Vector method to compute the Cartesian (X, Y, Z) to geodetic (φ, λ, h) transformation on a triaxial ellipsoid

The vector-based algorithm to transform Cartesian (X, Y, Z ) into geodetic coordinates (phi, lambda, h) presented by Feltens (J Geod, 2007, doi:10.1007/s00190-007-0198-1) has been extended for triaxial ellipsoids. The extended algorithm is again based on simple formulae and has successfully been tested for the Earth and other celestial bodies and for a wide range of positive and negative ellipsoidal heights.