[PROJ] Geodetic to Authalic latitude conversions

Thomas Knudsen knudsen.thomas at gmail.com
Wed Sep 11 09:18:21 PDT 2024


I totally agree with Charles regarding using Horner for polynomial
evaluation and Clenshaw for the trig series - for accuracy and speed.

I implemented all the material from Charles' preprint
https://arxiv.org/pdf/2212.05818 for Rust Geodesy, when the preprint
appeared about 1½ years ago.

And although (being an experiment) my handling of the raw coefficients
is rather clumsy, at least it gave me a reason to revise my PROJ horner
and clenshaw implementations (which in turn were based on material from
Poder & Engsager: "Some Conformal Mappings...").

So Jérôme, perhaps take a look at the functions "taylor" and "fourier"
over at https://github.com/busstoptaktik/geodesy/blob/main/src/math/series.rs

While written in Rust, translating to C++ should be rather trivial,
and they may be easier to follow than my decade-old versions already
in the PROJ code base.


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