Transverse Mercator with an accuracy of a few nanometers

Details Transverse Mercator with an accuracy of a few nanometers Transverse Mercator with an accuracy of a few nanometers

2010-02-08

arxiv.org/abs/1002.1417v3

J. Geodesy 85(8), 475-485 (Aug. 2011)

Physics

Computational Physics

LaTeX, 10 pages, 3 figures. Includes some revisions. Supplementary material is available at http://geographiclib.sourceforge.n

Scientific paper

10.1007/s00190-011-0445-3

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 Krueger's series for the projection 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 are also computed with similar accuracy. The speed of the series method is competitive with other less accurate algorithms and the exact method is about 5 times slower.

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