.NET wrapper for GeographicLib::TransverseMercatorExact. More...

#include <TransverseMercatorExact.h>

Public Member Functions
void	Forward (double lon0, double lat, double lon, [System::Runtime::InteropServices::Out] double% x, [System::Runtime::InteropServices::Out] double% y)

void	Forward (double lon0, double lat, double lon, [System::Runtime::InteropServices::Out] double% x, [System::Runtime::InteropServices::Out] double% y, [System::Runtime::InteropServices::Out] double% gamma, [System::Runtime::InteropServices::Out] double% k)

void	Reverse (double lon0, double x, double y, [System::Runtime::InteropServices::Out] double% lat, [System::Runtime::InteropServices::Out] double% lon)

void	Reverse (double lon0, double x, double y, [System::Runtime::InteropServices::Out] double% lat, [System::Runtime::InteropServices::Out] double% lon, [System::Runtime::InteropServices::Out] double% gamma, [System::Runtime::InteropServices::Out] double% k)

	TransverseMercatorExact ()

	TransverseMercatorExact (double a, double f, double k0, bool extendp)

	~TransverseMercatorExact ()

Public Attributes
Inspector functions
property double	MajorRadius { double get()

property double	Flattening { double get()

property double	CentralScale { double get()

Private Member Functions
	!TransverseMercatorExact (void)

Private Attributes
GeographicLib::TransverseMercatorExact *	m_pTransverseMercatorExact

Detailed Description

.NET wrapper for GeographicLib::TransverseMercatorExact.

This class allows .NET applications to access GeographicLib::TransverseMercatorExact.

Implementation of the Transverse Mercator Projection given in

L. P. Lee, Conformal Projections Based On Jacobian Elliptic Functions, Part V of Conformal Projections Based on Elliptic Functions, (B. V. Gutsell, Toronto, 1976), 128pp., ISBN: 0919870163 (also appeared as: Monograph 16, Suppl. No. 1 to Canadian Cartographer, Vol 13).
C. F. F. Karney, Transverse Mercator with an accuracy of a few nanometers, J. Geodesy 85(8), 475–485 (Aug. 2011); preprint arXiv:1002.1417.

Lee gives the correct results for forward and reverse transformations subject to the branch cut rules (see the description of the extendp argument to the constructor). The maximum error is about 8 nm (8 nanometers), ground distance, for the forward and reverse transformations. The error in the convergence is 2 × 10⁻¹⁵", the relative error in the scale is 7 × 10⁻¹²%%. See Sec. 3 of arXiv:1002.1417 for details. The method is "exact" in the sense that the errors are close to the round-off limit and that no changes are needed in the algorithms for them to be used with reals of a higher precision. Thus the errors using long double (with a 64-bit fraction) are about 2000 times smaller than using double (with a 53-bit fraction).

This algorithm is about 4.5 times slower than the 6th-order Krüger method, TransverseMercator, taking about 11 us for a combined forward and reverse projection on a 2.66 GHz Intel machine (g++, version 4.3.0, -O3).

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 TransverseMercatorExact::Forward and TransverseMercatorExact::Reverse functions. The latitude of origin is taken to be the equator. See the documentation on TransverseMercator for how to include a false easting, false northing, or a latitude of origin.

See tm-grid.kmz, for an illustration of the transverse Mercator grid in Google Earth.

See GeographicLib::TransverseMercatorExact.cpp for more information on the implementation.

See transversemercator for a discussion of this projection.

C# Example:

using System;
using NETGeographicLib;
 
namespace example_TransverseMercatorExact
{
    class Program
    {
        static void Main(string[] args)
        {
            try {
                TransverseMercatorExact proj = new TransverseMercatorExact(); // WGS84
                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, out x, out y);
                    Console.WriteLine(String.Format("{0} {1}", x, y));
                }
                {
                    // Sample reverse calculation
                    double x = 25e3, y = 4461e3;
                    double lat, lon;
                    proj.Reverse(lon0, x, y, out lat, out lon);
                    Console.WriteLine(String.Format("{0} {1}", lat, lon));
                }
            }
            catch (GeographicErr e) {
                Console.WriteLine(String.Format("Caught exception: {0}", e.Message));
            }
        }
    }
}

Managed C++ Example:

// Example of using the GeographicLib::TransverseMercatorExact class
 
#include <iostream>
#include <iomanip>
#include <exception>
#include <GeographicLib/TransverseMercatorExact.hpp>
 
using namespace std;
using namespace GeographicLib;
 
int main() {
  try {
    TransverseMercatorExact proj(Constants::WGS84_a(), Constants::WGS84_f(),
                                 Constants::UTM_k0());
    // Alternatively:
    // const TransverseMercatorExact& proj = TransverseMercatorExact::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;
  }
}

Visual Basic Example:

Imports NETGeographicLib
 
Module example_TransverseMercatorExact
    Sub Main()
        Try
            Dim proj As TransverseMercatorExact = New TransverseMercatorExact() ' WGS84
            Dim lon0 As Double = -75          ' Central meridian for UTM zone 18
            ' Sample forward calculation
            Dim lat As Double = 40.3, lon = -74.7 ' Princeton, NJ
            Dim x, y As Double
            proj.Forward(lon0, lat, lon, x, y)
            Console.WriteLine(String.Format("{0} {1}", x, y))
            ' Sample reverse calculation
            x = 25000.0 : y = 4461000.0
            proj.Reverse(lon0, x, y, lat, lon)
            Console.WriteLine(String.Format("{0} {1}", lat, lon))
        Catch ex As GeographicErr
            Console.WriteLine(String.Format("Caught exception: {0}", ex.Message))
        End Try
    End Sub
End Module

INTERFACE DIFFERENCES:
A default constructor is provided that assumes WGS84 parameters and a UTM scale factor.

The MajorRadius, Flattening, and CentralScale functions are implemented as properties.

Definition at line 84 of file TransverseMercatorExact.h.

Constructor & Destructor Documentation

◆ !TransverseMercatorExact()

TransverseMercatorExact::!TransverseMercatorExact ( void )

private

Definition at line 21 of file dotnet/NETGeographicLib/TransverseMercatorExact.cpp.

◆ TransverseMercatorExact() [1/2]

TransverseMercatorExact::TransverseMercatorExact	(	double	a,
		double	f,
		double	k0,
		bool	extendp
	)

Constructor for a ellipsoid with

Parameters

[in]	a	equatorial radius (meters).
[in]	f	flattening of ellipsoid.
[in]	k0	central scale factor.
[in]	extendp	use extended domain.

Exceptions

GeographicErr if a, f, or k0 is not positive.

The transverse Mercator projection has a branch point singularity at lat = 0 and lon − lon0 = 90 (1 − e) or (for TransverseMercatorExact::UTM) x = 18381 km, y = 0m. The extendp argument governs where the branch cut is placed. With extendp = false, the "standard" convention is followed, namely the cut is placed along x > 18381 km, y = 0m. Forward can be called with any lat and lon then produces the transformation shown in Lee, Fig 46. Reverse analytically continues this in the ± x direction. As a consequence, Reverse may map multiple points to the same geographic location; for example, for TransverseMercatorExact::UTM, x = 22051449.037349 m, y = −7131237.022729 m and x = 29735142.378357 m, y = 4235043.607933 m both map to lat = −2°, lon = 88°.

With extendp = true, the branch cut is moved to the lower left quadrant. The various symmetries of the transverse Mercator projection can be used to explore the projection on any sheet. In this mode the domains of lat, lon, x, and y are restricted to

the union of
- lat in [0, 90] and lon − lon0 in [0, 90]
- lat in (-90, 0] and lon − lon0 in [90 (1 − e), 90]
the union of
- x/(k0 a) in [0, ∞) and y/(k0 a) in [0, E(e²)]
- x/(k0 a) in [K(1 − e²) − E(1 − e²), ∞) and y/(k0 a) in (−∞, 0]

See Sec. 5 of arXiv:1002.1417 for a full discussion of the treatment of the branch cut.

The method will work for all ellipsoids used in terrestrial geodesy. The method cannot be applied directly to the case of a sphere (f = 0) because some the constants characterizing this method diverge in that limit, and in practice, f should be larger than about numeric_limits<double>::epsilon(). However, TransverseMercator treats the sphere exactly.

Definition at line 31 of file dotnet/NETGeographicLib/TransverseMercatorExact.cpp.

◆ TransverseMercatorExact() [2/2]

TransverseMercatorExact::TransverseMercatorExact ( )

The default constructor assumes a WGS84 ellipsoid and a UTM scale factor.

Definition at line 50 of file dotnet/NETGeographicLib/TransverseMercatorExact.cpp.

◆ ~TransverseMercatorExact()

NETGeographicLib::TransverseMercatorExact::~TransverseMercatorExact ( )

inline

The destructor calls the finalizer.

Definition at line 152 of file TransverseMercatorExact.h.

Member Function Documentation

◆ Forward() [1/2]

void TransverseMercatorExact::Forward	(	double	lon0,
		double	lat,
		double	lon,
		[System::Runtime::InteropServices::Out] double%	x,
		[System::Runtime::InteropServices::Out] double%	y
	)

TransverseMercatorExact::Forward without returning the convergence and scale.

Definition at line 97 of file dotnet/NETGeographicLib/TransverseMercatorExact.cpp.

◆ Forward() [2/2]

void TransverseMercatorExact::Forward	(	double	lon0,
		double	lat,
		double	lon,
		[System::Runtime::InteropServices::Out] double%	x,
		[System::Runtime::InteropServices::Out] double%	y,
		[System::Runtime::InteropServices::Out] double%	gamma,
		[System::Runtime::InteropServices::Out] double%	k
	)

Forward projection, from geographic to transverse Mercator.

Parameters

[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°].

Definition at line 65 of file dotnet/NETGeographicLib/TransverseMercatorExact.cpp.

◆ Reverse() [1/2]

void TransverseMercatorExact::Reverse	(	double	lon0,
		double	x,
		double	y,
		[System::Runtime::InteropServices::Out] double%	lat,
		[System::Runtime::InteropServices::Out] double%	lon
	)

TransverseMercatorExact::Reverse without returning the convergence and scale.

Definition at line 108 of file dotnet/NETGeographicLib/TransverseMercatorExact.cpp.

◆ Reverse() [2/2]

void TransverseMercatorExact::Reverse	(	double	lon0,
		double	x,
		double	y,
		[System::Runtime::InteropServices::Out] double%	lat,
		[System::Runtime::InteropServices::Out] double%	lon,
		[System::Runtime::InteropServices::Out] double%	gamma,
		[System::Runtime::InteropServices::Out] double%	k
	)

Reverse projection, from transverse Mercator to geographic.

Parameters

[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. The value of lon returned is in the range [−180°, 180°).

Definition at line 81 of file dotnet/NETGeographicLib/TransverseMercatorExact.cpp.

Member Data Documentation

◆ CentralScale

property double NETGeographicLib::TransverseMercatorExact::CentralScale { double get()

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 230 of file TransverseMercatorExact.h.

◆ Flattening

property double NETGeographicLib::TransverseMercatorExact::Flattening { double get()

Returns: f the flattening of the ellipsoid. This is the value used in the constructor.

Definition at line 224 of file TransverseMercatorExact.h.

◆ m_pTransverseMercatorExact

GeographicLib::TransverseMercatorExact* NETGeographicLib::TransverseMercatorExact::m_pTransverseMercatorExact

private

Definition at line 88 of file TransverseMercatorExact.h.

◆ MajorRadius

property double NETGeographicLib::TransverseMercatorExact::MajorRadius { double get()

Returns: a the equatorial radius of the ellipsoid (meters). This is the value used in the constructor.

Definition at line 218 of file TransverseMercatorExact.h.

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

Public Member Functions

Public Attributes

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ !TransverseMercatorExact()

◆ TransverseMercatorExact() [1/2]

◆ TransverseMercatorExact() [2/2]

◆ ~TransverseMercatorExact()

Member Function Documentation

◆ Forward() [1/2]

◆ Forward() [2/2]

◆ Reverse() [1/2]

◆ Reverse() [2/2]

Member Data Documentation

◆ CentralScale

◆ Flattening

◆ m_pTransverseMercatorExact

◆ MajorRadius