NETGeographicLib::TransverseMercatorExact Class Reference

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

#include <NETGeographicLib/TransverseMercatorExact.h>

List of all members.

Public Member Functions

 TransverseMercatorExact (double a, double f, double k0, bool extendp)
 TransverseMercatorExact ()
 ~TransverseMercatorExact ()
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,[System::Runtime::InteropServices::Out] double% gamma,[System::Runtime::InteropServices::Out] double% k)
void Forward (double lon0, double lat, double lon,[System::Runtime::InteropServices::Out] double% x,[System::Runtime::InteropServices::Out] double% y)
void Reverse (double lon0, double x, double y,[System::Runtime::InteropServices::Out] double% lat,[System::Runtime::InteropServices::Out] double% lon)

Properties

Inspector functions



double MajorRadius [get]
double Flattening [get]
double CentralScale [get]

Detailed Description

.NET wrapper for GeographicLib::TransverseMercatorExact.

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

Implementation of the Transverse Mercator Projection given in

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 1015", the relative error in the scale is 7 1012%%. 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 Transverse Mercator projection 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:

using namespace System;
using namespace NETGeographicLib;

int main(array<System::String ^> ^/*args*/)
{
    try {
        TransverseMercatorExact^ proj = gcnew 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, x, 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, lat, lon);
            Console::WriteLine(String::Format("{0} {1}", lat, lon));
        }
    }
    catch (GeographicErr^ e) {
        Console::WriteLine(String::Format("Caught exception: {0}", e->Message));
        return -1;
    }
    return 0;
}

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

NETGeographicLib::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. If f > 1, set flattening to 1/f.
[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.

NETGeographicLib::TransverseMercatorExact::TransverseMercatorExact (  ) 

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

Referenced by ~TransverseMercatorExact().

NETGeographicLib::TransverseMercatorExact::~TransverseMercatorExact (  )  [inline]

The destructor calls the finalizer.

Definition at line 153 of file TransverseMercatorExact.h.

References TransverseMercatorExact().


Member Function Documentation

void NETGeographicLib::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]; lon and lon0 should be in the range [540, 540).

void NETGeographicLib::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. lon0 should be in the range [540, 540). The value of lon returned is in the range [180, 180).

void NETGeographicLib::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.

void NETGeographicLib::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.


Property Documentation

double NETGeographicLib::TransverseMercatorExact::MajorRadius [get]
Returns:
a the equatorial radius of the ellipsoid (meters). This is the value used in the constructor.

Definition at line 221 of file TransverseMercatorExact.h.

double NETGeographicLib::TransverseMercatorExact::Flattening [get]
Returns:
f the flattening of the ellipsoid. This is the value used in the constructor.

Definition at line 227 of file TransverseMercatorExact.h.

double NETGeographicLib::TransverseMercatorExact::CentralScale [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 233 of file TransverseMercatorExact.h.


The documentation for this class was generated from the following file:
 All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Properties Friends

Generated on 6 Oct 2014 for NETGeographicLib by  doxygen 1.6.1