NETGeographicLib::Geodesic Class Reference

.NET wrapper for GeographicLib::Geodesic. More...

#include <NETGeographicLib/Geodesic.h>

List of all members.

Public Member Functions

 ~Geodesic ()
 the destructor calls the finalizer.
Constructor



 Geodesic (double a, double f)
 Geodesic ()
Direct geodesic problem specified in terms of distance.



double Direct (double lat1, double lon1, double azi1, double s12,[System::Runtime::InteropServices::Out] double% lat2,[System::Runtime::InteropServices::Out] double% lon2,[System::Runtime::InteropServices::Out] double% azi2,[System::Runtime::InteropServices::Out] double% m12,[System::Runtime::InteropServices::Out] double% M12,[System::Runtime::InteropServices::Out] double% M21,[System::Runtime::InteropServices::Out] double% S12)
double Direct (double lat1, double lon1, double azi1, double s12,[System::Runtime::InteropServices::Out] double% lat2,[System::Runtime::InteropServices::Out] double% lon2)
double Direct (double lat1, double lon1, double azi1, double s12,[System::Runtime::InteropServices::Out] double% lat2,[System::Runtime::InteropServices::Out] double% lon2,[System::Runtime::InteropServices::Out] double% azi2)
double Direct (double lat1, double lon1, double azi1, double s12,[System::Runtime::InteropServices::Out] double% lat2,[System::Runtime::InteropServices::Out] double% lon2,[System::Runtime::InteropServices::Out] double% azi2,[System::Runtime::InteropServices::Out] double% m12)
double Direct (double lat1, double lon1, double azi1, double s12,[System::Runtime::InteropServices::Out] double% lat2,[System::Runtime::InteropServices::Out] double% lon2,[System::Runtime::InteropServices::Out] double% azi2,[System::Runtime::InteropServices::Out] double% M12,[System::Runtime::InteropServices::Out] double% M21)
double Direct (double lat1, double lon1, double azi1, double s12,[System::Runtime::InteropServices::Out] double% lat2,[System::Runtime::InteropServices::Out] double% lon2,[System::Runtime::InteropServices::Out] double% azi2,[System::Runtime::InteropServices::Out] double% m12,[System::Runtime::InteropServices::Out] double% M12,[System::Runtime::InteropServices::Out] double% M21)
Direct geodesic problem specified in terms of arc length.



void ArcDirect (double lat1, double lon1, double azi1, double a12,[System::Runtime::InteropServices::Out] double% lat2,[System::Runtime::InteropServices::Out] double% lon2,[System::Runtime::InteropServices::Out] double% azi2,[System::Runtime::InteropServices::Out] double% s12,[System::Runtime::InteropServices::Out] double% m12,[System::Runtime::InteropServices::Out] double% M12,[System::Runtime::InteropServices::Out] double% M21,[System::Runtime::InteropServices::Out] double% S12)
void ArcDirect (double lat1, double lon1, double azi1, double a12,[System::Runtime::InteropServices::Out] double% lat2,[System::Runtime::InteropServices::Out] double% lon2)
void ArcDirect (double lat1, double lon1, double azi1, double a12,[System::Runtime::InteropServices::Out] double% lat2,[System::Runtime::InteropServices::Out] double% lon2,[System::Runtime::InteropServices::Out] double% azi2)
void ArcDirect (double lat1, double lon1, double azi1, double a12,[System::Runtime::InteropServices::Out] double% lat2,[System::Runtime::InteropServices::Out] double% lon2,[System::Runtime::InteropServices::Out] double% azi2,[System::Runtime::InteropServices::Out] double% s12)
void ArcDirect (double lat1, double lon1, double azi1, double a12,[System::Runtime::InteropServices::Out] double% lat2,[System::Runtime::InteropServices::Out] double% lon2,[System::Runtime::InteropServices::Out] double% azi2,[System::Runtime::InteropServices::Out] double% s12,[System::Runtime::InteropServices::Out] double% m12)
void ArcDirect (double lat1, double lon1, double azi1, double a12,[System::Runtime::InteropServices::Out] double% lat2,[System::Runtime::InteropServices::Out] double% lon2,[System::Runtime::InteropServices::Out] double% azi2,[System::Runtime::InteropServices::Out] double% s12,[System::Runtime::InteropServices::Out] double% M12,[System::Runtime::InteropServices::Out] double% M21)
void ArcDirect (double lat1, double lon1, double azi1, double a12,[System::Runtime::InteropServices::Out] double% lat2,[System::Runtime::InteropServices::Out] double% lon2,[System::Runtime::InteropServices::Out] double% azi2,[System::Runtime::InteropServices::Out] double% s12,[System::Runtime::InteropServices::Out] double% m12,[System::Runtime::InteropServices::Out] double% M12,[System::Runtime::InteropServices::Out] double% M21)
General version of the direct geodesic solution.



double GenDirect (double lat1, double lon1, double azi1, bool arcmode, double s12_a12, NETGeographicLib::Mask outmask,[System::Runtime::InteropServices::Out] double% lat2,[System::Runtime::InteropServices::Out] double% lon2,[System::Runtime::InteropServices::Out] double% azi2,[System::Runtime::InteropServices::Out] double% s12,[System::Runtime::InteropServices::Out] double% m12,[System::Runtime::InteropServices::Out] double% M12,[System::Runtime::InteropServices::Out] double% M21,[System::Runtime::InteropServices::Out] double% S12)
Inverse geodesic problem.



double Inverse (double lat1, double lon1, double lat2, double lon2,[System::Runtime::InteropServices::Out] double% s12,[System::Runtime::InteropServices::Out] double% azi1,[System::Runtime::InteropServices::Out] double% azi2,[System::Runtime::InteropServices::Out] double% m12,[System::Runtime::InteropServices::Out] double% M12,[System::Runtime::InteropServices::Out] double% M21,[System::Runtime::InteropServices::Out] double% S12)
double Inverse (double lat1, double lon1, double lat2, double lon2,[System::Runtime::InteropServices::Out] double% s12)
double Inverse (double lat1, double lon1, double lat2, double lon2,[System::Runtime::InteropServices::Out] double% azi1,[System::Runtime::InteropServices::Out] double% azi2)
double Inverse (double lat1, double lon1, double lat2, double lon2,[System::Runtime::InteropServices::Out] double% s12,[System::Runtime::InteropServices::Out] double% azi1,[System::Runtime::InteropServices::Out] double% azi2)
double Inverse (double lat1, double lon1, double lat2, double lon2,[System::Runtime::InteropServices::Out] double% s12,[System::Runtime::InteropServices::Out] double% azi1,[System::Runtime::InteropServices::Out] double% azi2,[System::Runtime::InteropServices::Out] double% m12)
double Inverse (double lat1, double lon1, double lat2, double lon2,[System::Runtime::InteropServices::Out] double% s12,[System::Runtime::InteropServices::Out] double% azi1,[System::Runtime::InteropServices::Out] double% azi2,[System::Runtime::InteropServices::Out] double% M12,[System::Runtime::InteropServices::Out] double% M21)
double Inverse (double lat1, double lon1, double lat2, double lon2,[System::Runtime::InteropServices::Out] double% s12,[System::Runtime::InteropServices::Out] double% azi1,[System::Runtime::InteropServices::Out] double% azi2,[System::Runtime::InteropServices::Out] double% m12,[System::Runtime::InteropServices::Out] double% M12,[System::Runtime::InteropServices::Out] double% M21)
General version of inverse geodesic solution.



double GenInverse (double lat1, double lon1, double lat2, double lon2, NETGeographicLib::Mask outmask,[System::Runtime::InteropServices::Out] double% s12,[System::Runtime::InteropServices::Out] double% azi1,[System::Runtime::InteropServices::Out] double% azi2,[System::Runtime::InteropServices::Out] double% m12,[System::Runtime::InteropServices::Out] double% M12,[System::Runtime::InteropServices::Out] double% M21,[System::Runtime::InteropServices::Out] double% S12)
Interface to GeodesicLine.



GeodesicLineLine (double lat1, double lon1, double azi1, NETGeographicLib::Mask caps)

Inspector functions.



double MajorRadius [get]
double Flattening [get]
double EllipsoidArea [get]
System::IntPtr^ GetUnmanaged ()

Detailed Description

.NET wrapper for GeographicLib::Geodesic.

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

The shortest path between two points on a ellipsoid at (lat1, lon1) and (lat2, lon2) is called the geodesic. Its length is s12 and the geodesic from point 1 to point 2 has azimuths azi1 and azi2 at the two end points. (The azimuth is the heading measured clockwise from north. azi2 is the "forward" azimuth, i.e., the heading that takes you beyond point 2 not back to point 1.)

Given lat1, lon1, azi1, and s12, we can determine lat2, lon2, and azi2. This is the direct geodesic problem and its solution is given by the function Geodesic::Direct. (If s12 is sufficiently large that the geodesic wraps more than halfway around the earth, there will be another geodesic between the points with a smaller s12.)

Given lat1, lon1, lat2, and lon2, we can determine azi1, azi2, and s12. This is the inverse geodesic problem, whose solution is given by Geodesic::Inverse. Usually, the solution to the inverse problem is unique. In cases where there are multiple solutions (all with the same s12, of course), all the solutions can be easily generated once a particular solution is provided.

The standard way of specifying the direct problem is the specify the distance s12 to the second point. However it is sometimes useful instead to specify the arc length a12 (in degrees) on the auxiliary sphere. This is a mathematical construct used in solving the geodesic problems. The solution of the direct problem in this form is provided by Geodesic::ArcDirect. An arc length in excess of 180 indicates that the geodesic is not a shortest path. In addition, the arc length between an equatorial crossing and the next extremum of latitude for a geodesic is 90.

This class can also calculate several other quantities related to geodesics. These are:

Overloaded versions of Geodesic::Direct, Geodesic::ArcDirect, and Geodesic::Inverse allow these quantities to be returned. In addition there are general functions Geodesic::GenDirect, and Geodesic::GenInverse which allow an arbitrary set of results to be computed. The quantities m12, M12, M21 which all specify the behavior of nearby geodesics obey addition rules. If points 1, 2, and 3 all lie on a single geodesic, then the following rules hold:

Additional functionality is provided by the GeodesicLine class, which allows a sequence of points along a geodesic to be computed.

The shortest distance returned by the solution of the inverse problem is (obviously) uniquely defined. However, in a few special cases there are multiple azimuths which yield the same shortest distance. Here is a catalog of those cases:

The calculations are accurate to better than 15 nm (15 nanometers) for the WGS84 ellipsoid. See Sec. 9 of arXiv:1102.1215v1 for details. The algorithms used by this class are based on series expansions using the flattening f as a small parameter. These are only accurate for |f| < 0.02; however reasonably accurate results will be obtained for |f| < 0.2. Here is a table of the approximate maximum error (expressed as a distance) for an ellipsoid with the same major radius as the WGS84 ellipsoid and different values of the flattening.

     |f|      error
     0.01     25 nm
     0.02     30 nm
     0.05     10 um
     0.1     1.5 mm
     0.2     300 mm
 

For very eccentric ellipsoids, use GeodesicExact instead.

The algorithms are described in

For more information on geodesics see Geodesics on an ellipsoid of revolution.

C# Example:

using System;
using NETGeographicLib;

namespace example_Geodesic
{
    class Program
    {
        static void Main(string[] args)
        {
            try {
                Geodesic geod = new Geodesic( Constants.WGS84.MajorRadius,
                                              Constants.WGS84.Flattening );
                // Alternatively: Geodesic geod = new Geodesic();
                {
                    // Sample direct calculation, travelling about NE from JFK
                    double lat1 = 40.6, lon1 = -73.8, s12 = 5.5e6, azi1 = 51;
                    double lat2, lon2;
                    geod.Direct(lat1, lon1, azi1, s12, out lat2, out lon2);
                    Console.WriteLine(String.Format("Latitude: {0} Longitude: {1}", lat2, lon2));
                }
                {
                    // Sample inverse calculation, JFK to LHR
                    double
                    lat1 = 40.6, lon1 = -73.8, // JFK Airport
                    lat2 = 51.6, lon2 = -0.5;  // LHR Airport
                    double s12;
                    geod.Inverse(lat1, lon1, lat2, lon2, out s12);
                    Console.WriteLine( s12 );
                }
            }
            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 {
        Geodesic^ geod = gcnew Geodesic( Constants::WGS84::MajorRadius,
                                         Constants::WGS84::Flattening );
        // Alternatively: Geodesic^ geod = gcnew Geodesic();
        {
            // Sample direct calculation, travelling about NE from JFK
            double lat1 = 40.6, lon1 = -73.8, s12 = 5.5e6, azi1 = 51;
            double lat2, lon2;
            geod->Direct(lat1, lon1, azi1, s12, lat2, lon2);
            Console::WriteLine(String::Format("Latitude: {0} Longitude: {1}", lat2, lon2));
        }
        {
            // Sample inverse calculation, JFK to LHR
            double
            lat1 = 40.6, lon1 = -73.8, // JFK Airport
            lat2 = 51.6, lon2 = -0.5;  // LHR Airport
            double s12;
            geod->Inverse(lat1, lon1, lat2, lon2, s12);
            Console::WriteLine( s12 );
        }
    }
    catch (GeographicErr^ e) {
        Console::WriteLine(String::Format("Caught exception: {0}", e->Message));
        return -1;
    }
    return 0;
}

Visual Basic Example:

Imports NETGeographicLib

Module example_Geodesic
    Sub Main()
        Try
            Dim geod As Geodesic = New Geodesic(Constants.WGS84.MajorRadius,
                                                Constants.WGS84.Flattening)
            ' Alternatively: Dim geod As Geodesic = new Geodesic()
            ' Sample direct calculation, travelling about NE from JFK
            Dim lat1 As Double = 40.6, lon1 = -73.8, s12 = 5500000.0, azi1 = 51
            Dim lat2, lon2 As Double
            geod.Direct(lat1, lon1, azi1, s12, lat2, lon2)
            Console.WriteLine(String.Format("Latitude: {0} Longitude: {1}", lat2, lon2))
            ' Sample inverse calculation, JFK to LHR
            lat1 = 40.6 : lon1 = -73.8 ' JFK Airport
            lat2 = 51.6 : lon2 = -0.5  ' LHR Airport
            geod.Inverse(lat1, lon1, lat2, lon2, s12)
            Console.WriteLine(s12)
        Catch ex As GeographicErr
            Console.WriteLine(String.Format("Caught exception: {0}", ex.Message))
        End Try
    End Sub
End Module

INTERFACE DIFFERENCES:
A default constructor has been provided that assumes WGS84 parameters.

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

The GenDirect, GenInverse, and Line functions accept the "capabilities mask" as a NETGeographicLib::Mask rather than an unsigned.

Definition at line 167 of file Geodesic.h.


Constructor & Destructor Documentation

NETGeographicLib::Geodesic::Geodesic ( double  a,
double  f 
)

Constructor for a ellipsoid with

Parameters:
[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.
Exceptions:
GeographicErr if a or (1 f ) a is not positive.
NETGeographicLib::Geodesic::Geodesic (  ) 

Constructor for the WGS84 ellipsoid.

Referenced by ~Geodesic().

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

the destructor calls the finalizer.

Definition at line 200 of file Geodesic.h.

References Geodesic().


Member Function Documentation

double NETGeographicLib::Geodesic::Direct ( double  lat1,
double  lon1,
double  azi1,
double  s12,
[System::Runtime::InteropServices::Out] double%   lat2,
[System::Runtime::InteropServices::Out] double%   lon2,
[System::Runtime::InteropServices::Out] double%   azi2,
[System::Runtime::InteropServices::Out] double%   m12,
[System::Runtime::InteropServices::Out] double%   M12,
[System::Runtime::InteropServices::Out] double%   M21,
[System::Runtime::InteropServices::Out] double%   S12 
)

Solve the direct geodesic problem where the length of the geodesic is specified in terms of distance.

Parameters:
[in] lat1 latitude of point 1 (degrees).
[in] lon1 longitude of point 1 (degrees).
[in] azi1 azimuth at point 1 (degrees).
[in] s12 distance between point 1 and point 2 (meters); it can be negative.
[out] lat2 latitude of point 2 (degrees).
[out] lon2 longitude of point 2 (degrees).
[out] azi2 (forward) azimuth at point 2 (degrees).
[out] m12 reduced length of geodesic (meters).
[out] M12 geodesic scale of point 2 relative to point 1 (dimensionless).
[out] M21 geodesic scale of point 1 relative to point 2 (dimensionless).
[out] S12 area under the geodesic (meters2).
Returns:
a12 arc length of between point 1 and point 2 (degrees).

lat1 should be in the range [90, 90]; lon1 and azi1 should be in the range [540, 540). The values of lon2 and azi2 returned are in the range [180, 180).

If either point is at a pole, the azimuth is defined by keeping the longitude fixed, writing lat = (90 ), and taking the limit 0+. An arc length greater that 180 signifies a geodesic which is not a shortest path. (For a prolate ellipsoid, an additional condition is necessary for a shortest path: the longitudinal extent must not exceed of 180.)

The following functions are overloaded versions of Geodesic::Direct which omit some of the output parameters. Note, however, that the arc length is always computed and returned as the function value.

double NETGeographicLib::Geodesic::Direct ( double  lat1,
double  lon1,
double  azi1,
double  s12,
[System::Runtime::InteropServices::Out] double%   lat2,
[System::Runtime::InteropServices::Out] double%   lon2 
)

See the documentation for Geodesic::Direct.

double NETGeographicLib::Geodesic::Direct ( double  lat1,
double  lon1,
double  azi1,
double  s12,
[System::Runtime::InteropServices::Out] double%   lat2,
[System::Runtime::InteropServices::Out] double%   lon2,
[System::Runtime::InteropServices::Out] double%   azi2 
)

See the documentation for Geodesic::Direct.

double NETGeographicLib::Geodesic::Direct ( double  lat1,
double  lon1,
double  azi1,
double  s12,
[System::Runtime::InteropServices::Out] double%   lat2,
[System::Runtime::InteropServices::Out] double%   lon2,
[System::Runtime::InteropServices::Out] double%   azi2,
[System::Runtime::InteropServices::Out] double%   m12 
)

See the documentation for Geodesic::Direct.

double NETGeographicLib::Geodesic::Direct ( double  lat1,
double  lon1,
double  azi1,
double  s12,
[System::Runtime::InteropServices::Out] double%   lat2,
[System::Runtime::InteropServices::Out] double%   lon2,
[System::Runtime::InteropServices::Out] double%   azi2,
[System::Runtime::InteropServices::Out] double%   M12,
[System::Runtime::InteropServices::Out] double%   M21 
)

See the documentation for Geodesic::Direct.

double NETGeographicLib::Geodesic::Direct ( double  lat1,
double  lon1,
double  azi1,
double  s12,
[System::Runtime::InteropServices::Out] double%   lat2,
[System::Runtime::InteropServices::Out] double%   lon2,
[System::Runtime::InteropServices::Out] double%   azi2,
[System::Runtime::InteropServices::Out] double%   m12,
[System::Runtime::InteropServices::Out] double%   M12,
[System::Runtime::InteropServices::Out] double%   M21 
)

See the documentation for Geodesic::Direct.

void NETGeographicLib::Geodesic::ArcDirect ( double  lat1,
double  lon1,
double  azi1,
double  a12,
[System::Runtime::InteropServices::Out] double%   lat2,
[System::Runtime::InteropServices::Out] double%   lon2,
[System::Runtime::InteropServices::Out] double%   azi2,
[System::Runtime::InteropServices::Out] double%   s12,
[System::Runtime::InteropServices::Out] double%   m12,
[System::Runtime::InteropServices::Out] double%   M12,
[System::Runtime::InteropServices::Out] double%   M21,
[System::Runtime::InteropServices::Out] double%   S12 
)

Solve the direct geodesic problem where the length of the geodesic is specified in terms of arc length.

Parameters:
[in] lat1 latitude of point 1 (degrees).
[in] lon1 longitude of point 1 (degrees).
[in] azi1 azimuth at point 1 (degrees).
[in] a12 arc length between point 1 and point 2 (degrees); it can be negative.
[out] lat2 latitude of point 2 (degrees).
[out] lon2 longitude of point 2 (degrees).
[out] azi2 (forward) azimuth at point 2 (degrees).
[out] s12 distance between point 1 and point 2 (meters).
[out] m12 reduced length of geodesic (meters).
[out] M12 geodesic scale of point 2 relative to point 1 (dimensionless).
[out] M21 geodesic scale of point 1 relative to point 2 (dimensionless).
[out] S12 area under the geodesic (meters2).

lat1 should be in the range [90, 90]; lon1 and azi1 should be in the range [540, 540). The values of lon2 and azi2 returned are in the range [180, 180).

If either point is at a pole, the azimuth is defined by keeping the longitude fixed, writing lat = (90 ), and taking the limit 0+. An arc length greater that 180 signifies a geodesic which is not a shortest path. (For a prolate ellipsoid, an additional condition is necessary for a shortest path: the longitudinal extent must not exceed of 180.)

The following functions are overloaded versions of Geodesic::Direct which omit some of the output parameters.

void NETGeographicLib::Geodesic::ArcDirect ( double  lat1,
double  lon1,
double  azi1,
double  a12,
[System::Runtime::InteropServices::Out] double%   lat2,
[System::Runtime::InteropServices::Out] double%   lon2 
)

See the documentation for Geodesic::ArcDirect.

void NETGeographicLib::Geodesic::ArcDirect ( double  lat1,
double  lon1,
double  azi1,
double  a12,
[System::Runtime::InteropServices::Out] double%   lat2,
[System::Runtime::InteropServices::Out] double%   lon2,
[System::Runtime::InteropServices::Out] double%   azi2 
)

See the documentation for Geodesic::ArcDirect.

void NETGeographicLib::Geodesic::ArcDirect ( double  lat1,
double  lon1,
double  azi1,
double  a12,
[System::Runtime::InteropServices::Out] double%   lat2,
[System::Runtime::InteropServices::Out] double%   lon2,
[System::Runtime::InteropServices::Out] double%   azi2,
[System::Runtime::InteropServices::Out] double%   s12 
)

See the documentation for Geodesic::ArcDirect.

void NETGeographicLib::Geodesic::ArcDirect ( double  lat1,
double  lon1,
double  azi1,
double  a12,
[System::Runtime::InteropServices::Out] double%   lat2,
[System::Runtime::InteropServices::Out] double%   lon2,
[System::Runtime::InteropServices::Out] double%   azi2,
[System::Runtime::InteropServices::Out] double%   s12,
[System::Runtime::InteropServices::Out] double%   m12 
)

See the documentation for Geodesic::ArcDirect.

void NETGeographicLib::Geodesic::ArcDirect ( double  lat1,
double  lon1,
double  azi1,
double  a12,
[System::Runtime::InteropServices::Out] double%   lat2,
[System::Runtime::InteropServices::Out] double%   lon2,
[System::Runtime::InteropServices::Out] double%   azi2,
[System::Runtime::InteropServices::Out] double%   s12,
[System::Runtime::InteropServices::Out] double%   M12,
[System::Runtime::InteropServices::Out] double%   M21 
)

See the documentation for Geodesic::ArcDirect.

void NETGeographicLib::Geodesic::ArcDirect ( double  lat1,
double  lon1,
double  azi1,
double  a12,
[System::Runtime::InteropServices::Out] double%   lat2,
[System::Runtime::InteropServices::Out] double%   lon2,
[System::Runtime::InteropServices::Out] double%   azi2,
[System::Runtime::InteropServices::Out] double%   s12,
[System::Runtime::InteropServices::Out] double%   m12,
[System::Runtime::InteropServices::Out] double%   M12,
[System::Runtime::InteropServices::Out] double%   M21 
)

See the documentation for Geodesic::ArcDirect.

double NETGeographicLib::Geodesic::GenDirect ( double  lat1,
double  lon1,
double  azi1,
bool  arcmode,
double  s12_a12,
NETGeographicLib::Mask  outmask,
[System::Runtime::InteropServices::Out] double%   lat2,
[System::Runtime::InteropServices::Out] double%   lon2,
[System::Runtime::InteropServices::Out] double%   azi2,
[System::Runtime::InteropServices::Out] double%   s12,
[System::Runtime::InteropServices::Out] double%   m12,
[System::Runtime::InteropServices::Out] double%   M12,
[System::Runtime::InteropServices::Out] double%   M21,
[System::Runtime::InteropServices::Out] double%   S12 
)

The general direct geodesic problem. Geodesic::Direct and Geodesic::ArcDirect are defined in terms of this function.

Parameters:
[in] lat1 latitude of point 1 (degrees).
[in] lon1 longitude of point 1 (degrees).
[in] azi1 azimuth at point 1 (degrees).
[in] arcmode boolean flag determining the meaning of the s12_a12.
[in] s12_a12 if arcmode is false, this is the distance between point 1 and point 2 (meters); otherwise it is the arc length between point 1 and point 2 (degrees); it can be negative.
[in] outmask a bitor'ed combination of NETGeographicLib::Mask values specifying which of the following parameters should be set.
[out] lat2 latitude of point 2 (degrees).
[out] lon2 longitude of point 2 (degrees).
[out] azi2 (forward) azimuth at point 2 (degrees).
[out] s12 distance between point 1 and point 2 (meters).
[out] m12 reduced length of geodesic (meters).
[out] M12 geodesic scale of point 2 relative to point 1 (dimensionless).
[out] M21 geodesic scale of point 1 relative to point 2 (dimensionless).
[out] S12 area under the geodesic (meters2).
Returns:
a12 arc length of between point 1 and point 2 (degrees).

The NETGeographicLib::Mask values possible for outmask are

  • outmask |= NETGeographicLib::Mask::LATITUDE for the latitude lat2;
  • outmask |= NETGeographicLib::Mask::LONGITUDE for the latitude lon2;
  • outmask |= NETGeographicLib::Mask::AZIMUTH for the latitude azi2;
  • outmask |= NETGeographicLib::Mask::DISTANCE for the distance s12;
  • outmask |= NETGeographicLib::Mask::REDUCEDLENGTH for the reduced length m12;
  • outmask |= NETGeographicLib::Mask::GEODESICSCALE for the geodesic scales M12 and M21;
  • outmask |= NETGeographicLib::Mask::AREA for the area S12;
  • outmask |= NETGeographicLib::Mask::ALL for all of the above.

The function value a12 is always computed and returned and this equals s12_a12 is arcmode is true. If outmask includes NETGeographicLib::Mask::DISTANCE and arcmode is false, then s12 = s12_a12. It is not necessary to include NETGeographicLib::Mask::DISTANCE_IN in outmask; this is automatically included is arcmode is false.

double NETGeographicLib::Geodesic::Inverse ( double  lat1,
double  lon1,
double  lat2,
double  lon2,
[System::Runtime::InteropServices::Out] double%   s12,
[System::Runtime::InteropServices::Out] double%   azi1,
[System::Runtime::InteropServices::Out] double%   azi2,
[System::Runtime::InteropServices::Out] double%   m12,
[System::Runtime::InteropServices::Out] double%   M12,
[System::Runtime::InteropServices::Out] double%   M21,
[System::Runtime::InteropServices::Out] double%   S12 
)

Solve the inverse geodesic problem.

Parameters:
[in] lat1 latitude of point 1 (degrees).
[in] lon1 longitude of point 1 (degrees).
[in] lat2 latitude of point 2 (degrees).
[in] lon2 longitude of point 2 (degrees).
[out] s12 distance between point 1 and point 2 (meters).
[out] azi1 azimuth at point 1 (degrees).
[out] azi2 (forward) azimuth at point 2 (degrees).
[out] m12 reduced length of geodesic (meters).
[out] M12 geodesic scale of point 2 relative to point 1 (dimensionless).
[out] M21 geodesic scale of point 1 relative to point 2 (dimensionless).
[out] S12 area under the geodesic (meters2).
Returns:
a12 arc length of between point 1 and point 2 (degrees).

lat1 and lat2 should be in the range [90, 90]; lon1 and lon2 should be in the range [540, 540). The values of azi1 and azi2 returned are in the range [180, 180).

If either point is at a pole, the azimuth is defined by keeping the longitude fixed, writing lat = (90 ), and taking the limit 0+.

The solution to the inverse problem is found using Newton's method. If this fails to converge (this is very unlikely in geodetic applications but does occur for very eccentric ellipsoids), then the bisection method is used to refine the solution.

The following functions are overloaded versions of Geodesic::Inverse which omit some of the output parameters. Note, however, that the arc length is always computed and returned as the function value.

double NETGeographicLib::Geodesic::Inverse ( double  lat1,
double  lon1,
double  lat2,
double  lon2,
[System::Runtime::InteropServices::Out] double%   s12 
)

See the documentation for Geodesic::Inverse.

double NETGeographicLib::Geodesic::Inverse ( double  lat1,
double  lon1,
double  lat2,
double  lon2,
[System::Runtime::InteropServices::Out] double%   azi1,
[System::Runtime::InteropServices::Out] double%   azi2 
)

See the documentation for Geodesic::Inverse.

double NETGeographicLib::Geodesic::Inverse ( double  lat1,
double  lon1,
double  lat2,
double  lon2,
[System::Runtime::InteropServices::Out] double%   s12,
[System::Runtime::InteropServices::Out] double%   azi1,
[System::Runtime::InteropServices::Out] double%   azi2 
)

See the documentation for Geodesic::Inverse.

double NETGeographicLib::Geodesic::Inverse ( double  lat1,
double  lon1,
double  lat2,
double  lon2,
[System::Runtime::InteropServices::Out] double%   s12,
[System::Runtime::InteropServices::Out] double%   azi1,
[System::Runtime::InteropServices::Out] double%   azi2,
[System::Runtime::InteropServices::Out] double%   m12 
)

See the documentation for Geodesic::Inverse.

double NETGeographicLib::Geodesic::Inverse ( double  lat1,
double  lon1,
double  lat2,
double  lon2,
[System::Runtime::InteropServices::Out] double%   s12,
[System::Runtime::InteropServices::Out] double%   azi1,
[System::Runtime::InteropServices::Out] double%   azi2,
[System::Runtime::InteropServices::Out] double%   M12,
[System::Runtime::InteropServices::Out] double%   M21 
)

See the documentation for Geodesic::Inverse.

double NETGeographicLib::Geodesic::Inverse ( double  lat1,
double  lon1,
double  lat2,
double  lon2,
[System::Runtime::InteropServices::Out] double%   s12,
[System::Runtime::InteropServices::Out] double%   azi1,
[System::Runtime::InteropServices::Out] double%   azi2,
[System::Runtime::InteropServices::Out] double%   m12,
[System::Runtime::InteropServices::Out] double%   M12,
[System::Runtime::InteropServices::Out] double%   M21 
)

See the documentation for Geodesic::Inverse.

double NETGeographicLib::Geodesic::GenInverse ( double  lat1,
double  lon1,
double  lat2,
double  lon2,
NETGeographicLib::Mask  outmask,
[System::Runtime::InteropServices::Out] double%   s12,
[System::Runtime::InteropServices::Out] double%   azi1,
[System::Runtime::InteropServices::Out] double%   azi2,
[System::Runtime::InteropServices::Out] double%   m12,
[System::Runtime::InteropServices::Out] double%   M12,
[System::Runtime::InteropServices::Out] double%   M21,
[System::Runtime::InteropServices::Out] double%   S12 
)

The general inverse geodesic calculation. Geodesic::Inverse is defined in terms of this function.

Parameters:
[in] lat1 latitude of point 1 (degrees).
[in] lon1 longitude of point 1 (degrees).
[in] lat2 latitude of point 2 (degrees).
[in] lon2 longitude of point 2 (degrees).
[in] outmask a bitor'ed combination of Geodesic::mask values specifying which of the following parameters should be set.
[out] s12 distance between point 1 and point 2 (meters).
[out] azi1 azimuth at point 1 (degrees).
[out] azi2 (forward) azimuth at point 2 (degrees).
[out] m12 reduced length of geodesic (meters).
[out] M12 geodesic scale of point 2 relative to point 1 (dimensionless).
[out] M21 geodesic scale of point 1 relative to point 2 (dimensionless).
[out] S12 area under the geodesic (meters2).
Returns:
a12 arc length of between point 1 and point 2 (degrees).

The Geodesic::mask values possible for outmask are

  • outmask |= Geodesic::DISTANCE for the distance s12;
  • outmask |= Geodesic::AZIMUTH for the latitude azi2;
  • outmask |= Geodesic::REDUCEDLENGTH for the reduced length m12;
  • outmask |= Geodesic::GEODESICSCALE for the geodesic scales M12 and M21;
  • outmask |= Geodesic::AREA for the area S12;
  • outmask |= Geodesic::ALL for all of the above.

The arc length is always computed and returned as the function value.

GeodesicLine ^ NETGeographicLib::Geodesic::Line ( double  lat1,
double  lon1,
double  azi1,
NETGeographicLib::Mask  caps 
)

Set up to compute several points on a single geodesic.

Parameters:
[in] lat1 latitude of point 1 (degrees).
[in] lon1 longitude of point 1 (degrees).
[in] azi1 azimuth at point 1 (degrees).
[in] caps bitor'ed combination of NETGeographicLib::Mask values specifying the capabilities the GeodesicLine object should possess, i.e., which quantities can be returned in calls to GeodesicLine::Position.
Returns:
a GeodesicLine object.

lat1 should be in the range [90, 90]; lon1 and azi1 should be in the range [540, 540).

The NETGeographicLib::Mask values are

  • caps |= NETGeographicLib::Mask::LATITUDE for the latitude lat2; this is added automatically;
  • caps |= NETGeographicLib::Mask::LONGITUDE for the latitude lon2;
  • caps |= NETGeographicLib::Mask::AZIMUTH for the azimuth azi2; this is added automatically;
  • caps |= NETGeographicLib::Mask::DISTANCE for the distance s12;
  • caps |= NETGeographicLib::Mask::REDUCEDLENGTH for the reduced length m12;
  • caps |= NETGeographicLib::Mask::GEODESICSCALE for the geodesic scales M12 and M21;
  • caps |= NETGeographicLib::Mask::AREA for the area S12;
  • caps |= NETGeographicLib::Mask::DISTANCE_IN permits the length of the geodesic to be given in terms of s12; without this capability the length can only be specified in terms of arc length;
  • caps |= NETGeographicLib::Mask::ALL for all of the above.

If the point is at a pole, the azimuth is defined by keeping lon1 fixed, writing lat1 = (90 ), and taking the limit 0+.

System::IntPtr ^ NETGeographicLib::Geodesic::GetUnmanaged (  ) 

return The unmanaged pointer to the GeographicLib::Geodesic.

This function is for internal use only.


Property Documentation

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

Definition at line 664 of file Geodesic.h.

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

Definition at line 670 of file Geodesic.h.

double NETGeographicLib::Geodesic::EllipsoidArea [get]
Returns:
total area of ellipsoid in meters2. The area of a polygon encircling a pole can be found by adding Geodesic::EllipsoidArea()/2 to the sum of S12 for each side of the polygon.

Definition at line 678 of file Geodesic.h.


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