[Qgis-developer] Interpretation of a 3 point CircularString with p0 == p2 (circle)

[Even Rouault]

Le jeudi 23 juin 2016 16:01:10, Marco Hugentobler a écrit :
> Hi Even
> 
> I agree it will be good to follow the postgres / gdal interpretation.
> Reading S2, I somehow thought the segment midpoint would be the circle
> midpoint, but it's not the same.

Filed as https://hub.qgis.org/issues/15116

> 
> Regards,
> Marco
> 
> On 06/23/16 15:32, Even Rouault wrote:
> > Hi,
> > 
> > I just came into a difference how QGIS and GDAL interpret a
> > CircularString made of a 3 points p0, p1, p2 where p0 == p2, which is a
> > way of representing a full circle.
> > 
> > GDAL interprets p1 as the symetrical point of p0 with respect to the
> > center
> > (https://github.com/osgeo/gdal/blob/trunk/gdal/ogr/ogrcircularstring.cpp
> > #L640), that is p1 is on the perimeter of the circle, or said otherwise
> > the center of the circle is the midpoint of [p0,p1].
> > Whereas QGIS interprets p1 as the center of the circle (
> > https://github.com/qgis/QGIS/blob/master/src/core/geometry/qgsgeometryuti
> > ls.cpp#L359 )
> > 
> > I'd think GDAL interpretation is the right one, since according to
> > http://jtc1sc32.org/doc/N1101-1150/32N1107-WD13249-3--spatial.pdf (ISO
> > SQL MM Part 3), paragraph 4.1.6 :
> > (let's call this sentence S1)
> > """ In the case where the segment is a circle, then the center is located
> > at the midpoint of the line connecting the start point with the
> > intermediate point. """
> > 
> > But if you look a bit above in the paragraph, there's a sentence (call it
> > S2)
> > 
> > : """In the special case where a segment is a complete circle, that is,
> > : the
> > 
> > start and end points are coincident, then the intermediate point shall be
> > the midpoint of the segment. """, which looks confusing at first. I
> > think this sentence must be interpreted considering distances along the
> > curve, in which case the "midpoint of the segment" when doing a full
> > walk along the circle from p0 back to p0 is the symetrical point of p0
> > with respect to the center.
> > 
> > I think this interpretation is also more logical since, even in that
> > particular case, p0,p1,p2 are all on the arc, like in the general case.
> > 
> > I can also see that PostGIS (in
> > https://github.com/postgis/postgis/blob/svn-
> > trunk/liblwgeom/lwalgorithm.c#L252 ) has the same interpretation as GDAL
> > (*)
> > 
> > I'd be happy to read opinions regarding this.
> > 
> > Even
> > 
> > (*) Can also be shown with :
> > 
> > # SELECT
> > ST_AsText(ST_Envelope(ST_CurveToLine(ST_GeomFromText('CIRCULARSTRING(-1
> > 0,1 0,-1 0)'))));
> > 
> >                st_astext
> > 
> > --------------------------------------
> > 
> >   POLYGON((-1 -1,-1 1,1 1,1 -1,-1 -1))
> > 
> > And http://postgis.net/docs/manual-2.2/using_postgis_dbmanagement.html
> > says "The exception to this is for a closed circle, where the start and
> > end points are the same. In this case the second point MUST be the
> > center of the arc, ie the opposite side of the circle.", which is
> > another way to rephrase S2.

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