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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 9-31, Table 9-32, and Table 9-33.

 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 9-31. 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? (One point in common makes this true.) 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 removed.

Table 9-32. 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 9-33. Geometric Type Conversion Functions

Function Return Type Description Example
`box(circle)` box circle to box box(circle '((0,0),2.0)')
`box(point)` box point to empty box box(point '(0,0)')
`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))')
```bound_box(box, box)``` box boxes to bounding box bound_box(box '((0,0),(1,1))', box '((3,3),(4,4))')
`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))')
`line(point, point)` line points to line line(point '(-1,0)', point '(1,0)')
`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 the point were an array with indexes 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 will not 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.