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

[Oscar van Vlijmen]

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!

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