[PROJ] Auxiliary latitudes, rhumb lines

[Thomas Knudsen]

Charles,

I did an implementation of your work on auxiliary latitudes for use in
Rust Geodesy (https://crates.io/crates/geodesy).

I found your work exceptionally clearly written and very easy to
transform into code.

My implementation is primarily in these four files:

https://github.com/busstoptaktik/geodesy/blob/main/src/ellipsoid/latitudes.rs
https://github.com/busstoptaktik/geodesy/blob/main/src/ellipsoid/constants.rs
https://github.com/busstoptaktik/geodesy/blob/main/src/math/mod.rs
https://github.com/busstoptaktik/geodesy/blob/main/src/inner_op/latitude.rs

The first 3 comprise the implementation per se, while the fourth is an
implementation of a generic coordinate operator (think proj=latitude...),

The manual for the operator is at
https://github.com/busstoptaktik/geodesy/blob/main/ruminations/002-rumination.md#operator-latitude

Rust Geodesy is, if anyone should be interested, a tiny
transformation system, intended as a platform for
architectural and conceptual experiments,
potentially as inspiration for future developments of PROJ.

/Thomas

Den man. 13. mar. 2023 kl. 15.12 skrev Charles Karney <
charles.karney at gmail.com>:

> Two papers which may be of interest to PROJ users are available as
> preprints:
>
>    C. F. F. Karney
>    On auxiliary latitudes (Dec. 2022)
>    https://arxiv.org/abs/2212.05818
>
>    C. F. F. Karney
>    The area of rhumb polygons (Mar. 2023)
>    https://arxiv.org/abs/2303.03219
>
> The first is of more immediate interest in the PROJ context...  A case
> could be made that all the conversions between auxiliary latitudes in
> PROJ should be centralized and should support both series approximations
> (fast and applicable to small flattening) and exact methods (slower and
> applicable to arbitrary eccentricity).
>
> I would single out the current treatment of authalic latitude in area
> preserving projections as most in need of some loving case.  These all
> end up determining the authalic latitude by taking the arc sine of the
> value returned by pj_qsfn (normalized).  This results in a severe loss
> of accuracy near the poles.
>
> The second paper implements solutions to rhumb problems in terms of
> auxiliary latitudes.  This could be used to provide an ellipsoid
> generalization of the loximuthal projection (but I'm not sure whether
> this is a pressing need).
>
> Note that I'm careful to use the subjunctive mood here (should, would,
> ...).  I don't have the time to undertake the suggested changes to PROJ
> myself; but I would be happy to guide someone else (perhaps these are
> suitable student projects?).
>
> --
> Charles Karney <charles at karney.com>
> 702 Prospect Ave
> Princeton, NJ 08540-4037
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>
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