# 6.9. 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 6-20, Table 6-21, and Table 6-22.

Table 6-20. Geometric Operators

OperatorDescriptionUsage
+ 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)'
# Intersection'((1,-1),(-1,1))' # '((1,1),(-1,-1))'
# Number of points in path or polygon# '((1,0),(0,1),(-1,0))'
## Point of closest proximitypoint '(0,0)' ## lseg '((2,0),(0,2))'
&& Overlaps?box '((0,0),(1,1))' && box '((0,0),(2,2))'
&< Overlaps to left?box '((0,0),(1,1))' &< box '((0,0),(2,2))'
&> Overlaps to right?box '((0,0),(3,3))' &> box '((0,0),(2,2))'
<-> Distance betweencircle '((0,0),1)' <-> circle '((5,0),1)'
<< Left of?circle '((0,0),1)' << circle '((5,0),1)'
<^ Is below?circle '((0,0),1)' <^ circle '((0,5),1)'
>> Is right of?circle '((5,0),1)' >> circle '((0,0),1)'
>^ Is above?circle '((0,5),1)' >^ circle '((0,0),1)'
?# Intersects or overlapslseg '((-1,0),(1,0))' ?# box '((-2,-2),(2,2))'
?- Is horizontal?point '(1,0)' ?- point '(0,0)'
?-| Is perpendicular?lseg '((0,0),(0,1))' ?-| lseg '((0,0),(1,0))'
@-@ Length or circumference@-@ path '((0,0),(1,0))'
?| Is vertical?point '(0,1)' ?| point '(0,0)'
?|| Is parallel?lseg '((-1,0),(1,0))' ?|| lseg '((-1,2),(1,2))'
@ Contained or onpoint '(1,1)' @ circle '((0,0),2)'
@@ Center of@@ circle '((0,0),10)'
~= Same aspolygon '((0,0),(1,1))' ~= polygon '((1,1),(0,0))'

Table 6-21. Geometric Functions

FunctionReturnsDescriptionExample
`area`(object)double precisionarea of itemarea(box '((0,0),(1,1))')
`box`(box, box)boxintersection boxbox(box '((0,0),(1,1))',box '((0.5,0.5),(2,2))')
`center`(object)pointcenter of itemcenter(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 precisionlength of itemlength(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 open pathpopen(path '((0,0),(1,1),(2,0))')
`radius`(circle)double precisionradius of circleradius(circle '((0,0),2.0)')
`width`(box)double precisionhorizontal sizewidth(box '((0,0),(1,1))')

Table 6-22. Geometric Type Conversion Functions

FunctionReturnsDescriptionExample
`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)circleto circlecircle(box '((0,0),(1,1))')
`circle`(point, double precision)circlepoint to circlecircle(point '(0,0)', 2.0)
`lseg`(box)lsegbox diagonal to lseglseg(box '((-1,0),(1,0))')
`lseg`(point, point)lsegpoints to lseglseg(point '(-1,0)', point '(1,0)')
`path`(polygon)pointpolygon to pathpath(polygon '((0,0),(1,1),(2,0))')
`point`(circle)pointcenterpoint(circle '((0,0),2.0)')
`point`(lseg, lseg)pointintersectionpoint(lseg '((-1,0),(1,0))', lseg '((-2,-2),(2,2))')
`point`(polygon)pointcenterpoint(polygon '((0,0),(1,1),(2,0))')
`polygon`(box)polygon4-point polygonpolygon(box '((0,0),(1,1))')
`polygon`(circle)polygon12-point polygonpolygon(circle '((0,0),2.0)')
`polygon`(npts, circle)polygonnpts 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 subscripts 0, 1. For example, if t.p is a point column then SELECT p[0] FROM t retrieves the X coordinate; UPDATE t SET p[1] = ... changes the Y coordinate. In the same way, a box or an lseg may be treated as an array of two points.