[Proj] Status of projection inverses
ovv at hetnet.nl
Sun Oct 26 06:19:26 EDT 2008
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
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
> 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
> deal of progress and converges faster than the simple Newton-Raphson and
> more tolerant of poor initial conditions.
> 3. gsl can also do the same job without a Jacobian requiring derivatives.
> those who have not already noticed, there are many inverseless projections
> where the derivatives would be impossible or nearly so---even with help
> Conclusions here are that I am going to finish up this project with the
> methodology in order to preserve my own sanity. ;-)
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