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9.11. Geometric Functions and Operators

9.11. Geometric Functions and Operators
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The geometric types point , box , lseg , line , path , polygon , and circle have a large set of native support functions and operators, shown in Table 9.33 , Table 9.34 , and Table 9.35 .

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 9.33. 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 box '((1,-1),(-1,1))' # box '((1,1),(-2,-2))'
# Number of points in path or polygon # path '((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 9.34. 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 9.35. 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 path s side by side on a piece of graph paper.

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