PostGIS
Name
ST_Within — Tests if no points of A lie in the exterior of B, and A and B have at least one interior point in common.
Description
Returns TRUE if geometry A is completely inside geometry B. For this function to make sense, the source geometries must both be of the same coordinate projection, having the same SRID. It is a given that if ST_Within(A,B) is true and ST_Within(B,A) is true, then the two geometries are considered spatially equal.
A subtlety of this definition is that the boundary of a geometry is not within the geometry. This means that lines and points lying in the boundary of a polygon or line are not within the geometry. For further details see Subtleties of OGC Covers, Contains, Within. (The ST_CoveredBy predicate provides a more inclusive relationship).
ST_Within is the inverse 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. |
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)