[MetaCRS] Stereographic Projections: stere and sterea

[Richard Marsden]

Thanks Mikael:  I think that explains it enough for my article.

Although the article and my demos are only interested in polar projections,
I'll use sterea in the implementations, and for the survey part I'll give a
quick summary of the differences as explained in your email and the libproj
docs (found it- thanks!).

I'm also only using these projections for display (with MapServer and
OpenLayers) rather than actual storage. My coords are stored as geographic
WGS84  (as most web mapping apps are).
As they are polar projections, I was also going to limit myself to 90deg
from the pole. I might need to truncate the antipodal hemisphere - something
I'll have to try and see. A hurdle to make the second (how-to) article more
interesting!


Frank: Thanks. I signed up to the proj list, but Mikael's reply came through
before I had confirmed my subscription (it came through overnight).

Thanks everyone,

Richard




.explain the differences.



On Fri, Nov 6, 2009 at 2:51 AM, Mikael Rittri <Mikael.Rittri at carmenta.com>wrote:

> > The Proj.4 documenation doesn't mention the "sterea" projection,
> > but pages found by Google suggest it is a recent alternative addition?
> > This would explain its absence from the original Snyder documentation
> > and addenda.
>
> The sterea formulas are documented in the libproj4 documentation
> at http://dl.maptools.org/dl/libproj4 ; I guess it was ported
> from libproj4 to Proj.4.
>
> stere and sterea coincide in the polar aspect, so there is no trouble
> if you never want an oblique or equatorial aspect.
>
> However, in the oblique Netherlands grid, for example, they differ
> by up to 8 meters.
>
> Both are valid projections, in the sense that both are exactly
> conformal mappings from ellipsoid to plane.  But only sterea has
> the nice property that the local scale factor is minimal at the
> projection center.  In oblique stere, the point of minimal scale
> factor is displaced towards the equator by up to 0.4 degrees.
>
> sterea has less distortion (near the center), but more complicated
> formulas.  On the other hand, stere is continuous globally, while
> sterea is discontiuous along the antipode of the central meridian,
> where the map overlaps itself along a strip that can be up to 1.2°
> wide, so sterea should not be used more than 90° of longitude from
> its central meridian.
>
> stere is never used for data storage, as far as I know.
> In fact, I doubt that it is used at all (except in its
> polar aspect, where it coincides with sterea anyway).
> It is a bit of a mystery why Snyder described stere but
> not sterea.
>
> sterea is used for data storage in Canada, Romania,
> and the Netherlands. (Confirmed by Oscar van Vlijmen,
> http://lists.maptools.org/pipermail/proj/2009-April/004603.html )
>
> Poland uses the Roussilhe version of stereographic projection,
> +proj=rouss, which is an approximation of sterea intended to
> be easier to calculate (I don't think it is exactly conformal).
> When I checked the difference between rouss and sterea, I found
> that the difference was at most 5 centimeters within 350 km
> from the projection center, at least in my test case.
> (I am not sure whether +proj=rouss uses exactly the same
> Roussilhe formulas as they do in Poland.)
>
> Best regards,
>
> --
> Mikael Rittri
> Carmenta AB
> SWEDEN
> www.carmenta.com
>
> ________________________________
>
> From: metacrs-bounces at lists.osgeo.org [mailto:
> metacrs-bounces at lists.osgeo.org] On Behalf Of Richard Marsden
> Sent: den 6 november 2009 00:50
> To: metacrs
> Subject: [MetaCRS] Stereographic Projections: stere and sterea
>
>
> Following on from equal-area-maps.com <http://equal-area-maps.com/> , I am
> putting together some samples for polar projections. Eventually I'll publish
> a couple of articles at GeoWebGuru.com.  I'm still at the survey stage, but
> it looks like there are two stereographic projections: "stere" and "sterea"
> and it isn't clear what the difference is.
>
> The Proj.4 documenation doesn't mention the "sterea" projection, but pages
> found by Google suggest it is a recent alternative addition?
> This would explain its absence from the original Snyder documentation and
> addenda.
>
> The best description I have found is on the GeoTIFF site which says that
> they are two different but valid approaches, with "stere" being the original
> (Snyder) approach. However it notes that the two approaches produce
> different results away from the centre! To me this suggests that it is
> unlikely that are both are equally valid.
>
> Considering both were ported to Proj4JS, I assume this issue has already
> come up?
> What does "sterea" offer over "stere", and which is usually recommended?
>
> Best regards,
>
> Richard Marsden
> Winwaed Software Technology LLC
> http://www.winwaed.com <http://www.winwaed.com/>
> http://www.mapping-tools.com <http://www.mapping-tools.com/>
> http://www.geowebguru.com <http://www.geowebguru.com/>
>
>
>
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