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<DIV dir=ltr align=left><SPAN class=215070509-01122008><FONT
face=Arial>Noel,</FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=215070509-01122008><FONT face=Arial>I
haven't checked your results, but there is no reason to expect that
</FONT></SPAN><SPAN class=215070509-01122008><FONT face=Arial>the two results
would be the same. </FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=215070509-01122008><FONT
face=Arial></FONT></SPAN> </DIV>
<DIV dir=ltr align=left><SPAN class=215070509-01122008><FONT face=Arial>As I see
it, Ellipsoid Mercator is one projection, and Sphere Mercator is a different
one. </FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=215070509-01122008><FONT face=Arial>Each one
is internally consistent, but the two are not the same. That is, since the
formulas </FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=215070509-01122008><FONT face=Arial>are
different, the (Easting,Northing) values are not the same for the same
(Lon,Lat). But </FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=215070509-01122008><FONT face=Arial>for each
projection, you can use its inverse to get exactly back to the original
(Lon,Lat). </FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=215070509-01122008><FONT
face=Arial></FONT></SPAN> </DIV>
<DIV dir=ltr align=left><SPAN class=215070509-01122008><FONT face=Arial>The
Ellipsoid Mercator is exactly conformal </FONT></SPAN><SPAN
class=215070509-01122008><FONT face=Arial>while Sphere Mercator is only
approximately conformal</FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=215070509-01122008><FONT face=Arial>(if you
regard the ellipsoid as the true shape of the Earth). I think the maximal
angle distortion </FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=215070509-01122008><FONT face=Arial>for
Sphere Mercator is 0.2 degrees, so for visual display it is hard to
notice.</FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=215070509-01122008><FONT
face=Arial></FONT></SPAN> </DIV>
<DIV dir=ltr align=left><SPAN class=215070509-01122008><FONT face=Arial>Since
the projections are distinct, we should not expect that analoguous calculations
done </FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=215070509-01122008><FONT face=Arial>in their
projected planes should </FONT></SPAN><SPAN class=215070509-01122008><FONT
face=Arial>give identical results. </FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=215070509-01122008><FONT
face=Arial></FONT></SPAN> </DIV>
<DIV dir=ltr align=left><SPAN class=215070509-01122008><FONT face=Arial>So, the
situation is similar to the French truncated Lambert Conformal Conic, which is
</FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=215070509-01122008><FONT face=Arial>not
exactly conformal, and is a different projection than the true Lambert Conformal
Conic. </FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=215070509-01122008><FONT
face=Arial></FONT></SPAN> </DIV>
<DIV dir=ltr align=left><SPAN class=215070509-01122008><FONT face=Arial>It is
tricky to create WKT to represent the Sphere Mercator projection together with
an ellipsoid datum. </FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=215070509-01122008><FONT face=Arial>But that
is a failure of WKT, not of the Sphere Mercator. One way to express it in
WKT has </FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=215070509-01122008><FONT face=Arial>been
suggested by Martin Desruisseaux of GeoTools, another way by Melita Kennedy of
ESRI. </FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=215070509-01122008><FONT face=Arial>See the
August 2008 archives for the MetaCRS mailing list, </FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=215070509-01122008><FONT face=Arial><A
href="http://lists.osgeo.org/pipermail/metacrs/2008-August/thread.html">http://lists.osgeo.org/pipermail/metacrs/2008-August/thread.html</A> .
</FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=215070509-01122008><FONT
face=Arial></FONT></SPAN> </DIV>
<DIV dir=ltr align=left><SPAN class=215070509-01122008><FONT face=Arial>And it
is not only Google that uses spherical projections. So does
</FONT></SPAN><SPAN class=215070509-01122008><FONT face=Arial>the National Snow
and Ice Data Center, USA. </FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=215070509-01122008><FONT face=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></FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=215070509-01122008><FONT
face=Arial></FONT></SPAN> </DIV>
<DIV dir=ltr align=left><SPAN class=215070509-01122008><FONT face=Arial>I think
it is unfortunate that EPSG insists that a spherical projection can only be used
</FONT></SPAN><SPAN class=215070509-01122008><FONT face=Arial>together with a
spherical datum, because </FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=215070509-01122008><FONT face=Arial>a) it is
not true,</FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=215070509-01122008><FONT face=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>).
</FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=215070509-01122008><FONT
face=Arial></FONT></SPAN> </DIV>
<DIV dir=ltr align=left><SPAN class=215070509-01122008><FONT face=Arial>Best
regards,</FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=215070509-01122008><FONT
face=Arial></FONT></SPAN> </DIV>
<DIV dir=ltr align=left><FONT size=2>--<BR>Mikael Rittri<BR>Carmenta AB<BR>Box
11354<BR>SE-404 28 Göteborg<BR>Visitors: Sankt Eriksgatan 5<BR>SWEDEN<BR>Tel:
+46-31-775 57 37<BR>Mob: +46-703-60 34
07<BR>mikael.rittri@carmenta.com<BR>www.carmenta.com</FONT> </DIV>
<DIV><FONT face=Arial></FONT> </DIV><BR>
<DIV class=OutlookMessageHeader lang=en-us dir=ltr align=left>
<HR tabIndex=-1>
<FONT face=Tahoma size=2><B>From:</B> proj-bounces@lists.maptools.org
[mailto:proj-bounces@lists.maptools.org] <B>On Behalf Of </B>Noel
Zinn<BR><B>Sent:</B> den 30 november 2008 06:05<BR><B>To:</B> 'PROJ.4 and
general Projections Discussions'<BR><B>Subject:</B> RE: [Proj] "Double
ellipsoid" case?<BR></FONT><BR></DIV>
<DIV></DIV>
<DIV class=Section1>
<P class=MsoNormal><FONT face=Arial color=navy size=2><SPAN
style="FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial">Not that Frank is
responsible for the geodesy and cartography in Google Maps (or their abuse
therein), but the phrase “</SPAN></FONT><FONT face=Arial size=2><SPAN
style="FONT-SIZE: 10pt; 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 face=Arial color=navy size=2><SPAN
style="FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial"><o:p> </o:p></SPAN></FONT></P>
<P class=MsoNormal><FONT face=Arial color=navy size=2><SPAN
style="FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial">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 face=Arial color=navy size=2><SPAN
style="FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial"><o:p> </o:p></SPAN></FONT></P>
<P class=MsoNormal><FONT face=Arial color=navy size=2><SPAN
style="FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial">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 face=Arial color=navy size=2><SPAN
style="FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial"><o:p> </o:p></SPAN></FONT></P>
<P class=MsoNormal><FONT face=Arial color=navy size=2><SPAN
style="FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial">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 face=Arial color=navy size=2><SPAN
style="FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial"><o:p> </o:p></SPAN></FONT></P>
<P class=MsoNormal><FONT face=Arial color=navy size=2><SPAN
style="FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial">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 face=Arial color=navy size=2><SPAN
style="FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial"><o:p> </o:p></SPAN></FONT></P>
<P class=MsoNormal><FONT face=Arial color=navy size=2><SPAN
style="FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial">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 face=Arial color=navy size=2><SPAN
style="FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial"><o:p> </o:p></SPAN></FONT></P>
<P class=MsoNormal><FONT face=Arial color=navy size=2><SPAN
style="FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial">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 face=Arial size=2><SPAN
style="FONT-SIZE: 10pt; 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 face=Arial size=2><SPAN
style="FONT-SIZE: 10pt; FONT-FAMILY: Arial"><o:p> </o:p></SPAN></FONT></P>
<P class=MsoNormal><FONT face=Arial size=2><SPAN
style="FONT-SIZE: 10pt; 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 face=Arial color=navy size=2><SPAN
style="FONT-SIZE: 10pt; COLOR: navy; FONT-FAMILY: Arial"><o:p> </o:p></SPAN></FONT></P>
<DIV>
<DIV class=MsoNormal style="TEXT-ALIGN: center" align=center><FONT
face="Times New Roman" size=3><SPAN style="FONT-SIZE: 12pt">
<HR tabIndex=-1 align=center width="100%" SIZE=2>
</SPAN></FONT></DIV>
<P class=MsoNormal><B><FONT face=Tahoma size=2><SPAN
style="FONT-WEIGHT: bold; FONT-SIZE: 10pt; FONT-FAMILY: Tahoma">From:</SPAN></FONT></B><FONT
face=Tahoma size=2><SPAN style="FONT-SIZE: 10pt; 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 face="Times New Roman" size=3><SPAN
style="FONT-SIZE: 12pt"><o:p> </o:p></SPAN></FONT></P>
<DIV id=idOWAReplyText1252>
<DIV>
<P class=MsoNormal><FONT face="Times New Roman" color=black size=2><SPAN
style="FONT-SIZE: 10pt; COLOR: black">Frank:</SPAN></FONT><o:p></o:p></P></DIV>
<DIV>
<P class=MsoNormal><FONT face="Times New Roman" size=3><SPAN
style="FONT-SIZE: 12pt"> <o:p></o:p></SPAN></FONT></P></DIV>
<DIV>
<P class=MsoNormal><FONT face="Times New Roman" size=2><SPAN
style="FONT-SIZE: 10pt">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 face="Times New Roman" size=3><SPAN
style="FONT-SIZE: 12pt"> <o:p></o:p></SPAN></FONT></P></DIV>
<DIV>
<P class=MsoNormal><FONT face="Times New Roman" size=2><SPAN
style="FONT-SIZE: 10pt">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 face="Times New Roman" size=3><SPAN
style="FONT-SIZE: 12pt"> <o:p></o:p></SPAN></FONT></P></DIV>
<DIV>
<P class=MsoNormal><FONT face="Times New Roman" size=2><SPAN
style="FONT-SIZE: 10pt">Cliff Mugnier</SPAN></FONT><o:p></o:p></P></DIV>
<DIV>
<P class=MsoNormal><FONT face="Times New Roman" size=2><SPAN
style="FONT-SIZE: 10pt">LSU</SPAN></FONT><o:p></o:p></P></DIV></DIV>
<DIV>
<P class=MsoNormal><FONT face="Times New Roman" size=3><SPAN
style="FONT-SIZE: 12pt"><o:p> </o:p></SPAN></FONT></P>
<DIV class=MsoNormal style="TEXT-ALIGN: center" align=center><FONT
face="Times New Roman" size=3><SPAN style="FONT-SIZE: 12pt">
<HR tabIndex=-1 align=center width="100%" SIZE=2>
</SPAN></FONT></DIV>
<P class=MsoNormal style="MARGIN-BOTTOM: 12pt"><B><FONT face=Tahoma size=2><SPAN
style="FONT-WEIGHT: bold; FONT-SIZE: 10pt; FONT-FAMILY: Tahoma">From:</SPAN></FONT></B><FONT
face=Tahoma size=2><SPAN style="FONT-SIZE: 10pt; 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 face="Times New Roman" size=2><SPAN
style="FONT-SIZE: 10pt">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>_______________________________________________<BR>Proj mailing
list<BR>Proj@lists.maptools.org<BR><A
href="http://lists.maptools.org/mailman/listinfo/proj">http://lists.maptools.org/mailman/listinfo/proj</A></SPAN></FONT><o:p></o:p></P></DIV></DIV></BODY></HTML>