9.9. 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 9-28, Table 9-29, and Table 9-30.

Table 9-28. 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?	`box '((0,0),(1,1))' && box '((0,0),(2,2))'`
`&<`	Overlaps or is left of?	`box '((0,0),(1,1))' &< box '((0,0),(2,2))'`
`&>`	Overlaps or is right of?	`box '((0,0),(3,3))' &> box '((0,0),(2,2))'`
`<<`	Is left of?	`circle '((0,0),1)' << circle '((5,0),1)'`
`>>`	Is right of?	`circle '((5,0),1)' >> circle '((0,0),1)'`
`<^`	Is below?	`circle '((0,0),1)' <^ circle '((0,5),1)'`
`>^`	Is above?	`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))'`

Table 9-29. Geometric Functions

Function	Return Type	Description	Example
`area(object)`	`double precision`	area	`area(box '((0,0),(1,1))')`
`box_intersect(box, box)`	`box`	intersection box	`box_intersect(box '((0,0),(1,1))',box '((0.5,0.5),(2,2))')`
`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)`	`integer`	number of points	`npoints(path '[(0,0),(1,1),(2,0)]')`
`npoints(polygon)`	`integer`	number of points	`npoints(polygon '((1,1),(0,0))')`
`pclose(path)`	`path`	convert path to closed	`popen(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 9-30. Geometric Type Conversion Functions

Function	Return Type	Description	Example
`box(circle)`	`box`	circle to box	`box(circle '((0,0),2.0)')`
`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))')`
`circle(box)`	`circle`	box to circle	`circle(box '((0,0),(1,1))')`
`circle(point, double precision)`	`circle`	point and radius to circle	`circle(point '(0,0)', 2.0)`
`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)`	`point`	polygon to path	`path(polygon '((0,0),(1,1),(2,0))')`
`point(circle)`	`point`	center of circle	`point(circle '((0,0),2.0)')`
`point(lseg, lseg)`	`point`	intersection	`point(lseg '((-1,0),(1,0))', lseg '((-2,-2),(2,2))')`
`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 it were an array with indices 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 may be treated as an array of two point values.