[Proj] Re: Discovery: libproj4 stmerc = French Gauss-Laborde projection

[Oscar van Vlijmen]

From: Strebe-aol.com

>> What magic twist allows Wallis to come up with the above map when
>> all others want to extend to infinity?
> You are misunderstanding the problem. The others don't "want" to extend to
> infinity; their accuracy simply degrades into uselessness.

Recently I've been looking for a moment at the Transverse Mercator method
Michael Gendt et al. present in a seminar paper. I get the impression that
he is following Klotz from his 1993 publication.
The derived code is very lean, but fails in the same regions as Dozier's:
low latitude at high delta-longitude and above latitude 89.9999993 deg or
so. At low lat/high delta-long there can be convergence in the iterations,
but the answer is wrong.

Reference:
Geodätisches Seminar zum Thema Koordinatentransformationen mittels einer
analytischen Lösung der Gaußschen Abbildung
Michael Gendt, Frank Oheim, Stephan Gehrke
Technische Universität Berlin, 2000-12-21
<http://www.geodesy.tu-berlin.de/~rainer/seminararbeit/gendt/ut.pdf>
Equation 2.14c is wrong: d_n should be k_n.

Other methods - possibly Wallis' - perform a transformation and probably
reposition the difficult areas.
That means that under the finite precision of IEEE-754 math one has to use
two or three methods to cover really a complete (hemi)sphere with high
accuracy.

>From mr. Evenden:
> And a remaining note: this projection has not been published in an any
> cartographic journal and has not been subject to normal peer review nor the
> review of subsequent readers.
>From mr. Strebe:
> Wallis solves the boundary condition in a different way. It's not without its
> problems; you need to find a root which, for arbitrary eccentricities, defies
> any formulaic seed value. Nonetheless that can be solved efficiently in most
> cases and merely solved in all cases. There are one or two places where one
> must be careful of numeric techniques, like many other projections.
Hush hush, say no more - it's a secret!
Either big money or the NSA/CIA must be involved?
[One might want to grin or laugh at this point.]

By the way: will more discussions on this subject follow? Shouldn't we
change the subject title into "Complex Transverse Mercator" or so?