I've kept out of this debate so far - partly waiting until I had my copy of
Snyder's 'Working Manual' (USGS Professional Paper 1395) in front of me. I've
also got ESRI's 'Understanding Map Projections' by Kennedy and Kopp (my copy is
dated 2000; ESRI Press) to hand. I had a hazy memory that this was a
complicated area ... as it indeed seems to be.
According to Kennedy and Kopp, the ESRI Stereographic projection uses the
ellipsoid directly, whilst the Double Stereographic projection takes the
ellipsoid to a Gaussian sphere before calculating the planar form.
According to Snyder (pp154-157) the basic Stereographic projection is an
azimuthal conformal perspective projection on the sphere but only azimuthal
conformal in the polar form on the ellipsoid, when it 'is not perspective'.
There are also modified forms (Snyder p 203) that are not symmetrical and in
which meridians and parallels are complex curves. Snyder provides separate
formulae for the spherical and ellipsoidal forms, implying that the spherical
form is not a simple special case of the ellipsoidal.
In both Bugayevskiy & Snyder (1995, Map Projections: A Reference Manual, London:
Taylor & Francis) and Yang, Snyder and Tobler (2000, Map Projection
Transformation: Principles and Applications, London: Taylor & Francis) a
"double" projection is defined as one in which the ellipsoidal form is first
projected onto a sphere and then the sphere to planar form. They also separate
the spherical and ellipsoidal forms for the stereographic formulae. This
suggests that Kennedy & Kopp do give the detail necessary when they mention
projection first onto the Gaussian sphere.
I have not examined the code of GDAL, nor of Proj4, so do not know whether these
have the facility to transform from ellipsoid to sphere to planar to replicate
the 'double' or whether the spherical or ellipsoidal form is provided - let
alone as to whether such a double method is supported. However, I suspect that
Even is correct to surmise that the issue is not straightforward.
Best wishes,
Peter
Maciej Sieczka wrote:
W dniu 05.02.2011 14:47, Hermann Peifer pisze:
On 05/02/2011 13:12, Even Rouault wrote:
I've just had a look, but not being neither Dutch nor a specialist
of (stereographic) projections, I don't feel competent enough to do
any action on it. Those tickets plus the reading of
http://udig.refractions.net/files/docs/api-
geotools/org/geotools/referencing/operation/projection/Stereographic.html
make me deeply confused and wondering if r21627 was really
appropriate.
Hmm. This page confirms what I mentioned in ticket #2869:
"Double_Stereographic" is simply the ESRI alias of
"Oblique_Stereographic" (EPSG code 9809).
About r21627: I am afraid I do not understand enough about the inner
workings of GDAL/OGR to make a judgement about whether this change
was appropriate or not.
But by the end of the day and from what I remember when looking
somewhat deeper into the issue, about 2 years ago: there is one
stereographic projection (known as "the USGS formula" or "the
approach given by Snyder") which translates into +proj=stere, and
there is the other "Double_Stereographic", aka
"Oblique_Stereographic" which is expected to end up as +proj=sterea.
I'm not an expert too, but Hermann findings are in accordance with my
findings for Polish stereographic CRS (from over 5 years ago):
http://lists.maptools.org/pipermail/proj/2005-March/001524.html
The Polish CRSs which use +proj=sterea version of stereographic are
3120, 2172-2174, 3328.
See also Gerald Evendeen's notes:
http://lists.maptools.org/pipermail/proj/2005-March/001526.html
Maciek
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