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
| 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 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 4-19. 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))') |
pclose(path) |
path | convert path to closed | popen(path '[(0,0),(1,1),(2,0)]') |
npoint(path) |
integer | number of points | npoints(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 4-20. 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 | 12 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))') |