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

[Gerald I. Evenden]

On Tuesday 13 June 2006 2:59 pm, Oscar van Vlijmen wrote:
	...
> >> For small values of lon-lon0, say less than 6 degrees, tmerc et alii
> >> perform very well, so nothing can be gained using the above mentioned
> >> TMs.
> >
> > One might question the practical need to go beyond 6 degrees.
>
> I understand that among others, ESRI has been busy developing such a TM. So
> there must be a professional need for it.

It is an interesting academic problem but I fail to see any practical 
application.  Scale factor and large scale distortion goes to hell rapidly 
from the central meridian for any expanded Mercator aspect and thus 
unsuitable for cadastral or grid systems.  Old style navigation that 
justified Mercator navigations charts seems to be on the way out.  So other 
than demonstrating loxodromes what is the use of continental size 
Mercator---especially for the ellipsoid?

It seems peculiar that someone who has to watch expenditures would spend time 
on this activity.  There must be an unknown, external driving dollar.

Reminds me of the book about men who watch goats.

> > BTW: what did you use to get the "exact" values?
>
> My own stuff.
> I had a very hard time finding solid code. Several people are guarding the
> principles as a secret and are deliberately vague. Or they are trying to
> get solid money from it by selling software or books.

You may be right, but I do not see any visible results yet.  But again, I 
cannot see anyone in their right mind buying such stuff without there being a 
strong NEED.

> But I persevered in trying to get the Dozier show on the road.
> You (mr. Evenden) already found one error in his code, but this error has
> to be corrected in 3 places. It's the error of the elliptic parameter m,
> which has to be the elliptic modulus k in 3 cases (tmfd, gk, tmid).
> It appeared that the Dozier code - the complex Newton iteration - was
> useless in some regions, especially large lon-lon0 and low latitudes. First
> I used somewhat better elliptic functions from Cernlib. But, to more
> effect, I concocted another iteration scheme based on TOMS algorithm 365, a
> very slow downhill walkaround method, yet very powerful.
> I checked my results with an on-line calculator from professor Schuhr,
> based on the Klotz algorithms.

I believe I saw a reference to the Klotz article the calculator page.  Is it 
worthwhile?

> <http://gauss.fb1.fh-frankfurt.de/cgi-bin/cgi_gk>

Interesting site but the above url failed on my browsers and I had to back up 
two levels and guess my way in.  At the moment I have not figured out enough 
German to effectively work the calculator.  I have an easier time with 
French, can slowly work through simple German and throw up my hands in defeat 
with Polish.  :-(  And working in Grads is a bit of a nuisance.

An unrelated aside: most people are unaware that proj/lproj accepts radian 
input---suffix the value with r (0.123r).  It might be an idea to add a g 
suffix for grad.

> This calculator fails for difficult areas (very large lon-lon0, small lat).
> So I can only 'proof' my results in the difficult areas by doing a complete
> round-trip and getting nearly the original data back.
> And yes, I do the lon-lon0=90 degrees too.
>
> The Dozier article:
> <http://www2.bren.ucsb.edu/~dozier/publications.htm>

Dozier was nice enough to send me a copy but i got the feeling later that he 
had lost interest in the project.

-- 
Jerry and the low-riders: Daisy Mae and Joshua
"Cogito cogito ergo cogito sum"
   Ambrose Bierce, The Devil's Dictionary