# 9.10. 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 .

 Caution Note that the "same as" operator, ~= , represents the usual notion of equality for the point , box , polygon , and circle types. Some of these types also have an = operator, but = compares for equal areas only. The other scalar comparison operators ( <= and so on) likewise compare areas for these types.

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))'
<< Is strictly left of? circle '((0,0),1)' << circle '((5,0),1)'
>> Is strictly right of? circle '((5,0),1)' >> circle '((0,0),1)'
&< Does not extend to the right of? box '((0,0),(1,1))' &< box '((0,0),(2,2))'
&> Does not extend to the left of? box '((0,0),(3,3))' &> box '((0,0),(2,2))'
<<| Is strictly below? box '((0,0),(3,3))' <<| box '((3,4),(5,5))'
|>> Is strictly above? box '((3,4),(5,5))' |>> box '((0,0),(3,3))'
&<| Does not extend above? box '((0,0),(1,1))' &<| box '((0,0),(2,2))'
|&> Does not extend below? box '((0,0),(3,3))' |&> box '((0,0),(2,2))'
<^ Is below (allows touching)? circle '((0,0),1)' <^ circle '((0,5),1)'
>^ Is above (allows touching)? 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))'

Note: Before PostgreSQL 8.2, the containment operators @> and <@ were respectively called ~ and @ . These names are still available, but are deprecated and will eventually be retired.

Table 9-29. Geometric Functions

Function Return Type Description Example
``` area``` ( object ) double precision area area(box '((0,0),(1,1))')
``` 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 ) int number of points npoints(path '[(0,0),(1,1),(2,0)]')
``` npoints``` ( polygon ) int number of points npoints(polygon '((1,1),(0,0))')
``` pclose``` ( path ) path convert path to closed pclose(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 center and radius to circle circle(point '(0,0)', 2.0)
``` circle``` ( polygon ) circle polygon to circle circle(polygon '((0,0),(1,1),(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``` ( double precision , double precision ) point construct point point(23.4, -44.5)
``` point``` ( box ) point center of box point(box '((-1,0),(1,0))')
``` point``` ( circle ) point center of circle point(circle '((0,0),2.0)')
``` point``` ( lseg ) point center of line segment point(lseg '((-1,0),(1,0))')
``` 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.

The ``` area``` function works for the types box , circle , and path . The ``` area``` function only works on the path data type if the points in the path are non-intersecting. For example, the path '((0,0),(0,1),(2,1),(2,2),(1,2),(1,0),(0,0))'::PATH won't work, however, the following visually identical path '((0,0),(0,1),(1,1),(1,2),(2,2),(2,1),(1,1),(1,0),(0,0))'::PATH will work. If the concept of an intersecting versus non-intersecting path is confusing, draw both of the above path s side by side on a piece of graph paper.