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.


Defines

#define GEOGRAPHICLIB_TRANSVERSEMERCATOREXACT_CPP   "$Id: TransverseMercatorExact.cpp 6813 2010-02-03 13:57:19Z karney $"

Detailed Description

Implementation for GeographicLib::TransverseMercatorExact class.

Copyright (c) Charles Karney (2008, 2009, 2010) <charles@karney.com> and licensed under the LGPL. For more information, see http://geographiclib.sourceforge.net/

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

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

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.


Define Documentation

#define GEOGRAPHICLIB_TRANSVERSEMERCATOREXACT_CPP   "$Id: TransverseMercatorExact.cpp 6813 2010-02-03 13:57:19Z karney $"

Definition at line 42 of file TransverseMercatorExact.cpp.


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