[Proj] projection of Madagascar

Clifford J Mugnier cjmce at lsu.edu
Tue Apr 29 17:06:16 EDT 2008

The problem with various software packages being unable to match the Laborde Oblique Mercator projection is not new.  I mentioned the problem in my "Grids and Datums" column of Photogrammetric Engineering and Remote Sensing back in February of 2000.  The Laborde projection is a triple projection on the Gaussian Sphere, and the Hotine Rectified Skew Orthomorphic projection is a triple projection on the aposphere.  They are quite different.  I spent many hours researching that projection back in the early 1980s, and I had to translate a lot from the original French, some of it in Laborde's original handwriting.  It certainly is a tough nut to crack, and apparently too formidable for many programmers that don't read scientific French.  
Some kluges have been worked up by ESRI in the past, but I thought Melita Kennedy told me that they (at ESRI) had indeed programmed Laborde's equations for one of their recent versions of Arc/View or Arc/Map.  (However, I could be mistaken.)
Cliff Mugnier
For more info on the Grids and Datums of Madagascar, see:     http://www.asprs.org/resources/GRIDS/


From: proj-bounces at lists.maptools.org on behalf of OvV_HN
Sent: Tue 29-Apr-08 12:01
To: PROJ.4 and general Projections Discussions
Subject: Re: [Proj] projection of Madagascar

Clovis wrote:

> I have been quickly through the archive but didn't find any topic on this.
> I have a projection issue concerning Madagascar.

There are no good nor usable alternatives for the Laborde projection.
Using the Oblique Mercator you'll get decimeters of error within the
Madagascar territory.
One example from my software:

Laborde Madagascar:
lat = -16d 11m 23.280s; lon = 44d 27m 27.260s;
lat0 = -18.9; lon0 = 46d 26m 14.025s;
x0 = 4e5; y0 = 8e5; k0 = 0.9995; Az = 18.9;
international 1924 ellipsoid
-> x, y = 188333.848, 1098841.091

Oblique Mercator approximation with the following parameters:
lat0 = -18.9; lon0 = 46d 26m 14.025s; lonc = lon0;
x0 = 4e5; y0 = 8e5; k0 = 0.9995; alfac = 18.9; gamma = alfac;
international 1924 ellipsoid
-> x, y = 188333.847, 1098841.111

(angles in degrees wrt Greenwich, lengths in meters)

These differences may seem small, but wait until you get farther away
from the central line.

See also section "Laborde projection for Madagascar", EPSG
Guidance Note 7-2, version April 2008.
There you can also find omerc examples with an error of several decimeters.

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