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# 4.9. 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.

Table 4-18. 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 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 4-19. 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))')
pclose(path)pathconvert path to closedpopen(path '[(0,0),(1,1),(2,0)]')
npoint(path)integernumber of pointsnpoints(path '[(0,0),(1,1),(2,0)]')
popen(path)pathconvert path to open pathpopen(path '((0,0),(1,1),(2,0))')
width(box)double precisionhorizontal sizewidth(box '((0,0),(1,1))')

Table 4-20. 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)polygon12 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))')