NETGeographicLib  1.43
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NETGeographicLib::TransverseMercatorExact Class Reference

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

#include <NETGeographicLib/TransverseMercatorExact.h>

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 × 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 Transverse Mercator projection for a discussion of this projection.

C# Example:

using System;
namespace example_TransverseMercatorExact
{
class Program
{
static void Main(string[] args)
{
try {
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 {
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

◆ TransverseMercatorExact() [1/2]

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

Constructor for a ellipsoid with

Parameters
[in]aequatorial radius (meters).
[in]fflattening of ellipsoid. If f > 1, set flattening to 1/f.
[in]k0central scale factor.
[in]extendpuse extended domain.
Exceptions
GeographicErrif a, f, or k0 is not positive.

The transverse Mercator projection has a branch point singularity at lat = 0 and lonlon0 = 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 lonlon0 in [0, 90]
    • lat in (-90, 0] and lonlon0 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.

◆ TransverseMercatorExact() [2/2]

NETGeographicLib::TransverseMercatorExact::TransverseMercatorExact ( )

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

Referenced by ~TransverseMercatorExact().

◆ ~TransverseMercatorExact()

NETGeographicLib::TransverseMercatorExact::~TransverseMercatorExact ( )
inline

The destructor calls the finalizer.

Definition at line 153 of file TransverseMercatorExact.h.

References Forward(), Reverse(), and TransverseMercatorExact().

Member Function Documentation

◆ Forward() [1/2]

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]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°]; lon and lon0 should be in the range [−540°, 540°).

Referenced by ~TransverseMercatorExact().

◆ Reverse() [1/2]

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]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. lon0 should be in the range [−540°, 540°). The value of lon returned is in the range [−180°, 180°).

Referenced by ~TransverseMercatorExact().

◆ Forward() [2/2]

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.

◆ Reverse() [2/2]

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

◆ MajorRadius

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.

◆ Flattening

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.

◆ CentralScale

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: