[PROJ] Geodetic to Authalic latitude conversions

[Even Rouault]

> We will surely find out when we run the unit tests for those projections?

Not sure which tolerance they have and how much those projections are 
tested (do not forget that much of the regression test suite was 
automatically generated with the results PROJ produced at that time, so 
with quite generic tolerances, etc.). I was more thinking about manually 
testing with proj/cct binaries before and after, and see the differences

>
>> It is also not immediately obvious to me to correlate your proposed 
>> code with the formulas in the paper by just starring at both at the 
>> same time. Looks like some "interpretation" of the paper has been done.
>>
> It's quite straightforward, but optimized for the precalculations like 
> PROJ was doing in /auth.cpp/. There is no "interpretation" involved.
Well, what you mention below is what I call "interpretation", that is 
not direct copying of ready-made formulas, where someone unqualified 
could trivially check if there's no typo ;-)
>
>
> It is of course still possible that I made a mistake with all this, 
> but I imagine that updating this and running the tests should help to 
> be confident about the results.

Running the existing PROJ test suite will show if the new formulas are 
consistent with the current less precise ones with maybe a quite loose 
tolerance, not necessarily that we reach the new level of precision we 
claim. Hence comparing with some random test points against 
GeographicLib which can hopefully be considered as a reference 
implementation, to check we have identical results (or at least share 
more common decimals up to the desired precision)


-- 
http://www.spatialys.com
My software is free, but my time generally not.
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