PostGIS: Substracting Geometries with ST_Difference()

The outer polygon

In a recent PostgreSQL/PostGIS project I was faced with the following problem:

• given two geometries A and B
• calculate that part of A that is (spatially) outside of B
• call this geometry C

Say we have two geometries “outer polygon” and “inner polygon”:
SELECT ST_AsText('POLYGON((0 0, 0 3, 3 3, 3 0, 0 0))'::geometry) AS "outer polygon";
SELECT ST_AsText('POLYGON((1 1, 1 2, 2 2, 2 1, 1 1))'::geometry) AS "inner polygon";

The outer and the inner polygon

Using the function ST_Difference() it is easy two get the geometry of outer polygon without the inner polygon (a nice documentatioon about this and other sPatial Functions can be found in the DB2-Documentation):

SELECT ST_Difference(
  'POLYGON((0 0, 0 3, 3 3, 3 0, 0 0))'::geometry,
  'POLYGON((1 1, 1 2, 2 2, 2 1, 1 1))'::geometry
) AS "the difference";

Displayed as Well Known Text (WKT) this is: POLYGON((0 0,0 3,3 3,3 0,0 0),(1 1,2 1,2 2,1 2,1 1))

The resulting geometry as difference of the input geometries

To test if the geometry is what we are expecting it to be lets test if the POINT(1.5 1.5) is contained in the resulting geometry… it should not:

SELECT ST_Contains(
  'POINT(1.5 1.5)'::geometry,
  ST_Difference(
    'POLYGON((0 0, 0 3, 3 3, 3 0, 0 0))'::geometry,
    'POLYGON((1 1, 1 2, 2 2, 2 1, 1 1))'::geometry
  )
) AS "Point is contained in difference (expect f)"; 

Update 2008-11-05, added images and links

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