# 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

OperatorDescriptionExample
+ Translationbox '((0,0),(1,1))' + point '(2.0,0)'
- Translationbox '((0,0),(1,1))' - point '(2.0,0)'
* Scaling/rotationbox '((0,0),(1,1))' * point '(2.0,0)'
/ Scaling/rotationbox '((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 operandpoint '(0,0)' ## lseg '((2,0),(0,2))'
<-> Distance betweencircle '((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

FunctionReturn TypeDescriptionExample
`area`(object)double precisionareaarea(box '((0,0),(1,1))')
`box_intersect`(box, box)boxintersection boxbox_intersect(box '((0,0),(1,1))',box '((0.5,0.5),(2,2))')
`center`(object)pointcentercenter(box '((0,0),(1,2))')
`diameter`(circle)double precisiondiameter of circlediameter(circle '((0,0),2.0)')
`height`(box)double precisionvertical size of boxheight(box '((0,0),(1,1))')
`isclosed`(path)booleana closed path?isclosed(path '((0,0),(1,1),(2,0))')
`isopen`(path)booleanan open path?isopen(path '[(0,0),(1,1),(2,0)]')
`length`(object)double precisionlengthlength(path '((-1,0),(1,0))')
`npoints`(path)integernumber of pointsnpoints(path '[(0,0),(1,1),(2,0)]')
`npoints`(polygon)integernumber of pointsnpoints(polygon '((1,1),(0,0))')
`pclose`(path)pathconvert path to closedpopen(path '[(0,0),(1,1),(2,0)]')
`popen`(path)pathconvert path to openpopen(path '((0,0),(1,1),(2,0))')
`radius`(circle)double precisionradius of circleradius(circle '((0,0),2.0)')
`width`(box)double precisionhorizontal size of boxwidth(box '((0,0),(1,1))')

Table 9-30. Geometric Type Conversion Functions

FunctionReturn TypeDescriptionExample
`box`(circle)boxcircle to boxbox(circle '((0,0),2.0)')
`box`(point, point)boxpoints to boxbox(point '(0,0)', point '(1,1)')
`box`(polygon)boxpolygon to boxbox(polygon '((0,0),(1,1),(2,0))')
`circle`(box)circlebox to circlecircle(box '((0,0),(1,1))')
`circle`(point, double precision)circlepoint and radius to circlecircle(point '(0,0)', 2.0)
`lseg`(box)lsegbox diagonal to line segmentlseg(box '((-1,0),(1,0))')
`lseg`(point, point)lsegpoints to line segmentlseg(point '(-1,0)', point '(1,0)')
`path`(polygon)pointpolygon to pathpath(polygon '((0,0),(1,1),(2,0))')
`point`(circle)pointcenter of circlepoint(circle '((0,0),2.0)')
`point`(lseg, lseg)pointintersectionpoint(lseg '((-1,0),(1,0))', lseg '((-2,-2),(2,2))')
`point`(polygon)pointcenter of polygonpoint(polygon '((0,0),(1,1),(2,0))')
`polygon`(box)polygonbox to 4-point polygonpolygon(box '((0,0),(1,1))')
`polygon`(circle)polygoncircle to 12-point polygonpolygon(circle '((0,0),2.0)')
`polygon`(npts, circle)polygoncircle to npts-point polygonpolygon(12, circle '((0,0),2.0)')
`polygon`(path)polygonpath to polygonpolygon(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.