2.0)')
`polygon`(npts, `circle`) | `polygon` | circle to npts-point polygon | polygon(12, circle '((0,0),2.0)')
`polygon`(`path`) | `polygon` | path to polygon | polygon(path '((0,0),(1,1),(2,0))')

It is possible to access the two component numbers of a `point` as though it were an array with indices 0 and 1. For example, if t.p is a `point` column then SELECT p[0] FROM t retrieves the X coordinate and UPDATE t SET p[1] = ... changes the Y coordinate. In the same way, a value of type `box` or `lseg` may be treated as an array of two `point` values.

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