[gdal-dev] Re: gdal_rasterize 1.8.0 options

Peter J Halls p.halls at york.ac.uk
Mon Feb 7 06:32:08 EST 2011


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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Peter J Halls, GIS Advisor & Acting Team Leader Applications Support Group,
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