GeodesicLineExact.hpp
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/**
* \file GeodesicLineExact.hpp
* \brief Header for GeographicLib::GeodesicLineExact class
*
* Copyright (c) Charles Karney (2012-2023) <karney@alum.mit.edu> and licensed
* under the MIT/X11 License. For more information, see
* https://geographiclib.sourceforge.io/
**********************************************************************/
#if !defined(GEOGRAPHICLIB_GEODESICLINEEXACT_HPP)
#define GEOGRAPHICLIB_GEODESICLINEEXACT_HPP 1
#include <GeographicLib/Constants.hpp>
#include <GeographicLib/GeodesicExact.hpp>
#include <GeographicLib/EllipticFunction.hpp>
#include <vector>
#if defined(_MSC_VER)
// Squelch warnings about dll vs vector
# pragma warning (push)
# pragma warning (disable: 4251)
#endif
namespace GeographicLib {
/**
* \brief An exact geodesic line
*
* GeodesicLineExact facilitates the determination of a series of points on a
* single geodesic. This is a companion to the GeodesicExact class. For
* additional information on this class see the documentation on the
* GeodesicLine class.
*
* Example of use:
* \include example-GeodesicLineExact.cpp
*
* <a href="GeodSolve.1.html">GeodSolve</a> is a command-line utility
* providing access to the functionality of GeodesicExact and
* GeodesicLineExact (via the -E option).
**********************************************************************/
class GEOGRAPHICLIB_EXPORT GeodesicLineExact {
private:
typedef Math::real real;
friend class GeodesicExact;
friend class GeodesicLine;
int _nC4;
real tiny_;
real _lat1, _lon1, _azi1;
real _a, _f, _b, _c2, _f1, _e2, _salp0, _calp0, _k2,
_salp1, _calp1, _ssig1, _csig1, _dn1, _stau1, _ctau1,
_somg1, _comg1, _cchi1,
_aA4, _eE0, _dD0, _hH0, _eE1, _dD1, _hH1;
real _a13, _s13;
real _bB41;
std::vector<real> _cC4a;
EllipticFunction _eE;
unsigned _caps;
void LineInit(const GeodesicExact& g,
real lat1, real lon1,
real azi1, real salp1, real calp1,
unsigned caps);
GeodesicLineExact(const GeodesicExact& g,
real lat1, real lon1,
real azi1, real salp1, real calp1,
unsigned caps, bool arcmode, real s13_a13);
enum captype {
CAP_NONE = GeodesicExact::CAP_NONE,
CAP_E = GeodesicExact::CAP_E,
CAP_D = GeodesicExact::CAP_D,
CAP_H = GeodesicExact::CAP_H,
CAP_C4 = GeodesicExact::CAP_C4,
CAP_ALL = GeodesicExact::CAP_ALL,
CAP_MASK = GeodesicExact::CAP_MASK,
OUT_ALL = GeodesicExact::OUT_ALL,
OUT_MASK = GeodesicExact::OUT_MASK,
};
public:
/**
* Bit masks for what calculations to do. They signify to the
* GeodesicLineExact::GeodesicLineExact constructor and to
* GeodesicExact::Line what capabilities should be included in the
* GeodesicLineExact object. This is merely a duplication of
* GeodesicExact::mask.
**********************************************************************/
enum mask {
/**
* No capabilities, no output.
* @hideinitializer
**********************************************************************/
NONE = GeodesicExact::NONE,
/**
* Calculate latitude \e lat2. (It's not necessary to include this as a
* capability to GeodesicLineExact because this is included by default.)
* @hideinitializer
**********************************************************************/
LATITUDE = GeodesicExact::LATITUDE,
/**
* Calculate longitude \e lon2.
* @hideinitializer
**********************************************************************/
LONGITUDE = GeodesicExact::LONGITUDE,
/**
* Calculate azimuths \e azi1 and \e azi2. (It's not necessary to
* include this as a capability to GeodesicLineExact because this is
* included by default.)
* @hideinitializer
**********************************************************************/
AZIMUTH = GeodesicExact::AZIMUTH,
/**
* Calculate distance \e s12.
* @hideinitializer
**********************************************************************/
DISTANCE = GeodesicExact::DISTANCE,
/**
* A combination of the common capabilities: GeodesicLineExact::LATITUDE,
* GeodesicLineExact::LONGITUDE, GeodesicLineExact::AZIMUTH,
* GeodesicLineExact::DISTANCE.
* @hideinitializer
**********************************************************************/
STANDARD = GeodesicExact::STANDARD,
/**
* Allow distance \e s12 to be used as input in the direct geodesic
* problem.
* @hideinitializer
**********************************************************************/
DISTANCE_IN = GeodesicExact::DISTANCE_IN,
/**
* Calculate reduced length \e m12.
* @hideinitializer
**********************************************************************/
REDUCEDLENGTH = GeodesicExact::REDUCEDLENGTH,
/**
* Calculate geodesic scales \e M12 and \e M21.
* @hideinitializer
**********************************************************************/
GEODESICSCALE = GeodesicExact::GEODESICSCALE,
/**
* Calculate area \e S12.
* @hideinitializer
**********************************************************************/
AREA = GeodesicExact::AREA,
/**
* Unroll \e lon2 in the direct calculation.
* @hideinitializer
**********************************************************************/
LONG_UNROLL = GeodesicExact::LONG_UNROLL,
/**
* All capabilities, calculate everything. (LONG_UNROLL is not
* included in this mask.)
* @hideinitializer
**********************************************************************/
ALL = GeodesicExact::ALL,
};
/**
* Typedef for the base class implementing geodesics.
**********************************************************************/
typedef GeodesicExact BaseClass;
/** \name Constructors
**********************************************************************/
///@{
/**
* Constructor for a geodesic line staring at latitude \e lat1, longitude
* \e lon1, and azimuth \e azi1 (all in degrees).
*
* @param[in] g A GeodesicExact object used to compute the necessary
* information about the GeodesicLineExact.
* @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 GeodesicLineExact::mask values
* specifying the capabilities the GeodesicLineExact object should
* possess, i.e., which quantities can be returned in calls to
* GeodesicLine::Position.
*
* \e lat1 should be in the range [&minus;90&deg;, 90&deg;].
*
* The GeodesicLineExact::mask values are
* - \e caps |= GeodesicLineExact::LATITUDE for the latitude \e lat2; this
* is added automatically;
* - \e caps |= GeodesicLineExact::LONGITUDE for the latitude \e lon2;
* - \e caps |= GeodesicLineExact::AZIMUTH for the latitude \e azi2; this
* is added automatically;
* - \e caps |= GeodesicLineExact::DISTANCE for the distance \e s12;
* - \e caps |= GeodesicLineExact::REDUCEDLENGTH for the reduced length \e
* m12;
* - \e caps |= GeodesicLineExact::GEODESICSCALE for the geodesic scales \e
* M12 and \e M21;
* - \e caps |= GeodesicLineExact::AREA for the area \e S12;
* - \e caps |= GeodesicLineExact::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 |= GeodesicLineExact::ALL for all of the above.
* .
* The default value of \e caps is GeodesicLineExact::ALL.
*
* If the point is at a pole, the azimuth is defined by keeping \e lon1
* fixed, writing \e lat1 = &plusmn;(90&deg; &minus; &epsilon;), and taking
* the limit &epsilon; &rarr; 0+.
**********************************************************************/
GeodesicLineExact(const GeodesicExact& g, real lat1, real lon1, real azi1,
unsigned caps = ALL);
/**
* A default constructor. If GeodesicLineExact::Position is called on the
* resulting object, it returns immediately (without doing any
* calculations). The object can be set with a call to
* GeodesicExact::Line. Use Init() to test whether object is still in this
* uninitialized state.
**********************************************************************/
GeodesicLineExact() : _caps(0U) {}
///@}
/** \name Position in terms of distance
**********************************************************************/
///@{
/**
* Compute the position of point 2 which is a distance \e s12 (meters)
* from point 1.
*
* @param[in] s12 distance from point 1 to point 2 (meters); it can be
* signed.
* @param[out] lat2 latitude of point 2 (degrees).
* @param[out] lon2 longitude of point 2 (degrees); requires that the
* GeodesicLineExact object was constructed with \e caps |=
* GeodesicLineExact::LONGITUDE.
* @param[out] azi2 (forward) azimuth at point 2 (degrees).
* @param[out] m12 reduced length of geodesic (meters); requires that the
* GeodesicLineExact object was constructed with \e caps |=
* GeodesicLineExact::REDUCEDLENGTH.
* @param[out] M12 geodesic scale of point 2 relative to point 1
* (dimensionless); requires that the GeodesicLineExact object was
* constructed with \e caps |= GeodesicLineExact::GEODESICSCALE.
* @param[out] M21 geodesic scale of point 1 relative to point 2
* (dimensionless); requires that the GeodesicLineExact object was
* constructed with \e caps |= GeodesicLineExact::GEODESICSCALE.
* @param[out] S12 area under the geodesic (meters<sup>2</sup>); requires
* that the GeodesicLineExact object was constructed with \e caps |=
* GeodesicLineExact::AREA.
* @return \e a12 arc length from point 1 to point 2 (degrees).
*
* The values of \e lon2 and \e azi2 returned are in the range
* [&minus;180&deg;, 180&deg;].
*
* The GeodesicLineExact object \e must have been constructed with \e caps
* |= GeodesicLineExact::DISTANCE_IN; otherwise Math::NaN() is returned and
* no parameters are set. Requesting a value which the GeodesicLineExact
* object is not capable of computing is not an error; the corresponding
* argument will not be altered.
*
* The following functions are overloaded versions of
* GeodesicLineExact::Position which omit some of the output parameters.
* Note, however, that the arc length is always computed and returned as
* the function value.
**********************************************************************/
Math::real Position(real s12, real& lat2, real& lon2, real& azi2,
real& m12, real& M12, real& M21, real& S12) const {
real t;
return GenPosition(false, s12,
LATITUDE | LONGITUDE | AZIMUTH |
REDUCEDLENGTH | GEODESICSCALE | AREA,
lat2, lon2, azi2, t, m12, M12, M21, S12);
}
/**
* See the documentation for GeodesicLineExact::Position.
**********************************************************************/
Math::real Position(real s12, real& lat2, real& lon2)
const {
real t;
return GenPosition(false, s12,
LATITUDE | LONGITUDE,
lat2, lon2, t, t, t, t, t, t);
}
/**
* See the documentation for GeodesicLineExact::Position.
**********************************************************************/
Math::real Position(real s12, real& lat2, real& lon2, real& azi2) const {
real t;
return GenPosition(false, s12,
LATITUDE | LONGITUDE | AZIMUTH,
lat2, lon2, azi2, t, t, t, t, t);
}
/**
* See the documentation for GeodesicLineExact::Position.
**********************************************************************/
Math::real Position(real s12, real& lat2, real& lon2, real& azi2,
real& m12) const {
real t;
return GenPosition(false, s12,
LATITUDE | LONGITUDE |
AZIMUTH | REDUCEDLENGTH,
lat2, lon2, azi2, t, m12, t, t, t);
}
/**
* See the documentation for GeodesicLineExact::Position.
**********************************************************************/
Math::real Position(real s12, real& lat2, real& lon2, real& azi2,
real& M12, real& M21) const {
real t;
return GenPosition(false, s12,
LATITUDE | LONGITUDE |
AZIMUTH | GEODESICSCALE,
lat2, lon2, azi2, t, t, M12, M21, t);
}
/**
* See the documentation for GeodesicLineExact::Position.
**********************************************************************/
Math::real Position(real s12, real& lat2, real& lon2, real& azi2,
real& m12, real& M12, real& M21) const {
real t;
return GenPosition(false, s12,
LATITUDE | LONGITUDE | AZIMUTH |
REDUCEDLENGTH | GEODESICSCALE,
lat2, lon2, azi2, t, m12, M12, M21, t);
}
///@}
/** \name Position in terms of arc length
**********************************************************************/
///@{
/**
* Compute the position of point 2 which is an arc length \e a12 (degrees)
* from point 1.
*
* @param[in] a12 arc length from point 1 to point 2 (degrees); it can
* be signed.
* @param[out] lat2 latitude of point 2 (degrees).
* @param[out] lon2 longitude of point 2 (degrees); requires that the
* GeodesicLineExact object was constructed with \e caps |=
* GeodesicLineExact::LONGITUDE.
* @param[out] azi2 (forward) azimuth at point 2 (degrees).
* @param[out] s12 distance from point 1 to point 2 (meters); requires
* that the GeodesicLineExact object was constructed with \e caps |=
* GeodesicLineExact::DISTANCE.
* @param[out] m12 reduced length of geodesic (meters); requires that the
* GeodesicLineExact object was constructed with \e caps |=
* GeodesicLineExact::REDUCEDLENGTH.
* @param[out] M12 geodesic scale of point 2 relative to point 1
* (dimensionless); requires that the GeodesicLineExact object was
* constructed with \e caps |= GeodesicLineExact::GEODESICSCALE.
* @param[out] M21 geodesic scale of point 1 relative to point 2
* (dimensionless); requires that the GeodesicLineExact object was
* constructed with \e caps |= GeodesicLineExact::GEODESICSCALE.
* @param[out] S12 area under the geodesic (meters<sup>2</sup>); requires
* that the GeodesicLineExact object was constructed with \e caps |=
* GeodesicLineExact::AREA.
*
* The values of \e lon2 and \e azi2 returned are in the range
* [&minus;180&deg;, 180&deg;].
*
* Requesting a value which the GeodesicLineExact object is not capable of
* computing is not an error; the corresponding argument will not be
* altered.
*
* The following functions are overloaded versions of
* GeodesicLineExact::ArcPosition which omit some of the output parameters.
**********************************************************************/
void ArcPosition(real a12, real& lat2, real& lon2, real& azi2,
real& s12, real& m12, real& M12, real& M21, real& S12)
const {
GenPosition(true, a12,
LATITUDE | LONGITUDE | AZIMUTH | DISTANCE |
REDUCEDLENGTH | GEODESICSCALE | AREA,
lat2, lon2, azi2, s12, m12, M12, M21, S12);
}
/**
* See the documentation for GeodesicLineExact::ArcPosition.
**********************************************************************/
void ArcPosition(real a12, real& lat2, real& lon2) const {
real t;
GenPosition(true, a12,
LATITUDE | LONGITUDE,
lat2, lon2, t, t, t, t, t, t);
}
/**
* See the documentation for GeodesicLineExact::ArcPosition.
**********************************************************************/
void ArcPosition(real a12, real& lat2, real& lon2, real& azi2) const {
real t;
GenPosition(true, a12,
LATITUDE | LONGITUDE | AZIMUTH,
lat2, lon2, azi2, t, t, t, t, t);
}
/**
* See the documentation for GeodesicLineExact::ArcPosition.
**********************************************************************/
void ArcPosition(real a12, real& lat2, real& lon2, real& azi2, real& s12)
const {
real t;
GenPosition(true, a12,
LATITUDE | LONGITUDE | AZIMUTH | DISTANCE,
lat2, lon2, azi2, s12, t, t, t, t);
}
/**
* See the documentation for GeodesicLineExact::ArcPosition.
**********************************************************************/
void ArcPosition(real a12, real& lat2, real& lon2, real& azi2,
real& s12, real& m12) const {
real t;
GenPosition(true, a12,
LATITUDE | LONGITUDE | AZIMUTH |
DISTANCE | REDUCEDLENGTH,
lat2, lon2, azi2, s12, m12, t, t, t);
}
/**
* See the documentation for GeodesicLineExact::ArcPosition.
**********************************************************************/
void ArcPosition(real a12, real& lat2, real& lon2, real& azi2,
real& s12, real& M12, real& M21) const {
real t;
GenPosition(true, a12,
LATITUDE | LONGITUDE | AZIMUTH |
DISTANCE | GEODESICSCALE,
lat2, lon2, azi2, s12, t, M12, M21, t);
}
/**
* See the documentation for GeodesicLineExact::ArcPosition.
**********************************************************************/
void ArcPosition(real a12, real& lat2, real& lon2, real& azi2,
real& s12, real& m12, real& M12, real& M21) const {
real t;
GenPosition(true, a12,
LATITUDE | LONGITUDE | AZIMUTH |
DISTANCE | REDUCEDLENGTH | GEODESICSCALE,
lat2, lon2, azi2, s12, m12, M12, M21, t);
}
///@}
/** \name The general position function.
**********************************************************************/
///@{
/**
* The general position function. GeodesicLineExact::Position and
* GeodesicLineExact::ArcPosition are defined in terms of this function.
*
* @param[in] arcmode boolean flag determining the meaning of the second
* parameter; if \e arcmode is false, then the GeodesicLineExact object
* must have been constructed with \e caps |=
* GeodesicLineExact::DISTANCE_IN.
* @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 GeodesicLineExact::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); requires that the
* GeodesicLineExact object was constructed with \e caps |=
* GeodesicLineExact::LONGITUDE.
* @param[out] azi2 (forward) azimuth at point 2 (degrees).
* @param[out] s12 distance from point 1 to point 2 (meters); requires
* that the GeodesicLineExact object was constructed with \e caps |=
* GeodesicLineExact::DISTANCE.
* @param[out] m12 reduced length of geodesic (meters); requires that the
* GeodesicLineExact object was constructed with \e caps |=
* GeodesicLineExact::REDUCEDLENGTH.
* @param[out] M12 geodesic scale of point 2 relative to point 1
* (dimensionless); requires that the GeodesicLineExact object was
* constructed with \e caps |= GeodesicLineExact::GEODESICSCALE.
* @param[out] M21 geodesic scale of point 1 relative to point 2
* (dimensionless); requires that the GeodesicLineExact object was
* constructed with \e caps |= GeodesicLineExact::GEODESICSCALE.
* @param[out] S12 area under the geodesic (meters<sup>2</sup>); requires
* that the GeodesicLineExact object was constructed with \e caps |=
* GeodesicLineExact::AREA.
* @return \e a12 arc length from point 1 to point 2 (degrees).
*
* The GeodesicLineExact::mask values possible for \e outmask are
* - \e outmask |= GeodesicLineExact::LATITUDE for the latitude \e lat2;
* - \e outmask |= GeodesicLineExact::LONGITUDE for the latitude \e lon2;
* - \e outmask |= GeodesicLineExact::AZIMUTH for the latitude \e azi2;
* - \e outmask |= GeodesicLineExact::DISTANCE for the distance \e s12;
* - \e outmask |= GeodesicLineExact::REDUCEDLENGTH for the reduced length
* \e m12;
* - \e outmask |= GeodesicLineExact::GEODESICSCALE for the geodesic scales
* \e M12 and \e M21;
* - \e outmask |= GeodesicLineExact::AREA for the area \e S12;
* - \e outmask |= GeodesicLineExact::ALL for all of the above;
* - \e outmask |= GeodesicLineExact::LONG_UNROLL to unroll \e lon2 instead
* of wrapping it into the range [&minus;180&deg;, 180&deg;].
* .
* Requesting a value which the GeodesicLineExact object is not capable of
* computing is not an error; the corresponding argument will not be
* altered. Note, however, that the arc length is always computed and
* returned as the function value.
*
* With the GeodesicLineExact::LONG_UNROLL bit set, the quantity \e lon2
* &minus; \e lon1 indicates how many times and in what sense the geodesic
* encircles the ellipsoid.
**********************************************************************/
Math::real GenPosition(bool arcmode, real s12_a12, unsigned outmask,
real& lat2, real& lon2, real& azi2,
real& s12, real& m12, real& M12, real& M21,
real& S12) const;
///@}
/** \name Setting point 3
**********************************************************************/
///@{
/**
* Specify position of point 3 in terms of distance.
*
* @param[in] s13 the distance from point 1 to point 3 (meters); it
* can be negative.
*
* This is only useful if the GeodesicLineExact object has been constructed
* with \e caps |= GeodesicLineExact::DISTANCE_IN.
**********************************************************************/
void SetDistance(real s13);
/**
* Specify position of point 3 in terms of arc length.
*
* @param[in] a13 the arc length from point 1 to point 3 (degrees); it
* can be negative.
*
* The distance \e s13 is only set if the GeodesicLineExact object has been
* constructed with \e caps |= GeodesicLineExact::DISTANCE.
**********************************************************************/
void SetArc(real a13);
/**
* Specify position of point 3 in terms of either distance or arc length.
*
* @param[in] arcmode boolean flag determining the meaning of the second
* parameter; if \e arcmode is false, then the GeodesicLineExact object
* must have been constructed with \e caps |=
* GeodesicLineExact::DISTANCE_IN.
* @param[in] s13_a13 if \e arcmode is false, this is the distance from
* point 1 to point 3 (meters); otherwise it is the arc length from
* point 1 to point 3 (degrees); it can be negative.
**********************************************************************/
void GenSetDistance(bool arcmode, real s13_a13);
/** \name Inspector functions
**********************************************************************/
///@{
/**
* @return true if the object has been initialized.
**********************************************************************/
bool Init() const { return _caps != 0U; }
/**
* @return \e lat1 the latitude of point 1 (degrees).
**********************************************************************/
Math::real Latitude() const
{ return Init() ? _lat1 : Math::NaN(); }
/**
* @return \e lon1 the longitude of point 1 (degrees).
**********************************************************************/
Math::real Longitude() const
{ return Init() ? _lon1 : Math::NaN(); }
/**
* @return \e azi1 the azimuth (degrees) of the geodesic line at point 1.
**********************************************************************/
Math::real Azimuth() const
{ return Init() ? _azi1 : Math::NaN(); }
/**
* The sine and cosine of \e azi1.
*
* @param[out] sazi1 the sine of \e azi1.
* @param[out] cazi1 the cosine of \e azi1.
**********************************************************************/
void Azimuth(real& sazi1, real& cazi1) const
{ if (Init()) { sazi1 = _salp1; cazi1 = _calp1; } }
/**
* @return \e azi0 the azimuth (degrees) of the geodesic line as it crosses
* the equator in a northward direction.
*
* The result lies in [&minus;90&deg;, 90&deg;].
**********************************************************************/
Math::real EquatorialAzimuth() const
{ return Init() ? Math::atan2d(_salp0, _calp0) : Math::NaN(); }
/**
* The sine and cosine of \e azi0.
*
* @param[out] sazi0 the sine of \e azi0.
* @param[out] cazi0 the cosine of \e azi0.
**********************************************************************/
void EquatorialAzimuth(real& sazi0, real& cazi0) const
{ if (Init()) { sazi0 = _salp0; cazi0 = _calp0; } }
/**
* @return \e a1 the arc length (degrees) between the northward equatorial
* crossing and point 1.
*
* The result lies in [&minus;180&deg;, 180&deg;].
**********************************************************************/
Math::real EquatorialArc() const {
using std::atan2;
return Init() ? atan2(_ssig1, _csig1) / Math::degree() : Math::NaN();
}
/**
* @return \e a the equatorial radius of the ellipsoid (meters). This is
* the value inherited from the GeodesicExact object used in the
* constructor.
**********************************************************************/
Math::real EquatorialRadius() const
{ return Init() ? _a : Math::NaN(); }
/**
* @return \e f the flattening of the ellipsoid. This is the value
* inherited from the GeodesicExact object used in the constructor.
**********************************************************************/
Math::real Flattening() const
{ return Init() ? _f : Math::NaN(); }
/**
* @return \e caps the computational capabilities that this object was
* constructed with. LATITUDE and AZIMUTH are always included.
**********************************************************************/
unsigned Capabilities() const { return _caps; }
/**
* Test what capabilities are available.
*
* @param[in] testcaps a set of bitor'ed GeodesicLineExact::mask values.
* @return true if the GeodesicLineExact object has all these capabilities.
**********************************************************************/
bool Capabilities(unsigned testcaps) const {
testcaps &= OUT_ALL;
return (_caps & testcaps) == testcaps;
}
/**
* The distance or arc length to point 3.
*
* @param[in] arcmode boolean flag determining the meaning of returned
* value.
* @return \e s13 if \e arcmode is false; \e a13 if \e arcmode is true.
**********************************************************************/
Math::real GenDistance(bool arcmode) const
{ return Init() ? (arcmode ? _a13 : _s13) : Math::NaN(); }
/**
* @return \e s13, the distance to point 3 (meters).
**********************************************************************/
Math::real Distance() const
{ return GenDistance(false); }
/**
* @return \e a13, the arc length to point 3 (degrees).
**********************************************************************/
Math::real Arc() const { return GenDistance(true); }
///@}
};
} // namespace GeographicLib
#if defined(_MSC_VER)
# pragma warning (pop)
#endif
#endif // GEOGRAPHICLIB_GEODESICLINEEXACT_HPP
Constants.hpp
Header for GeographicLib::Constants class.
GEOGRAPHICLIB_EXPORT
#define GEOGRAPHICLIB_EXPORT
Definition: Constants.hpp:67
EllipticFunction.hpp
Header for GeographicLib::EllipticFunction class.
real
GeographicLib::Math::real real
Definition: GeodSolve.cpp:29
GeodesicExact.hpp
Header for GeographicLib::GeodesicExact class.
GeographicLib::EllipticFunction
Elliptic integrals and functions.
Definition: EllipticFunction.hpp:63
GeographicLib::GeodesicExact
Exact geodesic calculations.
Definition: GeodesicExact.hpp:84
GeographicLib::GeodesicExact::DISTANCE
@ DISTANCE
Definition: GeodesicExact.hpp:192
GeographicLib::GeodesicExact::LONG_UNROLL
@ LONG_UNROLL
Definition: GeodesicExact.hpp:225
GeographicLib::GeodesicExact::AREA
@ AREA
Definition: GeodesicExact.hpp:220
GeographicLib::GeodesicExact::STANDARD
@ STANDARD
Definition: GeodesicExact.hpp:199
GeographicLib::GeodesicExact::DISTANCE_IN
@ DISTANCE_IN
Definition: GeodesicExact.hpp:205
GeographicLib::GeodesicExact::NONE
@ NONE
Definition: GeodesicExact.hpp:169
GeographicLib::GeodesicExact::LONGITUDE
@ LONGITUDE
Definition: GeodesicExact.hpp:180
GeographicLib::GeodesicExact::ALL
@ ALL
Definition: GeodesicExact.hpp:231
GeographicLib::GeodesicExact::AZIMUTH
@ AZIMUTH
Definition: GeodesicExact.hpp:187
GeographicLib::GeodesicExact::REDUCEDLENGTH
@ REDUCEDLENGTH
Definition: GeodesicExact.hpp:210
GeographicLib::GeodesicExact::LATITUDE
@ LATITUDE
Definition: GeodesicExact.hpp:175
GeographicLib::GeodesicExact::GEODESICSCALE
@ GEODESICSCALE
Definition: GeodesicExact.hpp:215
GeographicLib::GeodesicLineExact
An exact geodesic line.
Definition: GeodesicLineExact.hpp:42
GeographicLib::GeodesicLineExact::GeodesicLineExact
GeodesicLineExact()
Definition: GeodesicLineExact.hpp:218
GeographicLib::GeodesicLineExact::Init
bool Init() const
Definition: GeodesicLineExact.hpp:563
GeographicLib::GeodesicLineExact::Flattening
Math::real Flattening() const
Definition: GeodesicLineExact.hpp:633
GeographicLib::GeodesicLineExact::ArcPosition
void ArcPosition(real a12, real &lat2, real &lon2, real &azi2) const
Definition: GeodesicLineExact.hpp:394
GeographicLib::GeodesicLineExact::ArcPosition
void ArcPosition(real a12, real &lat2, real &lon2, real &azi2, real &s12) const
Definition: GeodesicLineExact.hpp:404
GeographicLib::GeodesicLineExact::EquatorialAzimuth
void EquatorialAzimuth(real &sazi0, real &cazi0) const
Definition: GeodesicLineExact.hpp:607
GeographicLib::GeodesicLineExact::Longitude
Math::real Longitude() const
Definition: GeodesicLineExact.hpp:574
GeographicLib::GeodesicLineExact::Arc
Math::real Arc() const
Definition: GeodesicLineExact.hpp:672
GeographicLib::GeodesicLineExact::EquatorialArc
Math::real EquatorialArc() const
Definition: GeodesicLineExact.hpp:616
GeographicLib::GeodesicLineExact::Position
Math::real Position(real s12, real &lat2, real &lon2, real &azi2, real &m12, real &M12, real &M21, real &S12) const
Definition: GeodesicLineExact.hpp:264
GeographicLib::GeodesicLineExact::Capabilities
unsigned Capabilities() const
Definition: GeodesicLineExact.hpp:640
GeographicLib::GeodesicLineExact::ArcPosition
void ArcPosition(real a12, real &lat2, real &lon2, real &azi2, real &s12, real &m12, real &M12, real &M21, real &S12) const
Definition: GeodesicLineExact.hpp:372
GeographicLib::GeodesicLineExact::BaseClass
GeodesicExact BaseClass
Definition: GeodesicLineExact.hpp:163
GeographicLib::GeodesicLineExact::ArcPosition
void ArcPosition(real a12, real &lat2, real &lon2, real &azi2, real &s12, real &M12, real &M21) const
Definition: GeodesicLineExact.hpp:427
GeographicLib::GeodesicLineExact::Latitude
Math::real Latitude() const
Definition: GeodesicLineExact.hpp:568
GeographicLib::GeodesicLineExact::mask
mask
Definition: GeodesicLineExact.hpp:90
GeographicLib::GeodesicLineExact::EquatorialAzimuth
Math::real EquatorialAzimuth() const
Definition: GeodesicLineExact.hpp:598
GeographicLib::GeodesicLineExact::ArcPosition
void ArcPosition(real a12, real &lat2, real &lon2) const
Definition: GeodesicLineExact.hpp:384
GeographicLib::GeodesicLineExact::Position
Math::real Position(real s12, real &lat2, real &lon2, real &azi2, real &M12, real &M21) const
Definition: GeodesicLineExact.hpp:309
GeographicLib::GeodesicLineExact::Azimuth
Math::real Azimuth() const
Definition: GeodesicLineExact.hpp:580
GeographicLib::GeodesicLineExact::GenDistance
Math::real GenDistance(bool arcmode) const
Definition: GeodesicLineExact.hpp:660
GeographicLib::GeodesicLineExact::Distance
Math::real Distance() const
Definition: GeodesicLineExact.hpp:666
GeographicLib::GeodesicLineExact::Position
Math::real Position(real s12, real &lat2, real &lon2, real &azi2, real &m12, real &M12, real &M21) const
Definition: GeodesicLineExact.hpp:321
GeographicLib::GeodesicLineExact::Position
Math::real Position(real s12, real &lat2, real &lon2) const
Definition: GeodesicLineExact.hpp:276
GeographicLib::GeodesicLineExact::ArcPosition
void ArcPosition(real a12, real &lat2, real &lon2, real &azi2, real &s12, real &m12) const
Definition: GeodesicLineExact.hpp:415
GeographicLib::GeodesicLineExact::Capabilities
bool Capabilities(unsigned testcaps) const
Definition: GeodesicLineExact.hpp:648
GeographicLib::GeodesicLineExact::ArcPosition
void ArcPosition(real a12, real &lat2, real &lon2, real &azi2, real &s12, real &m12, real &M12, real &M21) const
Definition: GeodesicLineExact.hpp:439
GeographicLib::GeodesicLineExact::Azimuth
void Azimuth(real &sazi1, real &cazi1) const
Definition: GeodesicLineExact.hpp:589
GeographicLib::GeodesicLineExact::EquatorialRadius
Math::real EquatorialRadius() const
Definition: GeodesicLineExact.hpp:626
GeographicLib::GeodesicLineExact::Position
Math::real Position(real s12, real &lat2, real &lon2, real &azi2) const
Definition: GeodesicLineExact.hpp:287
GeographicLib::GeodesicLineExact::Position
Math::real Position(real s12, real &lat2, real &lon2, real &azi2, real &m12) const
Definition: GeodesicLineExact.hpp:297
GeographicLib::GeodesicLine
A geodesic line.
Definition: GeodesicLine.hpp:74
GeographicLib::Math::degree
static T degree()
Definition: Math.hpp:193
GeographicLib::Math::atan2d
static T atan2d(T y, T x)
Definition: Math.cpp:183
GeographicLib::Math::NaN
static T NaN()
Definition: Math.cpp:250
GeographicLib::Math::real
double real
Definition: Math.hpp:100
GeographicLib
Namespace for GeographicLib.
Definition: Accumulator.cpp:12