# Transverse Mercator with an accuracy of a few nanometers

@article{Karney2010TransverseMW, title={Transverse Mercator with an accuracy of a few nanometers}, author={Charles F. F. Karney}, journal={Journal of Geodesy}, year={2010}, volume={85}, pages={475-485} }

Implementations of two algorithms for the transverse Mercator projection are described; these achieve accuracies close to machine precision. One is based on the exact equations of Thompson and Lee and the other uses an extension of Krüger’s series for the mapping to higher order. The exact method provides an accuracy of 9 nm over the entire ellipsoid, while the errors in the series method are less than 5 nm within 3900 km of the central meridian. In each case, the meridian convergence and scale…

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