[postgis-devel] Should EMPTY be spatially equal to self ?

[Sandro Santilli]

On Sat, Jan 14, 2012 at 12:44:34AM +0100, Havard Tveite wrote:

> How would you explain the result of ST_Equals(empty,empty)
> according to point set topology?  the 9-intersection
> model* says that "equals" has the following matrix (T:
> non-empty, F: empty, i: interior, b: boundary, e:
> exterior):
> 
>    i  b  e
> i  T  F  F
> b  F  T  F
> e  F  F  T

As I just said to regina, the above isn't always true.
A point has no boundary, so BB can't be T.

> I suppose that empty geometries have an empty interior and
> an empty boundary.  Then their exterior would be the
> universal set.  In that case (and if the empty set is a
> member of all sets, also for point set topology), I would
> think that the matrix should be all T's, and that is not
> the matrix of ST_Equals.

There's no such thing as the "equals matrix".

> So I don't think it makes sense to return anything else than
> NULL for ST_Equals on empty geometries.

The sense I see about is is that ST_Equals(A, A) should be true,
for anything which isn't NULL. If EMPTY should be threated the
same as NULL I don't see why we have EMPTY at all.

> In a practical situation, I would not like a spatial join
> with ST_Equals as the join predicate to get matches when one
> or both of the geometries are empty, since their spatial
> relationship cannot be determined (in my opinion).

I belive the spatial relationship of two empty geometries 
is well defined as :

     i  b  e
  i  F  F  F
  b  F  F  F
  e  F  F  2

--strk;

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