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))'
@-@	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

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.