[Proj] projection of Madagascar

Noel Zinn ndzinn at comcast.net
Tue Apr 29 17:40:49 EDT 2008



In February 2007 the EPSG added a correct (IMO) version of the Laborde in
guidance Note 7-2 (coordinate operation method 9813, ProjCRS 29701) based
(in part) on IGN sources.  I think this is what is referred to below.  This
version does use complex math that codes up nicely in Matlab but may be a
problem in other programming languages.  (The text is in English!)  It
agrees well (in results, not algorithm) with Brad Drew's DMA FORTRAN code
(circa 1982), but differs from the OM/HOM "kludge(s)" (ProjCRS 29702) in the
amount you cite (and also documented in GN7-2).  It's what we ought to be
using today.


Noel Zinn




From: proj-bounces at lists.maptools.org
[mailto:proj-bounces at lists.maptools.org] On Behalf Of Clifford J Mugnier
Sent: Tuesday, April 29, 2008 4:06 PM
To: ovv at hetnet.nl; PROJ.4 and general Projections Discussions
Cc: Proj at lists.maptools.org
Subject: RE: [Proj] projection of Madagascar


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:


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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