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

Oscar van Vlijmen ovv at hetnet.nl
Tue Jun 27 09:18:24 EDT 2006

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.

Geodätisches Seminar zum Thema Koordinatentransformationen mittels einer
analytischen Lösung der Gaußschen Abbildung
Michael Gendt, Frank Oheim, Stephan Gehrke
Technische Universität Berlin, 2000-12-21
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

>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?

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