[PROJ] Geodesics and projections for triaxial ellipsoids
Charles Karney
charles.karney at gmail.com
Wed Oct 1 06:53:03 PDT 2025
Version 2.6 of the C++ library GeographicLib
https://geographiclib.sourceforge.io/C++/2.6/index.html
offers some capabilities for dealing with triaxial ellipsoids which may
be of interest:
* Triaxial::Geodesic3
A treatment of the direct geodesic problem using the solution given by
Jacobi (1839) and Liouville (1844). The inverse problem is solved by
generalizing the method I used for biaxial ellipsoids.
* Triaxial::Conformal3
An implementation of Jacobi's conformal projection (1842-1843). This
maps lines of constant (ellipsoidal) latitude and longitude into
straight lines and so is the natural generalization of the Mercator
projection. A byproduct is the ability to conformally map a triaxial
ellipsoid onto a sphere and thence onto any other ellipsoid.
* Triaxial::Cartesian3
Methods for transforming between various triaxial coordinates
(cartesian to geodetic, etc.).
I am 3/4 the way through the paper detailing the geodesic problem. A
writeup of the conformal projection will follow.
--
Charles Karney <karney at alum.mit.edu>
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