Geodesics on an arbitrary ellipsoid of revolution

TL;DR

This paper extends existing geodesic algorithms to ellipsoids of revolution with arbitrary eccentricity, achieving high accuracy and providing open-source implementation for precise geodesic computations.

Contribution

It generalizes previous algorithms to handle ellipsoids with any eccentricity using elliptic integrals, enhancing accuracy and applicability.

Findings

Algorithms achieve near machine precision accuracy.

Implementation is open-source and widely applicable.

Handles both direct and inverse geodesic problems.

Abstract

The algorithms given in Karney, J. Geodesy 87, 43-55 (2013), to compute geodesics on terrestrial ellipsoids are extended to apply to ellipsoids of revolution with arbitrary eccentricity. For the direct and inverse geodesic problems, this entails implementing the formulation in terms of elliptic integrals given by Legendre and Cayley. The integral for the area of geodesic polygons is computed in terms of the discrete sine transform of the integrand. In all cases, accuracy close to full machine precision is achieved. An open-source implementation of these algorithms is available.