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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'>daan,<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'>Your objection constitutes a valid
perspective, as we agreed. I have a different perspective.<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 fact that “</span></font>the
original geographic coordinates are recoverable through a known, rigorous
process” d<font size=2 color=navy face=Arial><span style='font-size:10.0pt;
font-family:Arial;color:navy'>oes not support your case. The geographic
coordinates of the original datum are always recoverable with a reverse
transformation from the geographicals of the transformed datum (well, except
for the 10-parameter Molodensky-Badekas, which is almost invertible with negligible
discrepancies). That’s why consistent use of the same transformation is
more important than switching to a “more accurate” transformation
as new empirical evidence comes in. <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'>But you make a strong point in that “</span></font>There
is nothing empirical; no information is lost; and there is no error”, a<font
size=2 color=navy face=Arial><span style='font-size:10.0pt;font-family:Arial;
color:navy'>t least in the mathematical sense. On the other hand, my
experience is replete with naïve users switching ellipsoids with zero
geocentric offsets and getting into trouble. This is risky behavior that
should be discouraged in my perspective (working in an industry that is already
risky). But your statement is technically correct. Furthermore, this
ellipsoid switch in the first stage of Google Maps Projection (GMP) is not a
transformation of the 7-parameter of the similarity type (Helmert, Bursa Wolf),
which is conformal, at least in ECEF (XYZ) space. We have already established
that this ellipsoid switch is the cause of the non-conformality in the GMP. <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'>However, I take issue with your statement that
Google “</span></font>have simply defined a map projection”. A<font
size=2 color=navy face=Arial><span style='font-size:10.0pt;font-family:Arial;
color:navy'>ny defined map projection should have defined distortions, even
non-conformal projections. I demonstrated how a user can extract geodesic
distances from grid coordinates and point scale factors using Simpson’s
Approximation. That’s the way most surveyors work (I believe), not using
(recovered) geographicals and geodesic computations, though we may agree that’s
the best route. What user knows to take the WGS84 ratio of rho and nu (the
radii of curvature in the meridian and prime vertical) with the Equatorial
radius and apply those to the spherical Mercator point scales in order to find
the real distortions in GMP? If Google haven’t defined that they haven’t
defined a map projection. If they have, I’d appreciate a reference.<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'>These issues are buried in the noise for
small scale maps, as you have mentioned. But the “novelty” of GMP is
my concern, and that is that these undocumented distortions are present in
large scale maps that might be used for real work in the field. <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'>We have different perspectives. On one
hand, GMP is just another projection in the universe of possible projections
(which is true). On the other hand, GMP is risky (I’d rather say
deviant) cartographic behavior (which is also true). <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 catching my lapse,<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<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>
<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>strebe<br>
<b><span style='font-weight:bold'>Sent:</span></b> Sunday, December 07, 2008
8:09 PM<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> [Proj] RE: "Double
Ellipsoid" error, reproduction</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'>Noel, I object to this characterization:<o:p></o:p></span></font></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=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=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
</div>
<p class=MsoNormal><span class=apple-style-span><font size=1
face=-webkit-monospace><span style='font-size:8.5pt;font-family:-webkit-monospace'>Map
conversions (geographical</span></font></span><font size=1
face=-webkit-monospace><span style='font-size:8.5pt;font-family:-webkit-monospace'><br>
<span class=apple-style-span>to grid) are merely mathematical mappings that are
(theoretically) without</span><br>
<span class=apple-style-span>empirical error. Except - and this is my objection
in this thread</span><br>
<span class=apple-style-span>heretofore - except when the ellipsoid is changed
and a datum transformation</span><br>
<span class=apple-style-span>is implicitly coupled with a map conversion.</span></span></font><o:p></o:p></p>
<div>
<p class=MsoNormal><span class=apple-style-span><font size=1
face=-webkit-monospace><span style='font-size:8.5pt;font-family:-webkit-monospace'>______</span></font></span><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=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=3 face="Times New Roman"><span style='font-size:
12.0pt'>As we discussed, the original geographic coordinates are recoverable
through a known, rigorous process. There is nothing empirical; no information
is lost; and there is no error. There is not even a good reason to state that
the datum has changed in the case of Google Maps. They have simply defined a
map projection of WGS84 that is not conformal.<o:p></o:p></span></font></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><span class=apple-style-span><font size=1 face=Helvetica><span
style='font-size:9.0pt;font-family:Helvetica'>Regards,</span></font></span><o:p></o:p></p>
</div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>— daan Strebe<o:p></o:p></span></font></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=1 face=-webkit-monospace><span style='font-size:
8.5pt;font-family:-webkit-monospace'><br>
</span></font>On Dec 7, 2008, at 8:30:09 AM, "Noel Zinn"
<ndzinn@comcast.net> wrote:<o:p></o:p></p>
<div><span style='orphans: 2;text-align:auto;widows: 2;-webkit-border-horizontal-spacing: 0px;
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-webkit-text-size-adjust: auto;-webkit-text-stroke-width: 0;word-spacing:0px'>
<div style='border:none;border-bottom:solid silver 1.0pt;padding:0in 0in 12.0pt 0in;
margin-bottom:12.0pt' id=felix-mail-header-block>
<table class=MsoNormalTable border=0 cellspacing=1 cellpadding=0 width="100%"
style='width:100.0%'>
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<td valign=top style='padding:.75pt .75pt .75pt .75pt'>
<p class=MsoNormal align=right style='text-align:right'><b><font size=1
color=gray face="Lucida Grande"><span style='font-size:8.0pt;font-family:
"Lucida Grande";color:gray;font-weight:bold'>From:<o:p></o:p></span></font></b></p>
</td>
<td valign=top style='padding:.75pt .75pt .75pt 3.75pt'><span
title=""Noel Zinn" <ndzinn@comcast.net>">
<p class=MsoNormal><font size=1 color=black face="Lucida Grande"><span
style='font-size:8.0pt;font-family:"Lucida Grande";color:black'>"Noel
Zinn" <ndzinn@comcast.net></span><o:p></o:p></span></font></p>
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<p class=MsoNormal align=right style='text-align:right'><b><font size=1
color=gray face="Lucida Grande"><span style='font-size:8.0pt;font-family:
"Lucida Grande";color:gray;font-weight:bold'>Subject:<o:p></o:p></span></font></b></p>
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<td valign=top style='padding:.75pt .75pt .75pt 3.75pt'>
<p class=MsoNormal><b><font size=1 color=black face="Lucida Grande"><span
style='font-size:8.0pt;font-family:"Lucida Grande";color:black;font-weight:
bold'>RE: [Proj] "Double Ellipsoid" error, reproduction</span></font></b><font
size=1 color=black face="Lucida Grande"><span style='font-size:8.0pt;
font-family:"Lucida Grande";color:black'><o:p></o:p></span></font></p>
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<td valign=top style='padding:.75pt .75pt .75pt .75pt'>
<p class=MsoNormal align=right style='text-align:right'><b><font size=1
color=gray face="Lucida Grande"><span style='font-size:8.0pt;font-family:
"Lucida Grande";color:gray;font-weight:bold'>Date:<o:p></o:p></span></font></b></p>
</td>
<td valign=top style='padding:.75pt .75pt .75pt 3.75pt'>
<p class=MsoNormal><font size=1 color=black face="Lucida Grande"><span
style='font-size:8.0pt;font-family:"Lucida Grande";color:black'>December 7,
2008 8:30:09 AM PST<o:p></o:p></span></font></p>
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<p class=MsoNormal align=right style='text-align:right'><b><font size=1
color=gray face="Lucida Grande"><span style='font-size:8.0pt;font-family:
"Lucida Grande";color:gray;font-weight:bold'>To:<o:p></o:p></span></font></b></p>
</td>
<td valign=top style='padding:.75pt .75pt .75pt 3.75pt'><span
title=""'PROJ.4 and general Projections Discussions'" <proj@lists.maptools.org>">
<p class=MsoNormal><font size=1 color=black face="Lucida Grande"><span
style='font-size:8.0pt;font-family:"Lucida Grande";color:black'>"'<st1:PersonName
w:st="on">PROJ.4 and general Projections Discussions</st1:PersonName>'"
<proj@lists.maptools.org></span><o:p></o:p></span></font></p>
</td>
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<div id=felix-mail-content-block>
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<p class=MsoNormal style='margin-bottom:12.0pt;background:white'><font size=1
color=black face="Courier New"><span style='font-size:8.0pt;font-family:"Courier New";
color:black'>Gerald,<br>
<br>
The input and output of datum transformations are geographical coordinates.<br>
Some methods of datum transformation (e.g. NADCON, NTv2, multiple regression<br>
equations) work in geographicals and ellipsoid parameters are not required.<br>
Other methods of datum transformations (e.g. 3 through 7 parameter<br>
similarity, Helmert, Bursa-Wolf, 10-parameter Molodensky-Badekas) require a<br>
transit through geocentric Cartesian, Earth-Centered Earth-Fixed (ECEF)<br>
coordinates for which ellipsoid parameters are required. Datum<br>
transformation parameters are always empirically derived and spatially<br>
variant and, therefore, always contain error. Map conversions (geographical<br>
to grid) are merely mathematical mappings that are (theoretically) without<br>
empirical error. Except - and this is my objection in this thread<br>
heretofore - except when the ellipsoid is changed and a datum transformation<br>
is implicitly coupled with a map conversion.<br>
<br>
So, the answers to your questions are (1) true and (2) false (in some<br>
cases).<br>
<br>
You are absolutely correct that there is no LAW about what a cartographer<br>
does, limited by his or her own imagination, but there is a physical reality<br>
for those who have an interest in conforming to it as closely as possible.<br>
The best fit between physical reality and geographical coordinates is<br>
defined by the ellipsoid in which the datum's least-squares adjustment of<br>
survey data (collected in the real world, not in pixel space) was done.<br>
Change the ellipsoid and the quality of the fit deteriorates (even in a<br>
datum transformation and especially in a map conversion). I already<br>
demonstrated in this thread that Google Maps Projection grid coordinates<br>
bear an undocumented relationship with physical reality for the casual user.<br>
<br>
<br>
Regards,<br>
Noel<br>
<br>
-----Original Message-----<br>
From: proj-bounces@lists.maptools.org<br>
[mailto:proj-bounces@lists.maptools.org] On Behalf Of Gerald I. Evenden<br>
Sent: Sunday, December 07, 2008 9:25 AM<br>
To: <st1:PersonName w:st="on">PROJ.4 and general Projections Discussions</st1:PersonName><br>
Subject: Re: [Proj] "Double Ellipsoid" error, reproduction<br>
<br>
I find this thread so incredible confusing I have tried to stay out of it<span
class=apple-converted-space> </span><br>
entirely but I have one, maybe two questions:<br>
<br>
I thought the basic detail operations of datum conversion were done in<span
class=apple-converted-space> </span><br>
geographic data space (latitude-longitude) or perhaps x-y-z. That is, you<span
class=apple-converted-space> </span><br>
have to have the data in geographic space to do the datum conversion<span
class=apple-converted-space> </span><br>
calculation. True or False?<br>
<br>
Also, ellipsoid factors are not part of the datum conversion as long as the<span
class=apple-converted-space> </span><br>
data is in geographic coordinates: True or False?<br>
<br>
If the above is true, what does the ellipsoid values have to do with<br>
anything?<span class=apple-converted-space> </span><br>
That is a rhetorical question and the answer is obviously: nothing.<br>
<br>
The question of the ellipsoid parameters only comes up when dealing with<br>
data<span class=apple-converted-space> </span><br>
in Cartesian coordinates which need to be transformed back to geographic<span
class=apple-converted-space> </span><br>
coordinates for datum transformation. The ellipsoid values are only a<br>
factor<span class=apple-converted-space> </span><br>
in de-projecting the points.<br>
<br>
The ellipsoid chosen for the Cartesian projection is probably a capricious<br>
and<span class=apple-converted-space> </span><br>
arbitrary choice of the people who created the projected data in the first<span
class=apple-converted-space> </span><br>
place. I know of no LAW that requires someone to choose a particular<span
class=apple-converted-space> </span><br>
ellipsoid purely because of the datum of the data. The plotter may not have<br>
<br>
any idea as to the datum of the data.<br>
<br>
If the issue is simply two completely separate operations--- datum<br>
conversion<span class=apple-converted-space> </span><br>
and ellipsoid-projection--- then what is all the discussion about???<br>
<br>
What I am arguing is that the use of the ellipsoid parameters and datum<span
class=apple-converted-space> </span><br>
conversion are two completely separate issues. Thus the problem discussed<br>
in<span class=apple-converted-space> </span><br>
this thread is merely an issue finding the correct ellipsoid to get data<br>
back<span class=apple-converted-space> </span><br>
into geographic coordinates, doing a datum conversion, and selecting an<span
class=apple-converted-space> </span><br>
arbitrary a new ellipsoid for the target display map.<br>
<br>
--<span class=apple-converted-space> </span><br>
The whole religious complexion of the modern world is due<br>
to the absence from <st1:City w:st="on"><st1:place w:st="on">Jerusalem</st1:place></st1:City>
of a lunatic asylum.<br>
-- Havelock Ellis (1859-1939) British psychologist<br>
_______________________________________________<br>
Proj mailing list<br>
Proj@lists.maptools.org<br>
http://lists.maptools.org/mailman/listinfo/proj<br>
<br>
_______________________________________________<br>
Proj mailing list<br>
Proj@lists.maptools.org<br>
http://lists.maptools.org/mailman/listinfo/proj<o:p></o:p></span></font></p>
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<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
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