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#pragma once
/**
* \file NETGeographicLib/GeodesicExact.h
* \brief Header for NETGeographicLib::GeodesicExact class
*
* NETGeographicLib is copyright (c) Scott Heiman (2013)
* GeographicLib is Copyright (c) Charles Karney (2010-2012)
* <charles@karney.com> and licensed under the MIT/X11 License.
* For more information, see
* http://geographiclib.sourceforge.net/
**********************************************************************/
#include "NETGeographicLib.h"
namespace NETGeographicLib
{
ref class GeodesicLineExact;
/*!
\brief .NET wrapper for GeographicLib::GeodesicExact.
This class allows .NET applications to access GeographicLib::GeodesicExact.
*/
/**
* \brief .NET wrapper for GeographicLib::GeodesicExact.
*
* This class allows .NET applications to access GeographicLib::GeodesicExact.
*
* The equations for geodesics on an ellipsoid can be expressed in terms of
* incomplete elliptic integrals. The Geodesic class expands these integrals
* in a series in the flattening \e f and this provides an accurate solution
* for \e f &isin [-0.01, 0.01]. The GeodesicExact class computes the
* ellitpic integrals directly and so provides a solution which is valid for
* all \e f. However, in practice, its use should be limited to about \e
* b/\e a ∈ [0.01, 100] or \e f ∈ [-99, 0.99].
*
* For the WGS84 ellipsoid, these classes are 2--3 times \e slower than the
* series solution and 2--3 times \e less \e accurate (because it's less easy
* to control round-off errors with the elliptic integral formulation); i.e.,
* the error is about 40 nm (40 nanometers) instead of 15 nm. However the
* error in the series solution scales as <i>f</i><sup>7</sup> while the
* error in the elliptic integral solution depends weakly on \e f. If the
* quarter meridian distance is 10000 km and the ratio \e b/\e a = 1 −
* \e f is varied then the approximate maximum error (expressed as a
* distance) is <pre>
* 1 - f error (nm)
* 1/128 387
* 1/64 345
* 1/32 269
* 1/16 210
* 1/8 115
* 1/4 69
* 1/2 36
* 1 15
* 2 25
* 4 96
* 8 318
* 16 985
* 32 2352
* 64 6008
* 128 19024
* </pre>
*
* The computation of the area in these classes is via a 30th order series.
* This gives accurate results for \e b/\e a ∈ [1/2, 2]; the accuracy is
* about 8 decimal digits for \e b/\e a ∈ [1/4, 4].
*
* See \ref geodellip for the formulation. See the documentation on the
* Geodesic class for additional information on the geodesics problems.
*
* C# Example:
* \include example-GeodesicExact.cs
* Managed C++ Example:
* \include example-GeodesicExact.cpp
* Visual Basic Example:
* \include example-GeodesicExact.vb
*
* <B>INTERFACE DIFFERENCES:</B><BR>
* A default constructor is 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.
**********************************************************************/
public ref class GeodesicExact
{
private:
// pointer to the unmanaged GeographicLib::GeodesicExact.
const GeographicLib::GeodesicExact* m_pGeodesicExact;
// the finalizer deletes the unmanaged memory.
!GeodesicExact();
public:
/** \name Constructor
**********************************************************************/
///@{
/**
* Constructor for a WGS84 ellipsoid
**********************************************************************/
GeodesicExact();
/**
* Constructor for a ellipsoid with
*
* @param[in] a equatorial radius (meters).
* @param[in] f flattening of ellipsoid. Setting \e f = 0 gives a sphere.
* Negative \e f gives a prolate ellipsoid. If \e f > 1, set flattening
* to 1/\e f.
* @exception GeographicErr if \e a or (1 − \e f ) \e a is not
* positive.
**********************************************************************/
GeodesicExact(double a, double f);
///@}
/**
* The desstructor calls the finalizer.
**********************************************************************/
~GeodesicExact()
{ this->!GeodesicExact(); }
/** \name Direct geodesic problem specified in terms of distance.
**********************************************************************/
///@{
/**
* Perform the direct geodesic calculation where the length of the geodesic
* is specified in terms of distance.
*
* @param[in] lat1 latitude of point 1 (degrees).
* @param[in] lon1 longitude of point 1 (degrees).
* @param[in] azi1 azimuth at point 1 (degrees).
* @param[in] s12 distance between point 1 and point 2 (meters); it can be
* signed.
* @param[out] lat2 latitude of point 2 (degrees).
* @param[out] lon2 longitude of point 2 (degrees).
* @param[out] azi2 (forward) azimuth at point 2 (degrees).
* @param[out] m12 reduced length of geodesic (meters).
* @param[out] M12 geodesic scale of point 2 relative to point 1
* (dimensionless).
* @param[out] M21 geodesic scale of point 1 relative to point 2
* (dimensionless).
* @param[out] S12 area under the geodesic (meters<sup>2</sup>).
* @return \e a12 arc length of between point 1 and point 2 (degrees).
*
* \e lat1 should be in the range [−90°, 90°]; \e lon1 and \e
* azi1 should be in the range [−540°, 540°). The values of
* \e lon2 and \e 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 \e lat = ±(90° − ε),
* and taking the limit ε → 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 GeodesicExact::Direct
* which omit some of the output parameters. Note, however, that the arc
* length is always computed and returned as the function value.
**********************************************************************/
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);
/**
* See the documentation for GeodesicExact::Direct.
**********************************************************************/
double 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 GeodesicExact::Direct.
**********************************************************************/
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);
/**
* See the documentation for GeodesicExact::Direct.
**********************************************************************/
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);
/**
* See the documentation for GeodesicExact::Direct.
**********************************************************************/
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);
/**
* See the documentation for GeodesicExact::Direct.
**********************************************************************/
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);
///@}
/** \name Direct geodesic problem specified in terms of arc length.
**********************************************************************/
///@{
/**
* Perform the direct geodesic calculation where the length of the geodesic
* is specified in terms of arc length.
*
* @param[in] lat1 latitude of point 1 (degrees).
* @param[in] lon1 longitude of point 1 (degrees).
* @param[in] azi1 azimuth at point 1 (degrees).
* @param[in] a12 arc length between point 1 and point 2 (degrees); it can
* be signed.
* @param[out] lat2 latitude of point 2 (degrees).
* @param[out] lon2 longitude of point 2 (degrees).
* @param[out] azi2 (forward) azimuth at point 2 (degrees).
* @param[out] s12 distance between point 1 and point 2 (meters).
* @param[out] m12 reduced length of geodesic (meters).
* @param[out] M12 geodesic scale of point 2 relative to point 1
* (dimensionless).
* @param[out] M21 geodesic scale of point 1 relative to point 2
* (dimensionless).
* @param[out] S12 area under the geodesic (meters<sup>2</sup>).
*
* \e lat1 should be in the range [−90°, 90°]; \e lon1 and \e
* azi1 should be in the range [−540°, 540°). The values of
* \e lon2 and \e 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 \e lat = ±(90° − ε),
* and taking the limit ε → 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 GeodesicExact::Direct
* which omit some of the output parameters.
**********************************************************************/
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);
/**
* See the documentation for GeodesicExact::ArcDirect.
**********************************************************************/
void 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 GeodesicExact::ArcDirect.
**********************************************************************/
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);
/**
* See the documentation for GeodesicExact::ArcDirect.
**********************************************************************/
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);
/**
* See the documentation for GeodesicExact::ArcDirect.
**********************************************************************/
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);
/**
* See the documentation for GeodesicExact::ArcDirect.
**********************************************************************/
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);
/**
* See the documentation for GeodesicExact::ArcDirect.
**********************************************************************/
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);
///@}
/** \name General version of the direct geodesic solution.
**********************************************************************/
///@{
/**
* The general direct geodesic calculation. GeodesicExact::Direct and
* GeodesicExact::ArcDirect are defined in terms of this function.
*
* @param[in] lat1 latitude of point 1 (degrees).
* @param[in] lon1 longitude of point 1 (degrees).
* @param[in] azi1 azimuth at point 1 (degrees).
* @param[in] arcmode boolean flag determining the meaning of the second
* parameter.
* @param[in] s12_a12 if \e 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 signed.
* @param[in] outmask a bitor'ed combination of NETGeographicLib::Mask values
* specifying which of the following parameters should be set.
* @param[out] lat2 latitude of point 2 (degrees).
* @param[out] lon2 longitude of point 2 (degrees).
* @param[out] azi2 (forward) azimuth at point 2 (degrees).
* @param[out] s12 distance between point 1 and point 2 (meters).
* @param[out] m12 reduced length of geodesic (meters).
* @param[out] M12 geodesic scale of point 2 relative to point 1
* (dimensionless).
* @param[out] M21 geodesic scale of point 1 relative to point 2
* (dimensionless).
* @param[out] S12 area under the geodesic (meters<sup>2</sup>).
* @return \e a12 arc length of between point 1 and point 2 (degrees).
*
* The NETGeographicLib::Mask values possible for \e outmask are
* - \e outmask |= NETGeographicLib::Mask::LATITUDE for the latitude \e lat2;
* - \e outmask |= NETGeographicLib::Mask::LONGITUDE for the latitude \e lon2;
* - \e outmask |= NETGeographicLib::Mask::AZIMUTH for the latitude \e azi2;
* - \e outmask |= NETGeographicLib::Mask::DISTANCE for the distance \e s12;
* - \e outmask |= NETGeographicLib::Mask::REDUCEDLENGTH for the reduced length \e
* m12;
* - \e outmask |= NETGeographicLib::Mask::GEODESICSCALE for the geodesic scales \e
* M12 and \e M21;
* - \e outmask |= NETGeographicLib::Mask::AREA for the area \e S12;
* - \e outmask |= NETGeographicLib::Mask::ALL for all of the above.
* .
* The function value \e a12 is always computed and returned and this
* equals \e s12_a12 is \e arcmode is true. If \e outmask includes
* GeodesicExact::DISTANCE and \e arcmode is false, then \e s12 = \e
* s12_a12. It is not necessary to include NETGeographicLib::Mask::DISTANCE_IN in
* \e outmask; this is automatically included is \e arcmode is false.
**********************************************************************/
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);
///@}
/** \name Inverse geodesic problem.
**********************************************************************/
///@{
/**
* Perform the inverse geodesic calculation.
*
* @param[in] lat1 latitude of point 1 (degrees).
* @param[in] lon1 longitude of point 1 (degrees).
* @param[in] lat2 latitude of point 2 (degrees).
* @param[in] lon2 longitude of point 2 (degrees).
* @param[out] s12 distance between point 1 and point 2 (meters).
* @param[out] azi1 azimuth at point 1 (degrees).
* @param[out] azi2 (forward) azimuth at point 2 (degrees).
* @param[out] m12 reduced length of geodesic (meters).
* @param[out] M12 geodesic scale of point 2 relative to point 1
* (dimensionless).
* @param[out] M21 geodesic scale of point 1 relative to point 2
* (dimensionless).
* @param[out] S12 area under the geodesic (meters<sup>2</sup>).
* @return \e a12 arc length of between point 1 and point 2 (degrees).
*
* \e lat1 and \e lat2 should be in the range [−90°, 90°]; \e
* lon1 and \e lon2 should be in the range [−540°, 540°).
* The values of \e azi1 and \e 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 \e lat = ±(90° − ε),
* and taking the limit ε → 0+.
*
* The following functions are overloaded versions of GeodesicExact::Inverse
* which omit some of the output parameters. Note, however, that the arc
* length is always computed and returned as the function value.
**********************************************************************/
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);
/**
* See the documentation for GeodesicExact::Inverse.
**********************************************************************/
double Inverse(double lat1, double lon1, double lat2, double lon2,
[System::Runtime::InteropServices::Out] double% s12);
/**
* See the documentation for GeodesicExact::Inverse.
**********************************************************************/
double 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 GeodesicExact::Inverse.
**********************************************************************/
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);
/**
* See the documentation for GeodesicExact::Inverse.
**********************************************************************/
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);
/**
* See the documentation for GeodesicExact::Inverse.
**********************************************************************/
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);
/**
* See the documentation for GeodesicExact::Inverse.
**********************************************************************/
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);
///@}
/** \name General version of inverse geodesic solution.
**********************************************************************/
///@{
/**
* The general inverse geodesic calculation. GeodesicExact::Inverse is
* defined in terms of this function.
*
* @param[in] lat1 latitude of point 1 (degrees).
* @param[in] lon1 longitude of point 1 (degrees).
* @param[in] lat2 latitude of point 2 (degrees).
* @param[in] lon2 longitude of point 2 (degrees).
* @param[in] outmask a bitor'ed combination of NETGeographicLib::Mask values
* specifying which of the following parameters should be set.
* @param[out] s12 distance between point 1 and point 2 (meters).
* @param[out] azi1 azimuth at point 1 (degrees).
* @param[out] azi2 (forward) azimuth at point 2 (degrees).
* @param[out] m12 reduced length of geodesic (meters).
* @param[out] M12 geodesic scale of point 2 relative to point 1
* (dimensionless).
* @param[out] M21 geodesic scale of point 1 relative to point 2
* (dimensionless).
* @param[out] S12 area under the geodesic (meters<sup>2</sup>).
* @return \e a12 arc length of between point 1 and point 2 (degrees).
*
* The NETGeographicLib::Mask values possible for \e outmask are
* - \e outmask |= NETGeographicLib::Mask::DISTANCE for the distance \e s12;
* - \e outmask |= NETGeographicLib::Mask::AZIMUTH for the latitude \e azi2;
* - \e outmask |= NETGeographicLib::Mask::REDUCEDLENGTH for the reduced length \e
* m12;
* - \e outmask |= NETGeographicLib::Mask::GEODESICSCALE for the geodesic scales \e
* M12 and \e M21;
* - \e outmask |= NETGeographicLib::Mask::AREA for the area \e S12;
* - \e outmask |= NETGeographicLib::Mask::ALL for all of the above.
* .
* The arc length is always computed and returned as the function value.
**********************************************************************/
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);
///@}
/** \name Interface to GeodesicLineExact.
**********************************************************************/
///@{
/**
* Set up to compute several points on a single geodesic.
*
* @param[in] lat1 latitude of point 1 (degrees).
* @param[in] lon1 longitude of point 1 (degrees).
* @param[in] azi1 azimuth at point 1 (degrees).
* @param[in] caps bitor'ed combination of NETGeographicLib::Mask values
* specifying the capabilities the GeodesicLineExact object should
* possess, i.e., which quantities can be returned in calls to
* GeodesicLineExact::Position.
* @return a GeodesicLineExact object.
*
* \e lat1 should be in the range [−90°, 90°]; \e lon1 and \e
* azi1 should be in the range [−540°, 540°).
*
* The GeodesicExact::mask values are
* - \e caps |= NETGeographicLib::Mask::LATITUDE for the latitude \e lat2; this is
* added automatically;
* - \e caps |= NETGeographicLib::Mask::LONGITUDE for the latitude \e lon2;
* - \e caps |= NETGeographicLib::Mask::AZIMUTH for the azimuth \e azi2; this is
* added automatically;
* - \e caps |= NETGeographicLib::Mask::DISTANCE for the distance \e s12;
* - \e caps |= NETGeographicLib::Mask::REDUCEDLENGTH for the reduced length \e m12;
* - \e caps |= NETGeographicLib::Mask::GEODESICSCALE for the geodesic scales \e M12
* and \e M21;
* - \e caps |= NETGeographicLib::Mask::AREA for the area \e S12;
* - \e caps |= NETGeographicLib::Mask::DISTANCE_IN permits the length of the
* geodesic to be given in terms of \e s12; without this capability the
* length can only be specified in terms of arc length;
* - \e caps |= GeodesicExact::ALL for all of the above.
* .
* The default value of \e caps is GeodesicExact::ALL which turns on all
* the capabilities.
*
* If the point is at a pole, the azimuth is defined by keeping \e lon1
* fixed, writing \e lat1 = ±(90 − ε), and taking the
* limit ε → 0+.
**********************************************************************/
GeodesicLineExact^ Line(double lat1, double lon1, double azi1,
NETGeographicLib::Mask caps );
///@}
/** \name Inspector functions.
**********************************************************************/
///@{
/**
* @return \e a the equatorial radius of the ellipsoid (meters). This is
* the value used in the constructor.
**********************************************************************/
property double MajorRadius { double get(); }
/**
* @return \e f the flattening of the ellipsoid. This is the
* value used in the constructor.
**********************************************************************/
property double Flattening { double get(); }
/**
* @return total area of ellipsoid in meters<sup>2</sup>. The area of a
* polygon encircling a pole can be found by adding
* GeodesicExact::EllipsoidArea()/2 to the sum of \e S12 for each side of
* the polygon.
**********************************************************************/
property double EllipsoidArea { double get(); }
///@}
/**
* @return A pointer to the unmanaged GeographicLib::GeodesicExact.
*
* This function is for internal use only.
**********************************************************************/
System::IntPtr^ GetUnmanaged();
};
} // namespace NETGeographicLib
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