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GeographicLib::TransverseMercator Class Reference

Transverse Mercator projection. More...

#include <TransverseMercator.hpp>

Public Member Functions

void Forward (real lon0, real lat, real lon, real &x, real &y, real &gamma, real &k) const
 
void Forward (real lon0, real lat, real lon, real &x, real &y) const
 
void Reverse (real lon0, real x, real y, real &lat, real &lon, real &gamma, real &k) const
 
void Reverse (real lon0, real x, real y, real &lat, real &lon) const
 
 TransverseMercator (real a, real f, real k0)
 
Inspector functions
Math::real MajorRadius () const
 
Math::real Flattening () const
 
Math::real CentralScale () const
 

Static Public Member Functions

static const TransverseMercatorUTM ()
 

Private Types

typedef Math::real real
 

Private Attributes

real _a
 
real _a1
 
real _alp [maxpow_+1]
 
real _b1
 
real _bet [maxpow_+1]
 
real _c
 
real _e2
 
real _e2m
 
real _es
 
real _f
 
real _k0
 
real _n
 

Static Private Attributes

static const int maxpow_ = GEOGRAPHICLIB_TRANSVERSEMERCATOR_ORDER
 
static const int numit_ = 5
 

Friends

class Ellipsoid
 

Detailed Description

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 2 × 10−15" and the relative error in the scale is 6 × 10−12%%. See Sec. 4 of arXiv:1002.1417 for details. The speed penalty in going to 6th order is only about 1%.

There's a singularity in the projection at φ = 0°, λ − λ0 = ±(1 − e)90° (≈ ±82.6° for the WGS84 ellipsoid), where e is the eccentricity. Beyond this point, the series ceases to converge and the results from this method will be garbage. To be on the safe side, don't use this method if the angular distance from the central meridian exceeds (1 − 2e)90° (≈ 75° for the WGS84 ellipsoid)

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.

This class also returns the meridian convergence gamma and scale k. The meridian convergence is the bearing of grid north (the y axis) measured clockwise from true north.

See TransverseMercator.cpp for more information on the implementation.

See transversemercator for a discussion of this projection.

Example of use:

// Example of using the GeographicLib::TransverseMercator class
#include <iostream>
#include <iomanip>
#include <exception>
using namespace std;
using namespace GeographicLib;
// Define a UTM projection for an arbitrary ellipsoid
class UTMalt {
private:
TransverseMercator _tm; // The projection
double _lon0; // Central longitude
double _falseeasting, _falsenorthing;
public:
UTMalt(double a, // equatorial radius
double f, // flattening
int zone, // the UTM zone + hemisphere
bool northp)
: _tm(a, f, Constants::UTM_k0())
, _lon0(6 * zone - 183)
, _falseeasting(5e5)
, _falsenorthing(northp ? 0 : 100e5) {
if (!(zone >= 1 && zone <= 60))
throw GeographicErr("zone not in [1,60]");
}
void Forward(double lat, double lon, double& x, double& y) {
_tm.Forward(_lon0, lat, lon, x, y);
x += _falseeasting;
y += _falsenorthing;
}
void Reverse(double x, double y, double& lat, double& lon) {
x -= _falseeasting;
y -= _falsenorthing;
_tm.Reverse(_lon0, x, y, lat, lon);
}
};
int main() {
try {
UTMalt tm(6378388, 1/297.0, 30, true); // International ellipsoid, zone 30n
{
// Sample forward calculation
double lat = 40.4, lon = -3.7; // Madrid
double x, y;
tm.Forward(lat, lon, x, y);
cout << fixed << setprecision(0) << x << " " << y << "\n";
}
{
// Sample reverse calculation
double x = 441e3, y = 4472e3;
double lat, lon;
tm.Reverse(x, y, lat, lon);
cout << fixed << setprecision(5) << lat << " " << lon << "\n";
}
}
catch (const exception& e) {
cerr << "Caught exception: " << e.what() << "\n";
return 1;
}
}

TransverseMercatorProj is a command-line utility providing access to the functionality of TransverseMercator and TransverseMercatorExact.

Definition at line 93 of file TransverseMercator.hpp.

Member Typedef Documentation

Definition at line 95 of file TransverseMercator.hpp.

Constructor & Destructor Documentation

GeographicLib::TransverseMercator::TransverseMercator ( real  a,
real  f,
real  k0 
)

Constructor for a ellipsoid with

Parameters
[in]aequatorial radius (meters).
[in]fflattening of ellipsoid. Setting f = 0 gives a sphere. Negative f gives a prolate ellipsoid.
[in]k0central scale factor.
Exceptions
GeographicErrif a, (1 − f) a, or k0 is not positive.

Definition at line 45 of file src/TransverseMercator.cpp.

Member Function Documentation

Math::real GeographicLib::TransverseMercator::CentralScale ( ) const
inline
Returns
k0 central scale for the projection. This is the value of k0 used in the constructor and is the scale on the central meridian.

Definition at line 187 of file TransverseMercator.hpp.

Math::real GeographicLib::TransverseMercator::Flattening ( ) const
inline
Returns
f the flattening of the ellipsoid. This is the value used in the constructor.

Definition at line 181 of file TransverseMercator.hpp.

void GeographicLib::TransverseMercator::Forward ( real  lon0,
real  lat,
real  lon,
real x,
real y,
real gamma,
real k 
) const

Forward projection, from geographic to transverse Mercator.

Parameters
[in]lon0central meridian of the projection (degrees).
[in]latlatitude of point (degrees).
[in]lonlongitude of point (degrees).
[out]xeasting of point (meters).
[out]ynorthing of point (meters).
[out]gammameridian convergence at point (degrees).
[out]kscale of projection at point.

No false easting or northing is added. lat should be in the range [−90°, 90°].

Definition at line 350 of file src/TransverseMercator.cpp.

void GeographicLib::TransverseMercator::Forward ( real  lon0,
real  lat,
real  lon,
real x,
real y 
) const
inline

TransverseMercator::Forward without returning the convergence and scale.

Definition at line 153 of file TransverseMercator.hpp.

Math::real GeographicLib::TransverseMercator::MajorRadius ( ) const
inline
Returns
a the equatorial radius of the ellipsoid (meters). This is the value used in the constructor.

Definition at line 175 of file TransverseMercator.hpp.

void GeographicLib::TransverseMercator::Reverse ( real  lon0,
real  x,
real  y,
real lat,
real lon,
real gamma,
real k 
) const

Reverse projection, from transverse Mercator to geographic.

Parameters
[in]lon0central meridian of the projection (degrees).
[in]xeasting of point (meters).
[in]ynorthing of point (meters).
[out]latlatitude of point (degrees).
[out]lonlongitude of point (degrees).
[out]gammameridian convergence at point (degrees).
[out]kscale of projection at point.

No false easting or northing is added. The value of lon returned is in the range [−180°, 180°].

Definition at line 516 of file src/TransverseMercator.cpp.

void GeographicLib::TransverseMercator::Reverse ( real  lon0,
real  x,
real  y,
real lat,
real lon 
) const
inline

TransverseMercator::Reverse without returning the convergence and scale.

Definition at line 162 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 277 of file src/TransverseMercator.cpp.

Friends And Related Function Documentation

friend class Ellipsoid
friend

Definition at line 101 of file TransverseMercator.hpp.

Member Data Documentation

real GeographicLib::TransverseMercator::_a
private

Definition at line 98 of file TransverseMercator.hpp.

real GeographicLib::TransverseMercator::_a1
private

Definition at line 100 of file TransverseMercator.hpp.

real GeographicLib::TransverseMercator::_alp[maxpow_+1]
private

Definition at line 100 of file TransverseMercator.hpp.

real GeographicLib::TransverseMercator::_b1
private

Definition at line 100 of file TransverseMercator.hpp.

real GeographicLib::TransverseMercator::_bet[maxpow_+1]
private

Definition at line 100 of file TransverseMercator.hpp.

real GeographicLib::TransverseMercator::_c
private

Definition at line 98 of file TransverseMercator.hpp.

real GeographicLib::TransverseMercator::_e2
private

Definition at line 98 of file TransverseMercator.hpp.

real GeographicLib::TransverseMercator::_e2m
private

Definition at line 98 of file TransverseMercator.hpp.

real GeographicLib::TransverseMercator::_es
private

Definition at line 98 of file TransverseMercator.hpp.

real GeographicLib::TransverseMercator::_f
private

Definition at line 98 of file TransverseMercator.hpp.

real GeographicLib::TransverseMercator::_k0
private

Definition at line 98 of file TransverseMercator.hpp.

real GeographicLib::TransverseMercator::_n
private

Definition at line 98 of file TransverseMercator.hpp.

const int GeographicLib::TransverseMercator::maxpow_ = GEOGRAPHICLIB_TRANSVERSEMERCATOR_ORDER
staticprivate

Definition at line 96 of file TransverseMercator.hpp.

const int GeographicLib::TransverseMercator::numit_ = 5
staticprivate

Definition at line 97 of file TransverseMercator.hpp.


The documentation for this class was generated from the following files:


gtsam
Author(s):
autogenerated on Sat May 8 2021 02:58:00