The semantics of NULL are well defined for us already in SQL standards. However, in the world of Geometry / Geography we have another entity which is not quite NULL nor quite fully defined: the empty geometry. Empty geometries can be created with things like intersection calls that have have no intersection, e.g. ST_Intersect('POINT(0 0)', 'POINT(1 1)') == POINT EMPTY. So, in the presence of empty, how should functions behave?

• ST_Union(geometry, empty) == geometry

SQL Server 2008 geometry
   SELECT Geometry::STGeomFromText('POINT(1 2)',4326).STUnion(Geometry::STGeomFromText('POLYGON EMPTY',4326))
     => POINT (1 2)
   
SQL Server 2008 geography 
  SELECT (Geography::STGeomFromText('POINT(1 2)',4326).STUnion(Geography::STGeomFromText('POLYGON EMPTY',4326))).STAsText() 
    => POINT(1 2)

• ST_Union(empty, empty) == empty

   SQL Server 2008 Geometry
     SELECT (Geometry::STGeomFromText('POLYGON EMPTY',4326).STUnion(Geometry::STGeomFromText('POLYGON EMPTY',4326))).STAsText() 
       => GEOMETRYCOLLECTION EMPTY
   SQL Server 2008 Geography
      SELECT (Geography::STGeomFromText('POLYGON EMPTY',4326).STUnion(Geography::STGeomFromText('POLYGON EMPTY',4326))).STAsText() 
        => GEOMETRYCOLLECTION EMPTY
     
  

• ST_Difference(geometry, empty) == geometry

SQL Server 2008 Geometry: 
   SELECT (Geometry::STGeomFromText('POINT(1 3)',4326).STDifference(Geometry::STGeomFromText('POLYGON EMPTY',4326))).STAsText()
  => POINT (1 3)

• ST_Difference(empty, geometry) == empty

  SQL Server 2008 Geometry: 
   SELECT (Geometry::STGeomFromText('POLYGON EMPTY',4326).STDifference(Geometry::STGeomFromText('POLYGON EMPTY',4326))).STAsText()
    => GEOMETRY COLLECTION EMPTY
  

• ST_Distance(geometry, empty) == NULL
• ST_DWithin(geometry, empty, tolerance) == FALSE
• ST_Contains(geometry, empty) == FALSE

SQL Server 2008 Geometry
SELECT (Geometry::STGeomFromText('POINT(1 3)',4326).STContains(Geometry::STGeomFromText('POLYGON EMPTY',4326))) 
  => 0

• ??? ST_Contains(empty, empty) == FALSE

SQL Server 2008 Geometry
 SELECT (Geometry::STGeomFromText('POLYGON EMPTY',4326).STContains(Geometry::STGeomFromText('POLYGON EMPTY',4326)))
  => 0

• ST_Intersects(geometry, empty) == FALSE

SQL Server 2008 Geometry
  SELECT (Geometry::STGeomFromText('POINT(1 3)',4326).STIntersects(Geometry::STGeomFromText('POLYGON EMPTY',4326))) 
  => 0

• ??? ST_Intersects(empty, empty) == FALSE

  SQL Server 2008 Geometry
    SELECT (Geometry::STGeomFromText('POLYGON EMPTY',4326).STIntersects(Geometry::STGeomFromText('POLYGON EMPTY',4326))) 
      => 0
  

• ??? ST_Disjoint(empty, empty) == FALSE

SQL Server 2008 Geometry
 SELECT (Geometry::STGeomFromText('POLYGON EMPTY',4326).STDisjoint(Geometry::STGeomFromText('POLYGON EMPTY',4326)))
  => 1

• ??? ST_Disjoint(geometry, empty) == FALSE

  SQL Server 2008 Geometry
   SELECT (Geometry::STGeomFromText('POINT(1 3)',4326).STDisjoint(Geometry::STGeomFromText('POLYGON EMPTY',4326)))
    => 1
  

• ST_IsSimple(empty) == TRUE

SQL Server 2008 Geometry
   SELECT Geometry::STGeomFromText('POLYGON EMPTY',4326).STIsSimple() 
     => 1

• ST_IsValid(empty) == TRUE

SQL Server 2008 Geometry
  SELECT Geometry::STGeomFromText('POLYGON EMPTY',4326).STIsValid()
   => 1

Note: It might make sense to try to maintain the geometric truisms when specifying the semantics around empty - ie. things like:

• intersects( A, B ) ⇒ !disjoint( A, B )
• A == B ⇒ intersects( A, B )
• contains( A, B ) && contains( B, A ) ⇒ A == B

If we don't maintain these we will probably need to complicate logical comparisons with special cases for empty - it may be the case that this is necessary, but it would be nice if it just 'came out in the wash'.

This suggests to me that perhaps:

• ST_Intersects( empty, empty ) == TRUE
• ST_Disjoint( empty, empty ) == FALSE
• ST_Distance( empty, empty) == 0

SQL Server 2008 Geometry:
   SELECT (Geometry::STGeomFromText('POLYGON EMPTY',4326).STDistance(Geometry::STGeomFromText('POLYGON EMPTY',4326)))
 => NULL

• ST_DWithin( empty, empty, tolerance) == true

Hmmm.. perhaps this isn't even possible generally, as:

• intersects( A, B ) ⇒ intersection( A, B ) != empty

but I think that we certainly want:

• intersection( empty, empty) == empty

SQL Server 2008 Geometry: 
   SELECT (Geometry::STGeomFromText('POLYGON EMPTY',4326).STIntersection(Geometry::STGeomFromText('POLYGON EMPTY',4326))).STAsText()
=> GEOMETRY COLLECTION EMPTY