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) charl.nosp@m.es@k.nosp@m.arney.nosp@m..com 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.