On Jun 2, 2008, at 4:29 PM, Martin Davis wrote:
I use "topologically equal" because the OGC SFS specification uses
the term "topology" extensively in their discussion of the meaning
of the DE-9IM model, on which the semantics of ST_equals is based.
No doubt they do, because the spatial relationships that can be
determined by the DE-9IM are, generally speaking, topological in nature:
Disjoint, Touches, Crosses, Within and Overlaps
These are the ones defined here:
http://portal.opengeospatial.org/files/?artifact_id=829
Oddly, in this document they also mention "Equals" but they never
explicitly define it (though they claim to later in the document).
However, I did find a very complete description of DE-9IM here:
http://mlblog.osdir.com/gis.postgis/2004-02/pdfHaVE9FZPMj.pdf
and they say that for "equals", the "Geometries must be identical:
– Same dimension
– Same geometry type
– Same number of vertices
– All x,y coordinates must be identical"
So this definition would seem to agree with me that LINESTRING(0 0, 10
10) and LINESTRING(0 0, 5 5, 10 10) are not topologically equal. The
best way to think of this is that the second is a *polyline*, and the
vertex (5, 5) is a boundary between two lines, and that changes the
DE-9IM.
As you point out, however, ST_equals('LINESTRING(0 0, 10
10)','LINESTRING(0 0, 5 5, 10 10)') returns true; perhaps this was by
design to distinguish it from 'LINESTRING(0 0, 10 10)'::geometry ~=
'LINESTRING(0 0, 5 5, 10 10)'::geometry .
If you can point to further discussion on this issue, I would be
interested.
I don't like the term "spatially-equal", because I think "spatially"
is too vague and overloaded. How about "point-set equal"? The idea
is that A = B iff every point of A is in B and every point of B is
in A.
Personally, I don't have a problem with "spatially equal", it says to
me "they fill space in the same way", which in fact they do because a
point has no extent.
-- Andy
Andy Anderson wrote:
I wouldn't call this example "topologically" equal; one has two
vertices and the other has three, and that's the only
characteristic that's relevant in topology (not even their
positions :-)
"Coincident" is probably a better term, though "spatially equal" is
probably just as good, and contrasts well with the term
"geometrically equal" that the manual uses to describe the ~=
operator.
-- Andy
On May 30, 2008, at 7:54 PM, Martin Davis wrote:
Will ST_equals do what you want? It reports whether two
geometries are topologically equal.
(So for example, ST_equals('LINESTRING(0 0, 10 10)','LINESTRING(0
0, 5 5, 10 10)') is true)
Obe, Regina wrote:
I recall this having come up before. I always thought that ~=
would
tell me if 2 geometries are spatially equal but it doesn't seem to.
The only way I can figure to determine spatial equality is if
ST_Within(A,B) And ST_Within(B,A) (or ST_Difference(A,B) AND
ST_Difference(B,A) both return an empty geometry collection)
--So case in point
SELECT geom1 ~= geom2 as what, ST_Within(geom1, geom2) AND
ST_Within(geom2, geom1) As spatial_equal,
ST_AsText(ST_Difference(geom1, geom2)) as diffgeom12,
ST_AsText(ST_Difference(geom2, geom1)) as diffgeom21 FROM (SELECT
'LINESTRING(1 1, 1 2, 1 3)'::geometry As geom1, 'LINESTRING(1
1, 1 3)'::geometry As geom2) As foo
Results:
what | spatial_equal | diffgeom12 | diffgeom21
------+---------------+--------------------------
+----------------------
----
f | t | GEOMETRYCOLLECTION EMPTY |
GEOMETRYCOLLECTION
EMPTY
Is there a function / operator that does that (also what does
geom1 =
geom2 compare - is it just bounding boxes or is that the
spatially equal
operator I am looking for?)
Thanks,
Regina
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Martin Davis
Senior Technical Architect
Refractions Research, Inc.
(250) 383-3022
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--
Martin Davis
Senior Technical Architect
Refractions Research, Inc.
(250) 383-3022
_______________________________________________
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