GeographicLib
1.21
|
Transverse Mercator Projection. More...
#include <GeographicLib/TransverseMercator.hpp>
Public Member Functions | |
TransverseMercator (real a, real f, real k0) | |
void | Forward (real lon0, real lat, real lon, real &x, real &y, real &gamma, real &k) const throw () |
void | Reverse (real lon0, real x, real y, real &lat, real &lon, real &gamma, real &k) const throw () |
void | Forward (real lon0, real lat, real lon, real &x, real &y) const throw () |
void | Reverse (real lon0, real x, real y, real &lat, real &lon) const throw () |
Inspector functions | |
Math::real | MajorRadius () const throw () |
Math::real | Flattening () const throw () |
Math::real | CentralScale () const throw () |
Static Public Attributes | |
static const TransverseMercator | UTM |
Transverse Mercator Projection.
This uses Krüger's method which evaluates the projection and its inverse in terms of a series. See
Krüger's method has been extended from 4th to 6th order. The maximum error is 5 nm (5 nanometers), ground distance, for all positions within 35 degrees of the central meridian. The error in the convergence is 2e-15" and the relative error in the scale is 6e-12%%. See Sec. 4 of arXiv:1002.1417 for details. The speed penalty in going to 6th order is only about 1%. TransverseMercatorExact is an alternative implementation of the projection using exact formulas which yield accurate (to 8 nm) results over the entire ellipsoid.
The ellipsoid parameters and the central scale are set in the constructor. The central meridian (which is a trivial shift of the longitude) is specified as the lon0 argument of the TransverseMercator::Forward and TransverseMercator::Reverse functions. The latitude of origin is taken to be the equator. There is no provision in this class for specifying a false easting or false northing or a different latitude of origin. However these are can be simply included by the calling function. For example, the UTMUPS class applies the false easting and false northing for the UTM projections. A more complicated example is the British National Grid (EPSG:7405) which requires the use of a latitude of origin. This is implemented by the GeographicLib::OSGB class.
See TransverseMercator.cpp for more information on the implementation.
See Transverse Mercator projection for a discussion of this projection.
Example of use:
// Example of using the GeographicLib::TransverseMercator class // $Id: c01651412c934220e2293c344258773ac3d7131c $ #include <iostream> #include <exception> #include <string> #include <iomanip> #include <GeographicLib/TransverseMercator.hpp> using namespace std; using namespace GeographicLib; int main() { try { TransverseMercator proj(Constants::WGS84_a(), Constants::WGS84_f(), Constants::UTM_k0()); // Alternatively: const TransverseMercator& proj = TransverseMercator::UTM; double lon0 = -75; // Central meridian for UTM zone 18 { // Sample forward calculation double lat = 40.3, lon = -74.7; // Princeton, NJ double x, y; proj.Forward(lon0, lat, lon, x, y); cout << x << " " << y << "\n"; } { // Sample reverse calculation double x = 25e3, y = 4461e3; double lat, lon; proj.Reverse(lon0, x, y, lat, lon); cout << lat << " " << lon << "\n"; } } catch (const exception& e) { cerr << "Caught exception: " << e.what() << "\n"; return 1; } return 0; }
TransverseMercatorProj is a command-line utility providing access to the functionality of TransverseMercator and TransverseMercatorExact.
GeographicLib::TransverseMercator::TransverseMercator | ( | real | a, |
real | f, | ||
real | k0 | ||
) |
Constructor for a ellipsoid with
[in] | a | equatorial radius (meters). |
[in] | f | flattening of ellipsoid. Setting f = 0 gives a sphere. Negative f gives a prolate ellipsoid. If f > 1, set flattening to 1/f. |
[in] | k0 | central scale factor. |
An exception is thrown if either of the axes of the ellipsoid or k0 is not positive.
Definition at line 60 of file TransverseMercator.cpp.
References GeographicLib::Math::isfinite(), GeographicLib::Math::sq(), and STATIC_ASSERT.
void GeographicLib::TransverseMercator::Forward | ( | real | lon0, |
real | lat, | ||
real | lon, | ||
real & | x, | ||
real & | y, | ||
real & | gamma, | ||
real & | k | ||
) | const throw () |
Forward projection, from geographic to transverse Mercator.
[in] | lon0 | central meridian of the projection (degrees). |
[in] | lat | latitude of point (degrees). |
[in] | lon | longitude of point (degrees). |
[out] | x | easting of point (meters). |
[out] | y | northing of point (meters). |
[out] | gamma | meridian convergence at point (degrees). |
[out] | k | scale of projection at point. |
No false easting or northing is added. lat should be in the range [-90, 90]; lon and lon0 should be in the range [-180, 360].
Definition at line 217 of file TransverseMercator.cpp.
References GeographicLib::Math::hypot(), GeographicLib::Math::asinh(), and GeographicLib::Math::sq().
Referenced by GeographicLib::UTMUPS::Forward().
void GeographicLib::TransverseMercator::Reverse | ( | real | lon0, |
real | x, | ||
real | y, | ||
real & | lat, | ||
real & | lon, | ||
real & | gamma, | ||
real & | k | ||
) | const throw () |
Reverse projection, from transverse Mercator to geographic.
[in] | lon0 | central meridian of the projection (degrees). |
[in] | x | easting of point (meters). |
[in] | y | northing of point (meters). |
[out] | lat | latitude of point (degrees). |
[out] | lon | longitude of point (degrees). |
[out] | gamma | meridian convergence at point (degrees). |
[out] | k | scale of projection at point. |
No false easting or northing is added. lon0 should be in the range [-180, 360]. The value of lon returned is in the range [-180, 180).
Definition at line 387 of file TransverseMercator.cpp.
References GeographicLib::Math::hypot(), and GeographicLib::Math::sq().
Referenced by GeographicLib::UTMUPS::Reverse().
void GeographicLib::TransverseMercator::Forward | ( | real | lon0, |
real | lat, | ||
real | lon, | ||
real & | x, | ||
real & | y | ||
) | const throw () [inline] |
TransverseMercator::Forward without returning the convergence and scale.
Definition at line 153 of file TransverseMercator.hpp.
void GeographicLib::TransverseMercator::Reverse | ( | real | lon0, |
real | x, | ||
real | y, | ||
real & | lat, | ||
real & | lon | ||
) | const throw () [inline] |
TransverseMercator::Reverse without returning the convergence and scale.
Definition at line 162 of file TransverseMercator.hpp.
Math::real GeographicLib::TransverseMercator::MajorRadius | ( | ) | const throw () [inline] |
Definition at line 175 of file TransverseMercator.hpp.
Math::real GeographicLib::TransverseMercator::Flattening | ( | ) | const throw () [inline] |
Definition at line 181 of file TransverseMercator.hpp.
Math::real GeographicLib::TransverseMercator::CentralScale | ( | ) | const throw () [inline] |
Definition at line 195 of file TransverseMercator.hpp.
const TransverseMercator GeographicLib::TransverseMercator::UTM [static] |
A global instantiation of TransverseMercator with the WGS84 ellipsoid and the UTM scale factor. However, unlike UTM, no false easting or northing is added.
Definition at line 203 of file TransverseMercator.hpp.