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TransverseMercatorExact.cpp File Reference

Implementation for GeographicLib::TransverseMercatorExact class. More...

`#include <GeographicLib/TransverseMercatorExact.hpp>`

Go to the source code of this file.

## Namespaces

namespace | GeographicLib
| Namespace for GeographicLib.

## Detailed Description

Implementation for GeographicLib::TransverseMercatorExact class.

Copyright (c) Charles Karney (2008-2022) karne.nosp@m.y@al.nosp@m.um.mi.nosp@m.t.ed.nosp@m.u and licensed under the MIT/X11 License. For more information, see https://geographiclib.sourceforge.io/

The relevant section of Lee's paper is part V, pp 67–101, Conformal Projections Based On Jacobian Elliptic Functions; borrow from archive.org.

The method entails using the Thompson Transverse Mercator as an intermediate projection. The projections from the intermediate coordinates to [phi, lam] and [x, y] are given by elliptic functions. The inverse of these projections are found by Newton's method with a suitable starting guess.

This implementation and notation closely follows Lee, with the following exceptions:

Lee | here | Description
--- | --- | ---
x/a | xi | Northing (unit Earth)
y/a | eta | Easting (unit Earth)
s/a | sigma | xi + i * eta
y | x | Easting
x | y | Northing
k | e | eccentricity
k^2 | mu | elliptic function parameter
k'^2 | mv | elliptic function complementary parameter
m | k | scale
zeta | zeta | complex longitude = Mercator = chi in paper
s | sigma | complex GK = zeta in paper

Minor alterations have been made in some of Lee's expressions in an attempt to control round-off. For example atanh(sin(phi)) is replaced by asinh(tan(phi)) which maintains accuracy near phi = pi/2. Such changes are noted in the code.

Definition in file TransverseMercatorExact.cpp.