The geometric types point
, box
,
lseg
, line
, path
,
polygon
, and circle
have a large set of
native support functions and operators, shown in Table 9.35, Table 9.36, and Table 9.37.
Table 9.35. Geometric Operators
Operator Description Example(s) 

Adds the coordinates of the second

Concatenates two open paths (returns NULL if either path is closed).

Subtracts the coordinates of the second

Multiplies each point of the first argument by the second

Divides each point of the first argument by the second

Computes the total length.
Available for

Computes the center point.
Available for

Returns the number of points.
Available for

Computes the point of intersection, or NULL if there is none.
Available for

Computes the intersection of two boxes, or NULL if there is none.

Computes the closest point to the first object on the second object.
Available for these pairs of types:
(

Computes the distance between the objects.
Available for all geometric types except

Does first object contain second?
Available for these pairs of types:
(

Is first object contained in or on second?
Available for these pairs of types:
(

Do these objects overlap? (One point in common makes this true.)
Available for

Is first object strictly left of second?
Available for

Is first object strictly right of second?
Available for

Does first object not extend to the right of second?
Available for

Does first object not extend to the left of second?
Available for

Is first object strictly below second?
Available for

Is first object strictly above second?
Available for

Does first object not extend above second?
Available for

Does first object not extend below second?
Available for

Is first object below second (allows edges to touch)?

Is first object strictly below second?
(This operator is misnamed; it should be

Is first object above second (allows edges to touch)?

Is first object strictly above second?
(This operator is misnamed; it should be

Do these objects intersect?
Available for these pairs of types:
(

Is line horizontal?

Are points horizontally aligned (that is, have same y coordinate)?

Is line vertical?

Are points vertically aligned (that is, have same x coordinate)?

Are lines perpendicular?

Are lines parallel?

Are these objects the same?
Available for

^{[a] }“Rotating” a box with these operators only moves its corner points: the box is still considered to have sides parallel to the axes. Hence the box's size is not preserved, as a true rotation would do. 
Note that the “same as” operator, ~=
,
represents the usual notion of equality for the point
,
box
, polygon
, and circle
types.
Some of the geometric types also have an =
operator, but
=
compares for equal areas only.
The other scalar comparison operators (<=
and so
on), where available for these types, likewise compare areas.
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 9.36. Geometric Functions
Table 9.37. Geometric Type Conversion Functions
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[0] FROM t
retrieves the X coordinate and
UPDATE t SET p[1] = ...
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.