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<p class=MsoNormal><font size=3 color=black face="Comic Sans MS"><span
style='font-size:12.0pt;font-family:"Comic Sans MS";color:black'>daan, Mikael,
Cliff, and others,<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 color=black face="Comic Sans MS"><span
style='font-size:12.0pt;font-family:"Comic Sans MS";color:black'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=3 color=black face="Comic Sans MS"><span
style='font-size:12.0pt;font-family:"Comic Sans MS";color:black'>Thanks for
your persistence. Indeed, clarifying our terminology will help. For
me the Google Sphere (GS) is simply an ellipsoid with an eccentricity squared
of zero and semi-major axis (a) equal to the semi-major axis of the WGS84
ellipsoid. In this case the semi-minor axis (b) equals the semi-major
axis. <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 color=black face="Comic Sans MS"><span
style='font-size:12.0pt;font-family:"Comic Sans MS";color:black'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=3 color=black face="Comic Sans MS"><span
style='font-size:12.0pt;font-family:"Comic Sans MS";color:black'>Now, the
Google Sphere can have both geodetic and cartographic applications. That
distinction is admittedly confusing in this thread. I react viscerally to
the introduction of the GS into the WGS84 datum as a geodetic abomination.
You and Mikael see the GS as merely an intermediate stage in a total projection
method (which is non-conformal and, therefore, not the Mercator projection, and
about which you are both defensive). Cliff sees the GS as both bad
geodesy and as bad cartography. Frankly, I agree with Cliff. I also
accept Richard’s admonition to keep it civil.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 color=black face="Comic Sans MS"><span
style='font-size:12.0pt;font-family:"Comic Sans MS";color:black'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=3 color=black face="Comic Sans MS"><span
style='font-size:12.0pt;font-family:"Comic Sans MS";color:black'>So, before
moving on to the cartography, I’ll briefly recap my geodetic
objections. My physical geodesy argument is that since WGS84 is a best
fit to the geoid and since the Google Sphere is a terrible fit to the geoid no
matter how you orientate it, using the Google Sphere obviates reference to the WGS84
datum (in my opinion). <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 color=black face="Comic Sans MS"><span
style='font-size:12.0pt;font-family:"Comic Sans MS";color:black'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=3 color=black face="Comic Sans MS"><span
style='font-size:12.0pt;font-family:"Comic Sans MS";color:black'>My geometric
geodesy argument would be that geodesic direct and inverse computations would get
different results on the WGS84 ellipsoid and the GS no matter how you map the
WGS84 graticule onto the GS graticule. This is an indictment of the use
of the GS, since WGS84 computations better represent physical reality. No
one has suggested geodesic computations on the GS in this thread, but the
implicit association of the GS with WGS84 by Google regrettably risks that
abuse.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 color=black face="Comic Sans MS"><span
style='font-size:12.0pt;font-family:"Comic Sans MS";color:black'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=3 color=black face="Comic Sans MS"><span
style='font-size:12.0pt;font-family:"Comic Sans MS";color:black'>My appeals to
conventional practice are even more compelling in my view, though you may
disagree. For example, ED50 geodesic direct and inverse computations and
ED50 map projections are computed _only_ on the International ellipsoid. Why?
Computation on the ellipsoid of a datum’s least-squares adjustment
provides (by definition) the best conformation with physical reality and the
convention of doing so protects us from ignorant mistakes. We all (I believe)
follow this practice everywhere in the world (except in our use of Google Maps).
The risk to conventional practice introduced by Google is not progress.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 color=black face="Comic Sans MS"><span
style='font-size:12.0pt;font-family:"Comic Sans MS";color:black'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=3 color=black face="Comic Sans MS"><span
style='font-size:12.0pt;font-family:"Comic Sans MS";color:black'>Now, on to the
cartography. Having reread Mikael’s postings I appreciate (and
accept) his and daan’s perspective that this is a cartographic –
and not a geodetic – issue. The WGS84 datum can underlie this (unfortunate)
two-stage projection used by Google Maps (Mikael’s alternative A). Regarding
Mikael’s alternative B, I’ll have to study the EPSG Mercator methods
first before commenting. And regarding daan’s interpretation that
only one "ellipsoid" involved on the projection side, and that is the
"Google Sphere", I don’t see it yet. I stated previously
that the spherical Mercator projection is intuitively conformal. The
ellipsoidal Mercator is conformal over a range of eccentricity squared values
and there is no reason that that range shouldn’t include zero (the
sphere) while maintaining conformality. But first there is the
non-conformal mapping from the WGS84 ellipsoid to the Google Sphere before the
Mercator equations are applied. So, one thing is certain (and has already
been stated in this thread), and that is that the Google Maps projection cannot
be called the Mercator. It’s something else. Mikael
quantified the maximum angular distortion as 0.2 degrees. At this point
I’ll have to agree with Cliff that this is retrograde cartography. Quoting
Cliff, “using equivalent spheres in 19th and early 20th century
cartography was an attempt to simplify ellipsoidal computations” and
quoting Mikael, “the situation is similar to the French truncated Lambert
Conformal Conic, which is not exactly conformal, and is a different projection
than the true Lambert Conformal Conic”. My question is, Why are we
doing this in the 21<sup>st</sup> century?!? This is retrograde
cartography even if (no, especially if) the explanation is computational efficiency
(in light of the “clouds” of computers maintained by Google).
Google had an opportunity to expose a wide audience to good geodetic and
cartographic practice, but instead Google is exposing that audience to
malpractice (in my opinion). Yes, this is a judgment. And daan will
respond that it works for their purposes. I’m not so sure.
Google Maps is being used for lots of creative purposes encouraged by
Google. I believe that some user will stumble due to the poor choices
made by Google. Perhaps that can be documented in another thread. <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 color=black face="Comic Sans MS"><span
style='font-size:12.0pt;font-family:"Comic Sans MS";color:black'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=3 color=black face="Comic Sans MS"><span
style='font-size:12.0pt;font-family:"Comic Sans MS";color:black'>Regards and
thanks for the great discussion,<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 color=black face="Comic Sans MS"><span
style='font-size:12.0pt;font-family:"Comic Sans MS";color:black'>Noel Zinn<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 color=black face=Arial><span style='font-size:
12.0pt;font-family:Arial;color:black'><o:p> </o:p></span></font></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="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></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="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
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