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.

中文翻译：

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任意旋转椭球体上的测地线

Karney (J. Geodesy 87:43–55, 2013) 中给出的计算陆地椭球测地线的算法已扩展到适用于具有任意偏心率的旋转椭球体。对于正测地线和逆测地线问题，这需要根据勒让德和凯莱给出的椭圆积分来实现公式。测地多边形面积的积分是根据被积函数的离散正弦变换来计算的。在所有情况下，精度都接近机器的整体精度。这些算法的开源实现现已可用。