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# 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

Operator Description Usage
+ 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)'
# 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 proximity point '(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 between circle '((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 overlaps lseg '((-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 on point '(1,1)' @ circle '((0,0),2)'
@@ Center of @@ circle '((0,0),10)'
~= Same as polygon '((0,0),(1,1))' ~= polygon '((1,1),(0,0))'

Table 6-21. Geometric Functions

Function Returns Description Example
`area`(object) double precision area of item area(box '((0,0),(1,1))')
`box`(box, box) box intersection box box(box '((0,0),(1,1))',box '((0.5,0.5),(2,2))')
`center`(object) point center of item 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 of item 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 path 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 width(box '((0,0),(1,1))')

Table 6-22. Geometric Type Conversion Functions

Function Returns 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 to circle circle(box '((0,0),(1,1))')
`circle`(point, double precision) circle point to circle circle(point '(0,0)', 2.0)
`lseg`(box) lseg box diagonal to lseg lseg(box '((-1,0),(1,0))')
`lseg`(point, point) lseg points to lseg 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 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 point(polygon '((0,0),(1,1),(2,0))')
`polygon`(box) polygon 4-point polygon polygon(box '((0,0),(1,1))')
`polygon`(circle) polygon 12-point polygon polygon(circle '((0,0),2.0)')
`polygon`(npts, circle) polygon npts 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 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.