PostgreSQL

9.11. Geometric Functions and Operators
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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 9.34, Table 9.35, and Table 9.36.

Caution

Note that the “[.quote]#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 9.34. Geometric Operators

Operator Description Example

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))'`

+

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 9.35. Geometric Functions

Function Return Type Description Example

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))')`

+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 9.36. Geometric Type Conversion Functions

Function Return Type Description Example

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))')`

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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