[postgis-users] How to tell if 2 geometries are spatially equal

[Martin Davis]

As someone who spent way too much time implementing topological 
processing in the SFS model, I can comment on this.  The "finite 
point-set of intersection" rule for Polygonal geometry actually make a 
lot of sense, since it makes algorithm design easier and execution more 
efficient.  With this rule in place algorithms can assume that an edge 
of a polygonal geometry has interior on one side and exterior on the 
other.  This makes topological labelling easier.  Also, in certain 
computations you can determine an answer without having to compute the 
entire topology of a geometry. (The optimized PreparedGeometry 
predicates in JTS and GEOS depend on this, for instance).



Andy Anderson wrote:
> Ah. Not a big deal in 2 dimensions, but I have a real problem with 
> this in 3D! :-) But I see in OGC 99-049 where they say:
>
> "A Polyhedral Surface is not a MultiPolygon because it violates the 
> rule for MultiPolygons that the boundaries of the element Polygons 
> intersect only at a finite number of points."
>
> Seems like an unnecessary restriction, but I'm sure they have their 
> reasons for excluding this "degenerate" case.
>
> -- Andy
>
> On Jun 3, 2008, at 1:58 PM, Martin Davis wrote:
>
>> Andy Anderson wrote:
>>>
>>> I'll also note that, to be consistent, this must also mean that 
>>> MULTIPOLYGON((0 0, 5 5, 5 0, 0 0), (0 0, 0 5, 5 5, 0 0)) doesn't 
>>> have a boundary line at LINESTRING(0 0, 5 5).
>> Well, that Multipolygon is actually invalid - since MPs can't have 
>> coincident line segments. So the definition *is* consistent!
>>>
>>> I'm not sure which one that is.
>> It's the OGC document 99-049 (the first one you sent)
>>
>> -- 
>> Martin Davis
>> Senior Technical Architect
>> Refractions Research, Inc.
>> (250) 383-3022
>>
>> _______________________________________________
>> postgis-users mailing list
>> postgis-users at postgis.refractions.net
>> http://postgis.refractions.net/mailman/listinfo/postgis-users
>
> _______________________________________________
> postgis-users mailing list
> postgis-users at postgis.refractions.net
> http://postgis.refractions.net/mailman/listinfo/postgis-users
>

-- 
Martin Davis
Senior Technical Architect
Refractions Research, Inc.
(250) 383-3022