[PROJ] Geodesics on a triaxial ellipsoid

[Charles Karney]

Version 2.2 of the Octave/MATLAB package GeographicLib, now includes
some routines to solve problems on a triaxial ellipsoid.  See

   https://github.com/geographiclib/geographiclib-octave#readme
   https://geographiclib.sourceforge.io/doc/triaxial.html

The capabilities include

     - the solution of the direct and inverse geodesic problems,
     - conversions between various coordinate systems,
     - random sampling on the ellipsoid,
     - functions to aid plotting curves on the ellipsoid.

Some notes:

The direct geodesic problem is solved using the built-in ODE solvers on
the geodesic equations in cartesian coordinates, the same as Panou +
Korakitis (2019).  For an example, try triaxial.demo(1).

The inverse problem extends the technique I used for oblate ellipsoids,
Karney (2013).  This is the first "working" solution for the inverse
problem.  To see the cut locus, do triaxial.demo(6).

The conversion from cartesian to geodetic coordinates uses Ligas (2012)
but fixes the starting guess for Newton's method so that it's guaranteed
to converge.  This then is faster than the bisection method used by
Panou + Korakitis (2022).

A similar technique is for conversion to ellipsoidal coordinates.

Random sampling uses Marples + Williams (2023).

-- 
Charles Karney <karney at alum.mit.edu>
702 Prospect Ave
Princeton, NJ 08540-4037