9.11. 地理資訊函式及運算子

The geometric typespoint,box,lseg,line,path,polygon, andcirclehave a large set of native support functions and operators, shown inTable 9.33,Table 9.34, andTable 9.35.

Caution

Note that the“same as”operator,~=, represents the usual notion of equality for thepoint,box,polygon, andcircletypes. 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))'

@[email protected]

Length or circumference

@[email protected] 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

BeforePostgreSQL8.2, 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 tonpts-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 apointas though the point were an array with indexes 0 and 1. For example, ift.pis apointcolumn thenSELECT p[0] FROM tretrieves the X coordinate andUPDATE t SET p[1] = ...changes the Y coordinate. In the same way, a value of typeboxorlsegcan be treated as an array of twopointvalues.

Theareafunction works for the typesbox,circle, andpath. Theareafunction only works on thepathdata type if the points in thepathare non-intersecting. For example, thepath'((0,0),(0,1),(2,1),(2,2),(1,2),(1,0),(0,0))'::PATHwill not work; however, the following visually identicalpath'((0,0),(0,1),(1,1),(1,2),(2,2),(2,1),(1,1),(1,0),(0,0))'::PATHwill work. If the concept of an intersecting versus non-intersectingpathis confusing, draw both of the abovepaths side by side on a piece of graph paper.

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