[Proj] Unknown projection?

[Gerald I. Evenden]

On Saturday 13 September 2008 2:59:01 pm OvV_HN wrote:
> ----- Original Message -----
> From: "Paul B. Anderson" <pbander at cavtel.net>
> To: "PROJ.4 and general Projections Discussions" <proj at lists.maptools.org>
> Sent: Saturday, September 13, 2008 6:26 PM
> Subject: Re: [Proj] Unknown projection?
>
> > One person who has researched the inverse Winkel Tripel formulas issue is
> > Dr. Robert Schmunk http://www.giss.nasa.gov/staff/rschmunk.html
>
> Let's not forget:
>
> A GENERAL ALGORITHM FOR THE INVERSE TRANSFORMATION OF
> MAP PROJECTIONS USING JACOBIAN MATRICES,
> Cengizhan Ipbüker, I.Öztug Bildirici
> Proceedings of the Third International Symposium Mathematical &
> Computational Applications
> September 4-6, 2002. Konya, Turkey, pp. 175-182
> Istanbul Tech. University Faculty of Civil Eng., Div. of Cartography,
> Maslak Istanbul,
> Turkey
> Selcuk University, Faculty of Eng., Dept. of Geodesy & Photogrammetry,
> Konya,
> Turkey
> http://atlas.selcuk.edu.tr/paperdb/papers/130.pdf
>
> With a Newton iteration procedure for the inverse of Aitoff-Hammer,
> Winkel-Tripel and Mollweide.
>
> Oscar van Vlijmen

Yes, yes, an obvious approach and, as I was referring to earlier, one that can 
cost cpu ticks because it is an iterative process---bivariate Newton-Raphson.  
In addition, there can be problems with initial phi/lamda estimates but in 
this case they should not be too difficult.  A nasty bit is coming up with 
analytic derivatives or failing that, the more costly process of making 
numerical derivatives---more iterations on the forward equations and hassles 
near the projection limits with altering the numerical steps.  Etc., 
etc. ... .

One last problem is for those who might chafe under a GNU license because I 
would use GNU's Scientific Library for such efforts.  One projection in 
libproj4 already uses GSL but makefile flags allow for its exclusion if the 
eventual user does not have nor want the GSL library on their system.

Y'all may get a feeling for why I avoid the subject.  ;-)

-- 
The whole religious complexion of the modern world is due
to the absence from Jerusalem of a lunatic asylum.
-- Havelock Ellis (1859-1939) British psychologist