Equations for meridian convergence and partial derivatives reviewed (corrected) #526
I have found strange results for meridian convergence in non-conformal projections. As we know from map projection books (with Gauss-Bomford convention for convergence), meridian convergence should be calculated by formula fac->conv = - atan2(fac->der.x_p , fac->der.y_p).
Current formula used in Proj4 is fac->conv = - atan2(fac->der.y_l , fac->der.x_l), which can be useful only for conformal projections (due to Cauchy-Riemann equations), and in fact should be without minus sign, i.e. fac->conv = atan2(fac->der.y_l , fac->der.x_l). For non-conformal projections we now get angle between parallel and x-axis, instead of meridian convergence.
Minus sign currently used in formula comes from fact that fac->der.x_p and fac->der.y_l are calculated with opposite signs.
Corrected equations are:
One can question the practical use of meridian convergence in non-conformal projections, but nevertheless, it would be nice to have it calculated correctly.
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I am not able to comment on the details of this without researching a bit first, but at least it sounds sensible.
I have created a pull request with your changes in #527. I have reformatted the code as well. Please check that the changes are equivalent to your suggestion.