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# 9.11. 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 9-29, Table 9-30, and Table 9-31.

 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 9-29. 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 9-30. 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 9-31. 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) path 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 can 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 paths side by side on a piece of graph paper.