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<title>Re: [Proj] "Double ellipsoid" case?</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'>Mikael,<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'>Thanks for the useful links, which I’ll
follow later in the day (off to work soon).<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'>The only difference between the spherical
and ellipsoidal Mercator is that the eccentricity squared is zero in the former
case. I agree that both are valid. Intuition tells me that the spherical case
is conformal, too, though I haven’t checked. Of course, the LL</span></font><font
size=2 color=navy face=Wingdings><span style='font-size:10.0pt;font-family:
Wingdings;color:navy'>ó</span></font><font size=2 color=navy face=Arial><span
style='font-size:10.0pt;font-family:Arial;color:navy'>NE mapping is different,
largely because the meridional arc is so different. My example shows that, so I
used them relatively. <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'>My objection (well, one of my objections)
is the implicit expectation that one can do relative computations (whatever one
does on a map) on a spherical Mercator and “</span></font><font size=2
face=Arial><span style='font-size:10.0pt;font-family:Arial'>the resulting
lat/long coordinates are intended to be treated as WGS84 after that” (in
Frank’s paraphrasing of what the Google Maps model implies). That’s
not true. <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Datums CANNOT be switched under the projection, the whole
issue of this “double ellipsoid” thread. The Google Sphere is NOT
WGS84. Yes, it can be made to look similar at a point, but wander away from
that point and it’s very different. My intention was merely to quantify
the error with a numerical example. <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Regarding the EPSG, I respect their integrity in resisting
bogus geodesy. Misrepresentations aside, the Google Sphere is not WGS84.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Thanks,<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Noel<font color=navy><span style='color:navy'><o:p></o:p></span></font></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>
<div>
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face="Times New Roman"><span style='font-size:12.0pt'>
<hr size=2 width="100%" align=center tabindex=-1>
</span></font></div>
<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>Mikael Rittri<br>
<b><span style='font-weight:bold'>Sent:</span></b> Monday, December 01, 2008
3:44 AM<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] "Double
ellipsoid" case?</span></font><o:p></o:p></p>
</div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'>Noel,</span></font><o:p></o:p></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'>I haven't checked your results, but there is no reason to
expect that the two results would be the same. </span></font><o:p></o:p></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'>As I see it, Ellipsoid Mercator is one projection, and
Sphere Mercator is a different one. </span></font><o:p></o:p></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'>Each one is internally consistent, but the two are not the
same. That is, since the formulas </span></font><o:p></o:p></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'>are different, the (Easting,Northing) values
are not the same for the same (Lon,Lat). But </span></font><o:p></o:p></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'>for each projection, you can use its inverse to get
exactly back to the original (Lon,Lat). </span></font><o:p></o:p></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'>The Ellipsoid Mercator is exactly conformal while Sphere
Mercator is only approximately conformal</span></font><o:p></o:p></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'>(if you regard the ellipsoid as the true shape of the
Earth). I think the maximal angle distortion </span></font><o:p></o:p></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'>for Sphere Mercator is 0.2 degrees, so for visual display it
is hard to notice.</span></font><o:p></o:p></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'>Since the projections are distinct, we should not expect
that analoguous calculations done </span></font><o:p></o:p></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'>in their projected planes should give identical
results. </span></font><o:p></o:p></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'>So, the situation is similar to the French truncated Lambert
Conformal Conic, which is </span></font><o:p></o:p></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'>not exactly conformal, and is a different projection than
the true Lambert Conformal Conic. </span></font><o:p></o:p></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'>It is tricky to create WKT to represent the Sphere Mercator
projection together with an ellipsoid datum. </span></font><o:p></o:p></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'>But that is a failure of WKT, not of the Sphere
Mercator. One way to express it in WKT has </span></font><o:p></o:p></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'>been suggested by Martin Desruisseaux of GeoTools, another
way by Melita Kennedy of ESRI. </span></font><o:p></o:p></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'>See the August 2008 archives for the MetaCRS mailing list, </span></font><o:p></o:p></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'><a
href="http://lists.osgeo.org/pipermail/metacrs/2008-August/thread.html">http://lists.osgeo.org/pipermail/metacrs/2008-August/thread.html</a> .
</span></font><o:p></o:p></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'>And it is not only Google that uses spherical
projections. So does the National Snow and <st1:place w:st="on"><st1:City
w:st="on">Ice Data Center</st1:City>, <st1:country-region w:st="on">USA</st1:country-region></st1:place>.
</span></font><o:p></o:p></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'><a
href="ftp://sidads.colorado.edu/pub/ppp/conf_ppp/Haran/HDF-EOS_vs._GeoTIFF__GIS_Problems_when_Projection_and_Datum_Spheroids_are_Different.pdf">ftp://sidads.colorado.edu/pub/ppp/conf_ppp/Haran/HDF-EOS_vs._GeoTIFF__GIS_Problems_when_Projection_and_Datum_Spheroids_are_Different.pdf</a></span></font><o:p></o:p></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'>I think it is unfortunate that EPSG insists that a spherical
projection can only be used together with a spherical datum, because </span></font><o:p></o:p></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'>a) it is not true,</span></font><o:p></o:p></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'>b) spherical datums do not exist for the Earth (<a
href="http://lists.maptools.org/pipermail/proj/2008-August/003667.html">http://lists.maptools.org/pipermail/proj/2008-August/003667.html</a>).
</span></font><o:p></o:p></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'>Best regards,</span></font><o:p></o:p></p>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face="Times New Roman"><span style='font-size:
10.0pt'>--<br>
Mikael Rittri<br>
<st1:place w:st="on"><st1:City w:st="on">Carmenta</st1:City> <st1:State w:st="on">AB</st1:State></st1:place><br>
<st1:address w:st="on"><st1:Street w:st="on">Box</st1:Street> 11354</st1:address><br>
SE-404 28 Göteborg<br>
Visitors: Sankt Eriksgatan 5<br>
<st1:country-region w:st="on"><st1:place w:st="on">SWEDEN</st1:place></st1:country-region><br>
Tel: +46-31-775 57 37<br>
Mob: +46-703-60 34 07<br>
mikael.rittri@carmenta.com<br>
www.carmenta.com</span></font> <o:p></o:p></p>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
</div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
<div class=MsoNormal align=center style='text-align:center'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'>
<hr size=2 width="100%" align=center tabIndex=-1>
</span></font></div>
<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 [mailto:proj-bounces@lists.maptools.org] <b><span
style='font-weight:bold'>On Behalf Of </span></b>Noel Zinn<br>
<b><span style='font-weight:bold'>Sent:</span></b> den 30 november 2008 06:05<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] "Double
ellipsoid" case?</span></font><o:p></o:p></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>Not that Frank is responsible for the
geodesy and cartography in Google Maps (or their abuse therein), but the phrase
“</span></font><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>the resulting lat/long coordinates are intended to be
treated as WGS84 after that” so <font color=navy><span style='color:navy'>troubles
me that I am sympathetic to Cliff’s sentiments. So, let’s
quantify the offense with an experiment that anyone can duplicate, perhaps in
Proj4 (I work in Matlab).<o:p></o:p></span></font></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'>Consider the following Mercator grid
parameters defined on both WGS84 and the Google Sphere (whose radius equals the
semi-major axis of WGS84): CM = 95W, FN=FE=0. That’s all we need.<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'>Now consider at point at 30N / 95W.
That’s somewhere near <st1:place w:st="on"><st1:City w:st="on">Houston</st1:City>,
<st1:State w:st="on">Texas</st1:State></st1:place>, where I live.
Convert to Mercator in both systems. Then traverse to the NE about 141km
in both systems by adding 100km to both the Northing and Easting (in
Mercator). Convert the resulting Mercator coordinates back to
geographicals (lat / lon).<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'>Here’s what I get for WGS84:
30N / 95W is N3,503,549.84350437m / E0m with a point scale (Mercator is
conformal) of 1.15470053837925 and at the end of the traverse the geographicals
are 30-46-29.63568N /
94-06-06.06498W.<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'>For the Google Sphere the results
are: 30N / 95W is N3,482,189.08540862m / E0m with a point scale of
1.15373388324025 and at the end of the traverse the geographicals are
30-46-43.56897N / 94-06-06.06498W.<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'>Pardon the excessive precision; it’s
just what I get. And I hope that I haven’t blundered in my haste to
respond. Perhaps someone can confirm.<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'>Interestingly, the longitudes are the
same, but the latitudes are very different (more than might be accounted for by
the scale differences, a cartographic subtlety likely beyond the ken of most
Google Maps users anyway). I don’t believe </span></font><font
size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'>the
resulting lat/long coordinates can be treated as WGS84 at all. <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Noel Zinn<font color=navy><span style='color:navy'><o:p></o:p></span></font></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>
<div>
<div class=MsoNormal align=center style='text-align:center'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'>
<hr size=2 width="100%" align=center tabIndex=-1>
</span></font></div>
<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> Saturday, November 29, 2008
8:15 AM<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] "Double
ellipsoid" case?</span></font><o:p></o:p></p>
</div>
<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=idOWAReplyText1252>
<div>
<p class=MsoNormal><font size=2 color=black face="Times New Roman"><span
style='font-size:10.0pt;color:black'>Frank:</span></font><o:p></o:p></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=2 face="Times New Roman"><span style='font-size:
10.0pt'>Ah, there's a BIG difference between the true coordinate system
relations of geodesy used by national governments and one cooked up by an ignoramus
at Google Maps that did not know what they were doing ... I guess there's a lot
of that going around, too.</span></font><o:p></o:p></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
</div>
<div>
<p class=MsoNormal><font size=2 face="Times New Roman"><span style='font-size:
10.0pt'>I suppose even twits help contribute to keep knowledgeable consultants
in business.</span></font><o:p></o:p></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'> <o:p></o:p></span></font></p>
</div>
<div>
<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>
</div>
<div>
<p class=MsoNormal><font size=2 face="Times New Roman"><span style='font-size:
10.0pt'>LSU</span></font><o:p></o:p></p>
</div>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
<div class=MsoNormal align=center style='text-align:center'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'>
<hr size=2 width="100%" align=center tabIndex=-1>
</span></font></div>
<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 Frank Warmerdam<br>
<b><span style='font-weight:bold'>Sent:</span></b> Fri 28-Nov-08 10:52<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] "Double
ellipsoid" case?</span></font><o:p></o:p></p>
</div>
<div>
<p><font size=2 face="Times New Roman"><span style='font-size:10.0pt'>support.mn@elisanet.fi
wrote:<br>
> Hello,<br>
><br>
> I just started to think about a situation where there might be a double<br>
> ellipsoid case.<br>
><br>
> 1) projection uses ellipsoid A independently<br>
> 2) datum shift uses ellipsoid B<br>
><br>
> Is this possible to be handled with proj.4? Since there is only one<br>
> ellipsoid definition available<br>
<br>
Janne,<br>
<br>
PROJ.4 does not currently handle this situation conveniently. One special<br>
case is where the projection uses a particular ellipsoid, but datum shifts<br>
should treat the corresponding lat/long values as being WGS84. In that<br>
special case you can use +nadgrids=@null to effectively say the datum shift<br>
to WGS84 is a no-op.<br>
<br>
I have at times contemplated having a way of having a datum/ellipsoid<br>
definition used for datum shifting purposes that is independent of the<br>
normal ellipsoid used by the projection functions but I have not pursued it.<br>
<br>
Clifford J Mugnier wrote:<br>
> I've seen a few projections and datums in my day, and I've never
come<br>
> accross that. For there to be a different ellipsoid of
reference for a<br>
> projection than there is for a datum is a contradiction in terms.<br>
<br>
Cliff,<br>
<br>
The very common case we see a lot these days is the google maps mercator<br>
projection. The mercator calculations are done based on a particular<br>
spherical earth model, but the resulting lat/long coordinates are intended<br>
to be treated as WGS84 after that.<br>
<br>
Best regards,<br>
--<br>
---------------------------------------+--------------------------------------<br>
I set the clouds in motion - turn up | Frank Warmerdam,
warmerdam@pobox.com<br>
light and sound - activate the windows | <a href="http://pobox.com/~warmerdam">http://pobox.com/~warmerdam</a><br>
and watch the world go round - Rush | Geospatial Programmer
for Rent<br>
<br>
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