PostGIS
Description
Returns TRUE if geometry A is within geometry B. A is within B if and only if all points of A lie inside (i.e. in the interior or boundary of) B (or equivalently, no points of A lie in the exterior of B), and the interiors of A and B have at least one point in common.
For this function to make sense, the source geometries must both be of the same coordinate projection, having the same SRID.
In mathematical terms: [.emphasis]#ST_Within(A, B) ⇔ (A ⋂ B = A) ∧ (Int(A) ⋂ Int(B) ≠ ∅) #
The within relation is reflexive: every geometry is within itself. The
relation is antisymmetric: if ST_Within(A,B) = true and
ST_Within(B,A) = true, then the two geometries must be topologically
equal (ST_Equals(A,B) = true).
ST_Within is the converse of ST_Contains. So,
ST_Within(A,B) = ST_Contains(B,A).
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Performed by the GEOS module
Enhanced: 2.3.0 Enhancement to PIP short-circuit for geometry extended to support MultiPoints with few points. Prior versions only supported point in polygon.
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| this is the "allowable" version that returns a boolean, not an integer. |
[.inlinemediaobject]
This method implements the
OGC Simple Features
Implementation Specification for SQL 1.1.
s2.1.1.2 // s2.1.13.3 - a.Relate(b, 'T*FF*')
This
method implements the SQL/MM specification.
SQL-MM 3: 5.1.30
Examples
--a circle within a circle
SELECT ST_Within(smallc,smallc) As smallinsmall,
ST_Within(smallc, bigc) As smallinbig,
ST_Within(bigc,smallc) As biginsmall,
ST_Within(ST_Union(smallc, bigc), bigc) as unioninbig,
ST_Within(bigc, ST_Union(smallc, bigc)) as biginunion,
ST_Equals(bigc, ST_Union(smallc, bigc)) as bigisunion
FROM
(
SELECT ST_Buffer(ST_GeomFromText('POINT(50 50)'), 20) As smallc,
ST_Buffer(ST_GeomFromText('POINT(50 50)'), 40) As bigc) As foo;
--Result
smallinsmall | smallinbig | biginsmall | unioninbig | biginunion | bigisunion
--------------+------------+------------+------------+------------+------------
t | t | f | t | t | t
(1 row)