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<font face="Times New Roman">As far as the Dutch projection is
concerned (EPSG:28992), Peter's summary is correct: it first
projects the ellipsoid to the sphere and then projects the sphere
stereographically to the plane. I don't know if that is the way
PROJ4 computes the transformation, but I can garantee that using
"sterea" as parameter gives correct results here.<br>
<br>
Jan<br>
</font><br>
On 2011-02-07 12:32, Peter J Halls wrote:
<blockquote cite="mid:4D4FD838.7020008@york.ac.uk" type="cite">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.
<br>
<br>
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.
<br>
<br>
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.
<br>
<br>
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.
<br>
<br>
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.
<br>
<br>
Best wishes,
<br>
<br>
Peter
<br>
<br>
<br>
Maciej Sieczka wrote:
<br>
<blockquote type="cite">W dniu 05.02.2011 14:47, Hermann Peifer
pisze:
<br>
<blockquote type="cite">On 05/02/2011 13:12, Even Rouault wrote:
<br>
</blockquote>
<br>
<blockquote type="cite">
<blockquote type="cite">I've just had a look, but not being
neither Dutch nor a specialist
<br>
of (stereographic) projections, I don't feel competent
enough to do
<br>
any action on it. Those tickets plus the reading of
<br>
<a class="moz-txt-link-freetext" href="http://udig.refractions.net/files/docs/api">http://udig.refractions.net/files/docs/api</a>-
<br>
geotools/org/geotools/referencing/operation/projection/Stereographic.html
<br>
make me deeply confused and wondering if r21627 was really
<br>
appropriate.
<br>
</blockquote>
</blockquote>
<br>
<blockquote type="cite">Hmm. This page confirms what I mentioned
in ticket #2869:
<br>
"Double_Stereographic" is simply the ESRI alias of
<br>
"Oblique_Stereographic" (EPSG code 9809).
<br>
<br>
About r21627: I am afraid I do not understand enough about the
inner
<br>
workings of GDAL/OGR to make a judgement about whether this
change
<br>
was appropriate or not.
<br>
<br>
But by the end of the day and from what I remember when
looking
<br>
somewhat deeper into the issue, about 2 years ago: there is
one
<br>
stereographic projection (known as "the USGS formula" or "the
<br>
approach given by Snyder") which translates into +proj=stere,
and
<br>
there is the other "Double_Stereographic", aka
<br>
"Oblique_Stereographic" which is expected to end up as
+proj=sterea.
<br>
</blockquote>
<br>
I'm not an expert too, but Hermann findings are in accordance
with my
<br>
findings for Polish stereographic CRS (from over 5 years ago):
<br>
<br>
<a class="moz-txt-link-freetext" href="http://lists.maptools.org/pipermail/proj/2005-March/001524.html">http://lists.maptools.org/pipermail/proj/2005-March/001524.html</a>
<br>
<br>
The Polish CRSs which use +proj=sterea version of stereographic
are
<br>
3120, 2172-2174, 3328.
<br>
<br>
See also Gerald Evendeen's notes:
<br>
<br>
<a class="moz-txt-link-freetext" href="http://lists.maptools.org/pipermail/proj/2005-March/001526.html">http://lists.maptools.org/pipermail/proj/2005-March/001526.html</a>
<br>
<br>
Maciek
<br>
<br>
</blockquote>
<br>
</blockquote>
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