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9.11. 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 9.33, Table 9.34, and Table 9.35.

Caution

Note that the same as operator, `~=`, represents the usual notion of equality for the `point`, `box`, `polygon`, and `circle` types. Some of these types also have an `=` operator, but `=` compares for equal areas only. The other scalar comparison operators (`<=` and so on) likewise compare areas for these types.

Table 9.33. Geometric Operators

Operator Description Example
`+` 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)'`
`#` Point or box of intersection `box '((1,-1),(-1,1))' # box '((1,1),(-2,-2))'`
`#` Number of points in path or polygon `# path '((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 operand `point '(0,0)' ## lseg '((2,0),(0,2))'`
`<->` Distance between `circle '((0,0),1)' <-> circle '((5,0),1)'`
`&&` Overlaps? (One point in common makes this true.) `box '((0,0),(1,1))' && box '((0,0),(2,2))'`
`<<` Is strictly left of? `circle '((0,0),1)' << circle '((5,0),1)'`
`>>` Is strictly right of? `circle '((5,0),1)' >> circle '((0,0),1)'`
`&<` Does not extend to the right of? `box '((0,0),(1,1))' &< box '((0,0),(2,2))'`
`&>` Does not extend to the left of? `box '((0,0),(3,3))' &> box '((0,0),(2,2))'`
`<<|` Is strictly below? `box '((0,0),(3,3))' <<| box '((3,4),(5,5))'`
`|>>` Is strictly above? `box '((3,4),(5,5))' |>> box '((0,0),(3,3))'`
`&<|` Does not extend above? `box '((0,0),(1,1))' &<| box '((0,0),(2,2))'`
`|&>` Does not extend below? `box '((0,0),(3,3))' |&> box '((0,0),(2,2))'`
`<^` Is below (allows touching)? `circle '((0,0),1)' <^ circle '((0,5),1)'`
`>^` Is above (allows touching)? `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))'`

Note

Before PostgreSQL 8.2, the containment operators `@>` and `<@` were respectively called `~` and `@`. These names are still available, but are deprecated and will eventually be removed.

Table 9.34. Geometric Functions

Function Return Type Description Example
`area(object)` `double precision` area `area(box '((0,0),(1,1))')`
`center(object)` `point` center `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 `length(path '((-1,0),(1,0))')`
`npoints(path)` `int` number of points `npoints(path '[(0,0),(1,1),(2,0)]')`
`npoints(polygon)` `int` number of points `npoints(polygon '((1,1),(0,0))')`
`pclose(path)` `path` convert path to closed `pclose(path '[(0,0),(1,1),(2,0)]')`
`popen(path)` `path` convert path to open `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 of box `width(box '((0,0),(1,1))')`

Table 9.35. Geometric Type Conversion Functions

Function Return Type Description Example
`box(circle)` `box` circle to box `box(circle '((0,0),2.0)')`
`box(point)` `box` point to empty box `box(point '(0,0)')`
`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))')`
`bound_box(box, box)` `box` boxes to bounding box `bound_box(box '((0,0),(1,1))', box '((3,3),(4,4))')`
`circle(box)` `circle` box to circle `circle(box '((0,0),(1,1))')`
`circle(point, double precision)` `circle` center and radius to circle `circle(point '(0,0)', 2.0)`
`circle(polygon)` `circle` polygon to circle `circle(polygon '((0,0),(1,1),(2,0))')`
`line(point, point)` `line` points to line `line(point '(-1,0)', point '(1,0)')`
`lseg(box)` `lseg` box diagonal to line segment `lseg(box '((-1,0),(1,0))')`
`lseg(point, point)` `lseg` points to line segment `lseg(point '(-1,0)', point '(1,0)')`
`path(polygon)` `path` polygon to path `path(polygon '((0,0),(1,1),(2,0))')`
`point(double precision, double precision)` `point` construct point `point(23.4, -44.5)`
`point(box)` `point` center of box `point(box '((-1,0),(1,0))')`
`point(circle)` `point` center of circle `point(circle '((0,0),2.0)')`
`point(lseg)` `point` center of line segment `point(lseg '((-1,0),(1,0))')`
`point(polygon)` `point` center of polygon `point(polygon '((0,0),(1,1),(2,0))')`
`polygon(box)` `polygon` box to 4-point polygon `polygon(box '((0,0),(1,1))')`
`polygon(circle)` `polygon` circle to 12-point polygon `polygon(circle '((0,0),2.0)')`
`polygon(npts, circle)` `polygon` circle to `npts`-point 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 the point were an array with indexes 0 and 1. For example, if `t.p` is a `point` column then `SELECT p FROM t` retrieves the X coordinate and `UPDATE t SET p = ...` changes the Y coordinate. In the same way, a value of type `box` or `lseg` can be treated as an array of two `point` values.

The `area` function works for the types `box`, `circle`, and `path`. The `area` function only works on the `path` data type if the points in the `path` are non-intersecting. For example, the `path` `'((0,0),(0,1),(2,1),(2,2),(1,2),(1,0),(0,0))'::PATH` will not work; however, the following visually identical `path` `'((0,0),(0,1),(1,1),(1,2),(2,2),(2,1),(1,1),(1,0),(0,0))'::PATH` will work. If the concept of an intersecting versus non-intersecting `path` is confusing, draw both of the above `path`s side by side on a piece of graph paper.

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