[Proj] Troubles with Newton-Raphson inverse projections

[support.mn at elisanet.fi]

"Gerald I. Evenden" <geraldi.evenden at gmail.com> kirjoitti: 
>
> Secondly, finding the root may also be difficult when the precision of the 
> derivatives start to fail.  This is the case near the poles of both the 
> Hammer and Aitoff projections.  At a latitude greater than 89° the method 
> fails for both these projections.  One also gets suspicious that this will 
> occur when the nature of the curve flattens out like the top of a sine curve.  
> I have not tried the flat pole Winkel Triplel yet.
> 

Can't you just switch the method near poles? Something like:

if (lat > 88) use_special_derivatives();
else use_normal_derivatives();

And figure out from the formulas (code) what is causing the problem near poles
and then eliminate that by using something that is more efficient near poles.

Regards: Janne.