Vincenty's formulae

Summary

Vincenty's formulae are two iterative methods, published by Thaddeus Vincenty in 1975, for the geodesic problems on an ellipsoid. The direct method finds the endpoint of a geodesic of given start, azimuth and length. The inverse method finds the length and azimuths of the geodesic between two given points. They are accurate to about $0.5$ mm on the Earth ellipsoid, but the inverse iteration may fail for nearly antipodal points.