<div> <font face="Arial, Helvetica, sans-serif" size="3"><br>
<font face="Verdana, Arial, Helvetica, sans-serif">Thanks for running these tests.<br>
<br>
Quoting:<br>
</font></font><pre style="font-size: 9pt;"><font face="Courier New, Courier, mono" size="3">Extended geographic range usage of any conformal projection is a contentious issue as <br>
any resultant grid system has sufficiently large scale errors as to make the <br>
Cartesian usage of the grid very questionable.</font></pre><font face="Verdana, Arial, Helvetica, sans-serif" size="3">This is true of any projection. It is true that conformal projections carry an inevitable disproportion of areas, but that's not related to scale error.</font><font face="Verdana, Arial, Helvetica, sans-serif" size="3"><br>
</font><font face="Arial, Helvetica, sans-serif"><font size="3"><font face="Verdana, Arial, Helvetica, sans-serif"><br>
Regards,<br>
-- daan Strebe</font><br>
</font><br>
</font></div>
<blockquote style="border-left: 2px solid blue; padding-left: 3px;">
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<pre style="font-size: 9pt;"><tt>Two testing grids were made on tmerc, etmerc and ftmerc: in a geographic range <br>
of 0 to 6 degrees longitude by 0 to 84 degrees latitude and 0 to 500km <br>
Easting to 9,700km Northing. The most apparent problem is that for <br>
reasonable demonstration the results should be presented as contour maps of <br>
the errors but inclusion of same is not possible in this email list.<br>
<br>
A simple summary can be made: in the lat-lon tests tmerc maintained an <br>
accuracy of <0.7mm (as would be expected occurred at the equator) and <br>
comparison of etmerc and ftmerc was always less than 1micron. In the <br>
Easting/Northing test, tmerc failed dismally at 21 meters at about 58degrees <br>
longitude/84.78 degree latitude. Again, ftmerc and etmerc maintained <br>
agreement to within 1micron.<br>
<br>
I believe it is quite safe to say that tmerc remains the projection of choice <br>
for UTM applications: adequate accuracy performance and best computational <br>
speed. Note that the lat/lon test was for 12 degree zones and thus tmerc is <br>
would appear suitable for what I understand of the 10 degree zones used for <br>
some Canadian province grids.<br>
<br>
As for extended range, I will probably check the agreement of etmerc and <br>
ftmerc over extended range but this is of lesser priority. Extended <br>
geographic range usage of any conformal projection is a contentious issue as <br>
any resultant grid system has sufficiently large scale errors as to make the <br>
Cartesian usage of the grid very questionable. Usage of conformal maps for <br>
global mapping is very questionable because of the distortion. Normal <br>
Mercator persists only because of its usefulness in rhumbline navigation <br>
which is probably fading due to GPS. Lastly, equal-area mapping is far <br>
preferable for thematic mapping as it at least give a better perspective of <br>
the area extent of regions that is, in most cases, more important that an <br>
often poor preservation of regional shape.<br>
-- <br>
The whole religious complexion of the modern world is due<br>
to the absence from Jerusalem of a lunatic asylum.<br>
-- Havelock Ellis (1859-1939) British psychologist<br>
_______________________________________________<br>
Proj mailing list<br>
<a __removedlink__1353630948__href="mailto:Proj@lists.maptools.org">Proj@lists.maptools.org</a><br>
<a __removedlink__1353630948__href="http://lists.maptools.org/mailman/listinfo/proj" target="_blank">http://lists.maptools.org/mailman/listinfo/proj</a>
</tt></pre>
</div>
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</blockquote>
<div> <br>
</div>
<div> <br>
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-----Original Message-----<br>
From: Gerald I. Evenden <geraldi.evenden@gmail.com><br>
To: PROJ.4 and general Projections Discussions <proj@lists.maptools.org><br>
Sent: Thu, 12 Jun 2008 9:17 am<br>
Subject: [Proj] Comments of tmerc, etmerc and ftmerc errors<br>
<br>
<div id="AOLMsgPart_0_de61c111-08ba-49b0-896e-805a83e376ce" style="margin: 0px; font-family: Tahoma,Verdana,Arial,Sans-Serif; font-size: 12px; color: rgb(0, 0, 0); background-color: rgb(255, 255, 255);">
<pre style="font-size: 9pt;"><tt>Two testing grids were made on tmerc, etmerc and ftmerc: in a geographic range <br>
of 0 to 6 degrees longitude by 0 to 84 degrees latitude and 0 to 500km <br>
Easting to 9,700km Northing. The most apparent problem is that for <br>
reasonable demonstration the results should be presented as contour maps of <br>
the errors but inclusion of same is not possible in this email list.<br>
<br>
A simple summary can be made: in the lat-lon tests tmerc maintained an <br>
accuracy of <0.7mm (as would be expected occurred at the equator) and <br>
comparison of etmerc and ftmerc was always less than 1micron. In the <br>
Easting/Northing test, tmerc failed dismally at 21 meters at about 58degrees <br>
longitude/84.78 degree latitude. Again, ftmerc and etmerc maintained <br>
agreement to within 1micron.<br>
<br>
I believe it is quite safe to say that tmerc remains the projection of choice <br>
for UTM applications: adequate accuracy performance and best computational <br>
speed. Note that the lat/lon test was for 12 degree zones and thus tmerc is <br>
would appear suitable for what I understand of the 10 degree zones used for <br>
some Canadian province grids.<br>
<br>
As for extended range, I will probably check the agreement of etmerc and <br>
ftmerc over extended range but this is of lesser priority. Extended <br>
geographic range usage of any conformal projection is a contentious issue as <br>
any resultant grid system has sufficiently large scale errors as to make the <br>
Cartesian usage of the grid very questionable. Usage of conformal maps for <br>
global mapping is very questionable because of the distortion. Normal <br>
Mercator persists only because of its usefulness in rhumbline navigation <br>
which is probably fading due to GPS. Lastly, equal-area mapping is far <br>
preferable for thematic mapping as it at least give a better perspective of <br>
the area extent of regions that is, in most cases, more important that an <br>
often poor preservation of regional shape.<br>
-- <br>
The whole religious complexion of the modern world is due<br>
to the absence from Jerusalem of a lunatic asylum.<br>
-- Havelock Ellis (1859-1939) British psychologist<br>
_______________________________________________<br>
Proj mailing list<br>
<a __removedlink__1353630948__href="mailto:Proj@lists.maptools.org">Proj@lists.maptools.org</a><br>
<a __removedlink__1353630948__href="http://lists.maptools.org/mailman/listinfo/proj" target="_blank">http://lists.maptools.org/mailman/listinfo/proj</a>
</tt></pre>
</div>
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