[gdal-dev] Re: gdal_rasterize 1.8.0 options

[Jan Hartmann]

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.

Jan

On 2011-02-07 12:32, Peter J Halls wrote:
> 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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