Cartesian to geodetic coordinates conversion on an oblate spheroid using the bisection method

A new method to convert Cartesian to geodetic coordinates is presented. The geodetic longitude is computed by a simple formula while the geodetic latitude and height are determined after the computation of the foot point of the normal line to a meridian ellipse. For this reason, the simpler form of the latitude equation is used and the corresponding quartic equation is solved using the Homer's scheme and the bisection method, which guarantees the convergence. Care is given to error analysis when computing the geodetic latitude and height. The performance of the proposed numerical method is examined using an extensive test set of points. The results are also validated by comparison to the exact analytical method of Vermeille and the numerical method of Fukushima. We conclude that the presented method gives accurate results for all input points, for arbitrary semiaxes of an oblate spheroid and can be generalized on a triaxial ellipsoid.