PostgreSQL 7.2.1 Documentation
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# 4.9. 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.

Table 4-18. Geometric Operators

Operator | Description | Usage
--- | --- | ---
+ | 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)'`
# | Intersection | `'((1,-1),(-1,1))' # '((1,1),(-1,-1))'`
# | Number of points in polygon | `# '((1,0),(0,1),(-1,0))'`
## | Point of closest proximity | `point '(0,0)' ## lseg '((2,0),(0,2))'`
&& | Overlaps? | `box '((0,0),(1,1))' && box '((0,0),(2,2))'`
&< | Overlaps to left? | `box '((0,0),(1,1))' &< box '((0,0),(2,2))'`
&> | Overlaps to right? | `box '((0,0),(3,3))' &> box '((0,0),(2,2))'`
<-> | Distance between | `circle '((0,0),1)' <-> circle '((5,0),1)'`
<< | Left of? | `circle '((0,0),1)' << circle '((5,0),1)'`
<^ | Is below? | `circle '((0,0),1)' <^ circle '((0,5),1)'`
>> | Is right of? | `circle '((5,0),1)' >> circle '((0,0),1)'`
>^ | Is above? | `circle '((0,5),1)' >^ circle '((0,0),1)'`
?# | Intersects or overlaps | `lseg '((-1,0),(1,0))' ?# box '((-2,-2),(2,2))'`
?- | Is horizontal? | `point '(1,0)' ?- point '(0,0)'`
?-| | Is perpendicular? | `lseg '((0,0),(0,1))' ?-| lseg '((0,0),(1,0))'`
@-@ | Length or circumference | `@-@ path '((0,0),(1,0))'`
?| | Is vertical? | `point '(0,1)' ?| point '(0,0)'`
?|| | Is parallel? | `lseg '((-1,0),(1,0))' ?|| lseg '((-1,2),(1,2))'`
@ | Contained or on | `point '(1,1)' @ circle '((0,0),2)'`
@@ | Center of | `@@ circle '((0,0),10)'`
~= | Same as | `polygon '((0,0),(1,1))' ~= polygon '((1,1),(0,0))'`

Table 4-19. Geometric Functions

Function | Returns | Description | Example
--- | --- | --- | ---
`area`(object) | `double precision` | area of item | `area(box '((0,0),(1,1))')`
`box`(box, box) | `box` | intersection box | `box(box '((0,0),(1,1))',box '((0.5,0.5),(2,2))')`
`center`(object) | `point` | center of item | `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 of item | `length(path '((-1,0),(1,0))')`
`pclose`(path) | `path` | convert path to closed | `popen(path '[(0,0),(1,1),(2,0)]')`
`npoint`(path) | `integer` | number of points | `npoints(path '[(0,0),(1,1),(2,0)]')`
`popen`(path) | `path` | convert path to open path | `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 | `width(box '((0,0),(1,1))')`

Table 4-20. Geometric Type Conversion Functions

Function | Returns | 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` | to circle | `circle(box '((0,0),(1,1))')`
`circle`(`point`, `double precision`) | `circle` | point to circle | `circle(point '(0,0)', 2.0)`
`lseg`(`box`) | `lseg` | box diagonal to lseg | `lseg(box '((-1,0),(1,0))')`
`lseg`(`point`, `point`) | `lseg` | points to lseg | `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 | `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 | `point(polygon '((0,0),(1,1),(2,0))')`
`polygon`(`box`) | `polygon` | 12 point polygon | `polygon(box '((0,0),(1,1))')`
`polygon`(`circle`) | `polygon` | 12-point polygon | `polygon(circle '((0,0),2.0)')`
`polygon`(`npts`, `circle`) | `polygon` | `npts` polygon | `polygon(12, circle '((0,0),2.0)')`
`polygon`(`path`) | `polygon` | path to polygon | `polygon(path '((0,0),(1,1),(2,0))')`

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