[Proj] Re: "Double ellipsoid" case?

Noel Zinn ndzinn at comcast.net
Tue Dec 2 10:31:14 EST 2008

daan, Mikael, Cliff, and others,


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


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.


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).  


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.


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.


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 21st 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.  


Regards and thanks for the great discussion,

Noel Zinn






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