@GabrielDeLuca thank you! :) and sorry for not passing by sooner

could anyone point me to a source? (and should I ask this on the main site?)

@Federico you re welcome. The formula for the ellipsoidal model of the direct and inverse transformation of UTM is not an iteration, but the expansion of a series, which can be implemented in different ways. I think the worst of the implementations ensures an error of less than a millimeter in the fourth term of the series, and the best of them less than a nanometer.

It is a good question to ask, if it is not yet asked, and a specialist's response would be welcome. In general, the development of the formulas is not very well researched, and we rely on the formulas already solved and the libraries that are already written implementing those formulas.

If you want to investigate it, a good starting point is the small section on implementations of the transformation in the ellipsoidal model of the wikipedia article on the Transverse Mercator projection: en.wikipedia.org/wiki/…

Regarding the Niko Lilja library, the implementation seems to be the one described in the specific UTM article: en.wikipedia.org/wiki/…

Regarding the confusion with the iterative method, I think it is due to the method used for the calculation of lengths of geodetic distances by spherical approximations.

The main problem there, is the ignorance of the parameters of the ellipse to which the curve belongs.

In determining a meridian arc, at least the parameters of the ellipse are known.

@GabrielDeLuca ah, I see. ok, I'll try to ask the question on monday, right now I don't have the references I've used so far at hand

thank you!