[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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