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<title>Re: [Proj] projection of Madagascar</title>
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<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>Cliff,<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>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.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>Noel Zinn<o:p></o:p></span></font></p>
<p class=MsoNormal><st1:City w:st="on"><st1:place w:st="on"><font size=2
color=navy face=Arial><span style='font-size:10.0pt;font-family:Arial;
color:navy'>Houston</span></font></st1:place></st1:City><font size=2
color=navy face=Arial><span style='font-size:10.0pt;font-family:Arial;
color:navy'><o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p> </o:p></span></font></p>
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<p class=MsoNormal><b><font size=2 face=Tahoma><span style='font-size:10.0pt;
font-family:Tahoma;font-weight:bold'>From:</span></font></b><font size=2
face=Tahoma><span style='font-size:10.0pt;font-family:Tahoma'>
proj-bounces@lists.maptools.org [mailto:proj-bounces@lists.maptools.org] <b><span
style='font-weight:bold'>On Behalf Of </span></b>Clifford J Mugnier<br>
<b><span style='font-weight:bold'>Sent:</span></b> Tuesday, April 29, 2008 4:06
PM<br>
<b><span style='font-weight:bold'>To:</span></b> ovv@hetnet.nl; <st1:PersonName
w:st="on">PROJ.4 and general Projections Discussions</st1:PersonName><br>
<b><span style='font-weight:bold'>Cc:</span></b> Proj@lists.maptools.org<br>
<b><span style='font-weight:bold'>Subject:</span></b> RE: [Proj] projection of <st1:country-region
w:st="on"><st1:place w:st="on">Madagascar</st1:place></st1:country-region></span></font><o:p></o:p></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
<div id=idOWAReplyText71002>
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<p class=MsoNormal><font size=2 color=black face="Times New Roman"><span
style='font-size:10.0pt;color:black'>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 <em><i><font
face="Times New Roman">Photogrammetric Engineering and Remote Sensing</font></i></em>
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. </span></font><o:p></o:p></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=2 color=black face="Times New Roman"><span
style='font-size:10.0pt;color:black'>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.)</span></font><o:p></o:p></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=2 face="Times New Roman"><span style='font-size:
10.0pt'>Cliff Mugnier</span></font><o:p></o:p></p>
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<p class=MsoNormal><st1:place w:st="on"><st1:PlaceName w:st="on"><font size=2
face="Times New Roman"><span style='font-size:10.0pt'>LOUISIANA</span></font></st1:PlaceName><font
size=2><span style='font-size:10.0pt'> <st1:PlaceType w:st="on">STATE</st1:PlaceType>
<st1:PlaceType w:st="on">UNIVERSITY</st1:PlaceType></span></font></st1:place><o:p></o:p></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=2 face="Times New Roman"><span style='font-size:
10.0pt'>For more info on the Grids and Datums of Madagascar,
see: </span></font><a
href="https://email.lsu.edu/exchweb/bin/redir.asp?URL=https://email.lsu.edu/exchweb/bin/redir.asp?URL=https://email.lsu.edu/exchweb/bin/redir.asp?URL=https://email.lsu.edu/exchweb/bin/redir.asp?URL=https://email.lsu.edu/exchweb/bin/redir.asp?URL=https://email.lsu.edu/exchweb/bin/redir.asp?URL=https://email.lsu.edu/exchweb/bin/redir.asp?URL=https://email.lsu.edu/exchweb/bin/redir.asp?URL=https://email.lsu.edu/exchweb/bin/redir.asp?URL=https://email.lsu.edu/exchweb/bin/redir.asp?URL=https://email.lsu.edu/exchweb/bin/redir.asp?URL=https://email.lsu.edu/exchweb/bin/redir.asp?URL=https://email.lsu.edu/exchweb/bin/redir.asp?URL=https://email.lsu.edu/exchweb/bin/redir.asp?URL=https://email.lsu.edu/exchweb/bin/redir.asp?URL=https://email.lsu.edu/exchweb/bin/redir.asp?URL=https://email.lsu.edu/exchweb/bin/redir.asp?URL=https://email.lsu.edu/exchweb/bin/redir.asp?URL=https://email.lsu.edu/exchweb/bin/redir.asp?URL=https://email.lsu.edu/exchweb/bin/redir.asp?URL=https://email.lsu.edu/exchweb/bin/redir.asp?URL=https://email.lsu.edu/exchweb/bin/redir.asp?URL=https://email.ls"
target="_blank"><font size=2><span style='font-size:10.0pt'>http://www.asprs.org/resources/GRIDS/</span></font></a><o:p></o:p></p>
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<p class=MsoNormal style='margin-bottom:12.0pt'><b><font size=2 face=Tahoma><span
style='font-size:10.0pt;font-family:Tahoma;font-weight:bold'>From:</span></font></b><font
size=2 face=Tahoma><span style='font-size:10.0pt;font-family:Tahoma'>
proj-bounces@lists.maptools.org on behalf of OvV_HN<br>
<b><span style='font-weight:bold'>Sent:</span></b> Tue 29-Apr-08 12:01<br>
<b><span style='font-weight:bold'>To:</span></b> <st1:PersonName w:st="on">PROJ.4
and general Projections Discussions</st1:PersonName><br>
<b><span style='font-weight:bold'>Subject:</span></b> Re: [Proj] projection of <st1:country-region
w:st="on"><st1:place w:st="on">Madagascar</st1:place></st1:country-region></span></font><o:p></o:p></p>
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<p><st1:City w:st="on"><st1:place w:st="on"><font size=2 face="Times New Roman"><span
style='font-size:10.0pt'>Clovis</span></font></st1:place></st1:City><font
size=2><span style='font-size:10.0pt'> wrote:<br>
<br>
> I have been quickly through the archive but didn't find any topic on this.<br>
> I have a projection issue concerning <st1:country-region w:st="on"><st1:place
w:st="on">Madagascar</st1:place></st1:country-region>.<br>
<br>
<br>
There are no good nor usable alternatives for the Laborde projection.<br>
Using the Oblique Mercator you'll get decimeters of error within the<br>
<st1:country-region w:st="on"><st1:place w:st="on">Madagascar</st1:place></st1:country-region>
territory.<br>
One example from my software:<br>
<br>
Laborde <st1:country-region w:st="on"><st1:place w:st="on">Madagascar</st1:place></st1:country-region>:<br>
lat = -16d 11m 23.280s; lon = 44d 27m 27.260s;<br>
lat0 = -18.9; lon0 = 46d 26m 14.025s;<br>
x0 = 4e5; y0 = 8e5; k0 = 0.9995; Az = 18.9;<br>
international 1924 ellipsoid<br>
-> x, y = 188333.848, 1098841.091<br>
<br>
Oblique Mercator approximation with the following parameters:<br>
lat0 = -18.9; lon0 = 46d 26m 14.025s; lonc = lon0;<br>
x0 = 4e5; y0 = 8e5; k0 = 0.9995; alfac = 18.9; gamma = alfac;<br>
international 1924 ellipsoid<br>
-> x, y = 188333.847, 1098841.111<br>
<br>
(angles in degrees wrt <st1:City w:st="on"><st1:place w:st="on">Greenwich</st1:place></st1:City>,
lengths in meters)<br>
<br>
These differences may seem small, but wait until you get farther away<br>
from the central line.<br>
<br>
See also section 1.3.6.1 "Laborde projection for <st1:country-region
w:st="on"><st1:place w:st="on">Madagascar</st1:place></st1:country-region>",
EPSG<br>
Guidance Note 7-2, version April 2008.<br>
There you can also find omerc examples with an error of several decimeters.<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
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