[Proj] Status of projection inverses

[OvV_HN]

I can't see why it is necessary to go through all the computational overhead 
of GNU GSL.
The inverse of the Winkel-Tripel as outlined in the Ipbucker-Bildirici paper 
didn't give much problems, apart from some extreme regions which should be 
forbidden.
The inverse of the Aitoff-Hammer was even less problematic. Only for a 
latitude of +/-90d the longitude couldn't be restored from the inverse, but 
this situation can probably be cured in another way.
The Aitoff-Hammer needed only a couple of iterations (less than 11 for a 
loop-break error of 1e-14). For starting values in the iteration I simply 
used lat=0, lon=0.
So, please enlighten me and tell us where the actual problems can be found.

Oscar van Vlijmen


----- Original Message ----- 
From: "Gerald I. Evenden" <geraldi.evenden at gmail.com>
To: "PROJ.4 and general Projections Discussions" <proj at lists.maptools.org>
Sent: Sunday, October 26, 2008 3:43 AM
Subject: [Proj] Status of projection inverses


> Several days have gone by without any comments on the subject but that 
> does
> not mean that I am not working on it.
>
> 1. trying to get a better initial  guess process via some rough polynomial
> method pretty well went up in flames.
>
> 2. but using the gsl library of multidimensional root finding shows a 
> great
> deal of progress and converges faster than the simple Newton-Raphson and 
> is
> more tolerant of poor initial conditions.
>
> 3. gsl can also do the same job without a Jacobian requiring derivatives. 
> For
> those who have not already noticed, there are many inverseless projections
> where the derivatives would be impossible or nearly so---even with help 
> from
> maxima.
>
> Conclusions here are that I am going to finish up this project with the 
> gsl
> methodology in order to preserve my own sanity.  ;-)