[Proj] Discovery: libproj4 stmerc = French Gauss-Laborde projection

Gerald I. Evenden gerald.evenden at verizon.net
Mon Jun 12 10:30:59 EDT 2006

On Monday 12 June 2006 5:47 am, Oscar van Vlijmen wrote:
> stmerc is a projection in the libproj4 package. There is no documentation.
> Mr. Evenden mentioned it on this discussion list on 2004-03-26.
> Recently I found a connection with a projection in real use, the
> Gauss-Laborde type "sphère de courbure" (probably meaning: the projection
> sphere has a radius equal to the radius of curvature at the point of
> origin).
> What is the connection? They are the same!

The 's' in smerc comes from Schreiber Mercator fir which I have found very 
little documentation.  Snyder refers to it as an alternative transverse 
Mercator but gives no further useful information.

The libproj4 smerc is a Gauss transformation to the sphere, radius at lat_0,
and spherical transverse Mercator projection.

I cannot add anything about French usage but it has nothing to do with the 
Laborde projection used in Madagascar.

If anyone has mathematic documentation of the Schreiber Transverse Mercator I 
would be greatful for a copy.

> There is documentation available at the French Institut Géographique
> National, publication "Notes Techniques", NT/G 73.
> <http://www.ign.fr/affiche_rubrique.asp?rbr_id=1700&lng_id=FR#68096>
> <http://www.ign.fr/telechargement/MPro/geodesie/CIRCE/NTG_73.pdf>
> This publication gives the algorithms of two more Gauss-Laborde type
> projections, one with a "sphère equatoriale" and one with a "sphère
> bitangente".
> The "sphère de courbure" projection was or is still in use for Réunion.
> I have no idea where the other two Labordes were used for.
> More background information in:
> ENSG-IGN, Didier Bouteloup, Cours de Géodésie, Chapitre 3: §4.5.d
> "Représentation de Gauss-Laborde"
> <http://www.ensg.ign.fr/~bouteloup/www/wwwfad/site_fad/pdf/index_pdf.htm>
> <http://www.ensg.ign.fr/~bouteloup/www/wwwfad/site_fad/pdf/chap3.pdf>
> Example:
> International ellipsoid;
> lat=-21; lon=55.5;
> lat0=-21d7m; lon0=55d32m; x0=1.6e5; y0=5e4; k0=1;
> x,y Laborde type 1 = stmerc = 156534.17713, 62916.92507
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