Karney, C. F. (2022). On auxiliary latitudes. arXiv preprint arXiv:2212.05818.
The auxiliary latitudes are essential tools in cartography. This paper summarizes methods for converting between them with an emphasis on providing full double-precision accuracy. This includes series expansions in the third flattening, where the truncation error is precisely measured and where estimates of the radii of convergence are given. Also new formulas are given for computing the rectifying and authalic latitudes with minimal roundoff error.
Keywords: auxiliary latitudes; map projections; geometrical geodesy; eccentric ellipsoids; numerical methods