709 baris
30 KiB
C++
709 baris
30 KiB
C++
/**
|
|
* \file GeodesicLine.hpp
|
|
* \brief Header for GeographicLib::GeodesicLine class
|
|
*
|
|
* Copyright (c) Charles Karney (2009-2020) <charles@karney.com> and licensed
|
|
* under the MIT/X11 License. For more information, see
|
|
* https://geographiclib.sourceforge.io/
|
|
**********************************************************************/
|
|
|
|
#if !defined(GEOGRAPHICLIB_GEODESICLINE_HPP)
|
|
#define GEOGRAPHICLIB_GEODESICLINE_HPP 1
|
|
|
|
#include <GeographicLib/Constants.hpp>
|
|
#include <GeographicLib/Geodesic.hpp>
|
|
|
|
namespace GeographicLib {
|
|
|
|
/**
|
|
* \brief A geodesic line
|
|
*
|
|
* GeodesicLine facilitates the determination of a series of points on a
|
|
* single geodesic. The starting point (\e lat1, \e lon1) and the azimuth \e
|
|
* azi1 are specified in the constructor; alternatively, the Geodesic::Line
|
|
* method can be used to create a GeodesicLine. GeodesicLine.Position
|
|
* returns the location of point 2 a distance \e s12 along the geodesic. In
|
|
* addition, GeodesicLine.ArcPosition gives the position of point 2 an arc
|
|
* length \e a12 along the geodesic.
|
|
*
|
|
* You can register the position of a reference point 3 a distance (arc
|
|
* length), \e s13 (\e a13) along the geodesic with the
|
|
* GeodesicLine.SetDistance (GeodesicLine.SetArc) functions. Points a
|
|
* fractional distance along the line can be found by providing, for example,
|
|
* 0.5 * Distance() as an argument to GeodesicLine.Position. The
|
|
* Geodesic::InverseLine or Geodesic::DirectLine methods return GeodesicLine
|
|
* objects with point 3 set to the point 2 of the corresponding geodesic
|
|
* problem. GeodesicLine objects created with the public constructor or with
|
|
* Geodesic::Line have \e s13 and \e a13 set to NaNs.
|
|
*
|
|
* The default copy constructor and assignment operators work with this
|
|
* class. Similarly, a vector can be used to hold GeodesicLine objects.
|
|
*
|
|
* The calculations are accurate to better than 15 nm (15 nanometers). See
|
|
* Sec. 9 of
|
|
* <a href="https://arxiv.org/abs/1102.1215v1">arXiv:1102.1215v1</a> for
|
|
* details. The algorithms used by this class are based on series expansions
|
|
* using the flattening \e f as a small parameter. These are only accurate
|
|
* for |<i>f</i>| < 0.02; however reasonably accurate results will be
|
|
* obtained for |<i>f</i>| < 0.2. For very eccentric ellipsoids, use
|
|
* GeodesicLineExact instead.
|
|
*
|
|
* The algorithms are described in
|
|
* - C. F. F. Karney,
|
|
* <a href="https://doi.org/10.1007/s00190-012-0578-z">
|
|
* Algorithms for geodesics</a>,
|
|
* J. Geodesy <b>87</b>, 43--55 (2013);
|
|
* DOI: <a href="https://doi.org/10.1007/s00190-012-0578-z">
|
|
* 10.1007/s00190-012-0578-z</a>;
|
|
* addenda:
|
|
* <a href="https://geographiclib.sourceforge.io/geod-addenda.html">
|
|
* geod-addenda.html</a>.
|
|
* .
|
|
* For more information on geodesics see \ref geodesic.
|
|
*
|
|
* Example of use:
|
|
* \include example-GeodesicLine.cpp
|
|
*
|
|
* <a href="GeodSolve.1.html">GeodSolve</a> is a command-line utility
|
|
* providing access to the functionality of Geodesic and GeodesicLine.
|
|
**********************************************************************/
|
|
|
|
class GEOGRAPHICLIB_EXPORT GeodesicLine {
|
|
private:
|
|
typedef Math::real real;
|
|
friend class Geodesic;
|
|
static const int nC1_ = Geodesic::nC1_;
|
|
static const int nC1p_ = Geodesic::nC1p_;
|
|
static const int nC2_ = Geodesic::nC2_;
|
|
static const int nC3_ = Geodesic::nC3_;
|
|
static const int nC4_ = Geodesic::nC4_;
|
|
|
|
real tiny_;
|
|
real _lat1, _lon1, _azi1;
|
|
real _a, _f, _b, _c2, _f1, _salp0, _calp0, _k2,
|
|
_salp1, _calp1, _ssig1, _csig1, _dn1, _stau1, _ctau1, _somg1, _comg1,
|
|
_A1m1, _A2m1, _A3c, _B11, _B21, _B31, _A4, _B41;
|
|
real _a13, _s13;
|
|
// index zero elements of _C1a, _C1pa, _C2a, _C3a are unused
|
|
real _C1a[nC1_ + 1], _C1pa[nC1p_ + 1], _C2a[nC2_ + 1], _C3a[nC3_],
|
|
_C4a[nC4_]; // all the elements of _C4a are used
|
|
unsigned _caps;
|
|
|
|
void LineInit(const Geodesic& g,
|
|
real lat1, real lon1,
|
|
real azi1, real salp1, real calp1,
|
|
unsigned caps);
|
|
GeodesicLine(const Geodesic& g,
|
|
real lat1, real lon1,
|
|
real azi1, real salp1, real calp1,
|
|
unsigned caps, bool arcmode, real s13_a13);
|
|
|
|
enum captype {
|
|
CAP_NONE = Geodesic::CAP_NONE,
|
|
CAP_C1 = Geodesic::CAP_C1,
|
|
CAP_C1p = Geodesic::CAP_C1p,
|
|
CAP_C2 = Geodesic::CAP_C2,
|
|
CAP_C3 = Geodesic::CAP_C3,
|
|
CAP_C4 = Geodesic::CAP_C4,
|
|
CAP_ALL = Geodesic::CAP_ALL,
|
|
CAP_MASK = Geodesic::CAP_MASK,
|
|
OUT_ALL = Geodesic::OUT_ALL,
|
|
OUT_MASK = Geodesic::OUT_MASK,
|
|
};
|
|
public:
|
|
|
|
/**
|
|
* Bit masks for what calculations to do. They signify to the
|
|
* GeodesicLine::GeodesicLine constructor and to Geodesic::Line what
|
|
* capabilities should be included in the GeodesicLine object. This is
|
|
* merely a duplication of Geodesic::mask.
|
|
**********************************************************************/
|
|
enum mask {
|
|
/**
|
|
* No capabilities, no output.
|
|
* @hideinitializer
|
|
**********************************************************************/
|
|
NONE = Geodesic::NONE,
|
|
/**
|
|
* Calculate latitude \e lat2. (It's not necessary to include this as a
|
|
* capability to GeodesicLine because this is included by default.)
|
|
* @hideinitializer
|
|
**********************************************************************/
|
|
LATITUDE = Geodesic::LATITUDE,
|
|
/**
|
|
* Calculate longitude \e lon2.
|
|
* @hideinitializer
|
|
**********************************************************************/
|
|
LONGITUDE = Geodesic::LONGITUDE,
|
|
/**
|
|
* Calculate azimuths \e azi1 and \e azi2. (It's not necessary to
|
|
* include this as a capability to GeodesicLine because this is included
|
|
* by default.)
|
|
* @hideinitializer
|
|
**********************************************************************/
|
|
AZIMUTH = Geodesic::AZIMUTH,
|
|
/**
|
|
* Calculate distance \e s12.
|
|
* @hideinitializer
|
|
**********************************************************************/
|
|
DISTANCE = Geodesic::DISTANCE,
|
|
/**
|
|
* Allow distance \e s12 to be used as input in the direct geodesic
|
|
* problem.
|
|
* @hideinitializer
|
|
**********************************************************************/
|
|
DISTANCE_IN = Geodesic::DISTANCE_IN,
|
|
/**
|
|
* Calculate reduced length \e m12.
|
|
* @hideinitializer
|
|
**********************************************************************/
|
|
REDUCEDLENGTH = Geodesic::REDUCEDLENGTH,
|
|
/**
|
|
* Calculate geodesic scales \e M12 and \e M21.
|
|
* @hideinitializer
|
|
**********************************************************************/
|
|
GEODESICSCALE = Geodesic::GEODESICSCALE,
|
|
/**
|
|
* Calculate area \e S12.
|
|
* @hideinitializer
|
|
**********************************************************************/
|
|
AREA = Geodesic::AREA,
|
|
/**
|
|
* Unroll \e lon2 in the direct calculation.
|
|
* @hideinitializer
|
|
**********************************************************************/
|
|
LONG_UNROLL = Geodesic::LONG_UNROLL,
|
|
/**
|
|
* All capabilities, calculate everything. (LONG_UNROLL is not
|
|
* included in this mask.)
|
|
* @hideinitializer
|
|
**********************************************************************/
|
|
ALL = Geodesic::ALL,
|
|
};
|
|
|
|
/** \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 Geodesic object used to compute the necessary information
|
|
* about the GeodesicLine.
|
|
* @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 GeodesicLine::mask values
|
|
* specifying the capabilities the GeodesicLine object should possess,
|
|
* i.e., which quantities can be returned in calls to
|
|
* GeodesicLine::Position.
|
|
*
|
|
* \e lat1 should be in the range [−90°, 90°].
|
|
*
|
|
* The GeodesicLine::mask values are
|
|
* - \e caps |= GeodesicLine::LATITUDE for the latitude \e lat2; this is
|
|
* added automatically;
|
|
* - \e caps |= GeodesicLine::LONGITUDE for the latitude \e lon2;
|
|
* - \e caps |= GeodesicLine::AZIMUTH for the latitude \e azi2; this is
|
|
* added automatically;
|
|
* - \e caps |= GeodesicLine::DISTANCE for the distance \e s12;
|
|
* - \e caps |= GeodesicLine::REDUCEDLENGTH for the reduced length \e m12;
|
|
* - \e caps |= GeodesicLine::GEODESICSCALE for the geodesic scales \e M12
|
|
* and \e M21;
|
|
* - \e caps |= GeodesicLine::AREA for the area \e S12;
|
|
* - \e caps |= GeodesicLine::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 |= GeodesicLine::ALL for all of the above.
|
|
* .
|
|
* The default value of \e caps is GeodesicLine::ALL.
|
|
*
|
|
* 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+.
|
|
**********************************************************************/
|
|
GeodesicLine(const Geodesic& g, real lat1, real lon1, real azi1,
|
|
unsigned caps = ALL);
|
|
|
|
/**
|
|
* A default constructor. If GeodesicLine::Position is called on the
|
|
* resulting object, it returns immediately (without doing any
|
|
* calculations). The object can be set with a call to Geodesic::Line.
|
|
* Use Init() to test whether object is still in this uninitialized state.
|
|
**********************************************************************/
|
|
GeodesicLine() : _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
|
|
* negative.
|
|
* @param[out] lat2 latitude of point 2 (degrees).
|
|
* @param[out] lon2 longitude of point 2 (degrees); requires that the
|
|
* GeodesicLine object was constructed with \e caps |=
|
|
* GeodesicLine::LONGITUDE.
|
|
* @param[out] azi2 (forward) azimuth at point 2 (degrees).
|
|
* @param[out] m12 reduced length of geodesic (meters); requires that the
|
|
* GeodesicLine object was constructed with \e caps |=
|
|
* GeodesicLine::REDUCEDLENGTH.
|
|
* @param[out] M12 geodesic scale of point 2 relative to point 1
|
|
* (dimensionless); requires that the GeodesicLine object was constructed
|
|
* with \e caps |= GeodesicLine::GEODESICSCALE.
|
|
* @param[out] M21 geodesic scale of point 1 relative to point 2
|
|
* (dimensionless); requires that the GeodesicLine object was constructed
|
|
* with \e caps |= GeodesicLine::GEODESICSCALE.
|
|
* @param[out] S12 area under the geodesic (meters<sup>2</sup>); requires
|
|
* that the GeodesicLine object was constructed with \e caps |=
|
|
* GeodesicLine::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
|
|
* [−180°, 180°].
|
|
*
|
|
* The GeodesicLine object \e must have been constructed with \e caps |=
|
|
* GeodesicLine::DISTANCE_IN; otherwise Math::NaN() is returned and no
|
|
* parameters are set. Requesting a value which the GeodesicLine object is
|
|
* not capable of computing is not an error; the corresponding argument
|
|
* will not be altered.
|
|
*
|
|
* The following functions are overloaded versions of
|
|
* GeodesicLine::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 GeodesicLine::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 GeodesicLine::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 GeodesicLine::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 GeodesicLine::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 GeodesicLine::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 negative.
|
|
* @param[out] lat2 latitude of point 2 (degrees).
|
|
* @param[out] lon2 longitude of point 2 (degrees); requires that the
|
|
* GeodesicLine object was constructed with \e caps |=
|
|
* GeodesicLine::LONGITUDE.
|
|
* @param[out] azi2 (forward) azimuth at point 2 (degrees).
|
|
* @param[out] s12 distance from point 1 to point 2 (meters); requires
|
|
* that the GeodesicLine object was constructed with \e caps |=
|
|
* GeodesicLine::DISTANCE.
|
|
* @param[out] m12 reduced length of geodesic (meters); requires that the
|
|
* GeodesicLine object was constructed with \e caps |=
|
|
* GeodesicLine::REDUCEDLENGTH.
|
|
* @param[out] M12 geodesic scale of point 2 relative to point 1
|
|
* (dimensionless); requires that the GeodesicLine object was constructed
|
|
* with \e caps |= GeodesicLine::GEODESICSCALE.
|
|
* @param[out] M21 geodesic scale of point 1 relative to point 2
|
|
* (dimensionless); requires that the GeodesicLine object was constructed
|
|
* with \e caps |= GeodesicLine::GEODESICSCALE.
|
|
* @param[out] S12 area under the geodesic (meters<sup>2</sup>); requires
|
|
* that the GeodesicLine object was constructed with \e caps |=
|
|
* GeodesicLine::AREA.
|
|
*
|
|
* The values of \e lon2 and \e azi2 returned are in the range
|
|
* [−180°, 180°].
|
|
*
|
|
* Requesting a value which the GeodesicLine object is not capable of
|
|
* computing is not an error; the corresponding argument will not be
|
|
* altered.
|
|
*
|
|
* The following functions are overloaded versions of
|
|
* GeodesicLine::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 GeodesicLine::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 GeodesicLine::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 GeodesicLine::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 GeodesicLine::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 GeodesicLine::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 GeodesicLine::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. GeodesicLine::Position and
|
|
* GeodesicLine::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 GeodesicLine object must
|
|
* have been constructed with \e caps |= GeodesicLine::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 negative.
|
|
* @param[in] outmask a bitor'ed combination of GeodesicLine::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
|
|
* GeodesicLine object was constructed with \e caps |=
|
|
* GeodesicLine::LONGITUDE.
|
|
* @param[out] azi2 (forward) azimuth at point 2 (degrees).
|
|
* @param[out] s12 distance from point 1 to point 2 (meters); requires
|
|
* that the GeodesicLine object was constructed with \e caps |=
|
|
* GeodesicLine::DISTANCE.
|
|
* @param[out] m12 reduced length of geodesic (meters); requires that the
|
|
* GeodesicLine object was constructed with \e caps |=
|
|
* GeodesicLine::REDUCEDLENGTH.
|
|
* @param[out] M12 geodesic scale of point 2 relative to point 1
|
|
* (dimensionless); requires that the GeodesicLine object was constructed
|
|
* with \e caps |= GeodesicLine::GEODESICSCALE.
|
|
* @param[out] M21 geodesic scale of point 1 relative to point 2
|
|
* (dimensionless); requires that the GeodesicLine object was constructed
|
|
* with \e caps |= GeodesicLine::GEODESICSCALE.
|
|
* @param[out] S12 area under the geodesic (meters<sup>2</sup>); requires
|
|
* that the GeodesicLine object was constructed with \e caps |=
|
|
* GeodesicLine::AREA.
|
|
* @return \e a12 arc length from point 1 to point 2 (degrees).
|
|
*
|
|
* The GeodesicLine::mask values possible for \e outmask are
|
|
* - \e outmask |= GeodesicLine::LATITUDE for the latitude \e lat2;
|
|
* - \e outmask |= GeodesicLine::LONGITUDE for the latitude \e lon2;
|
|
* - \e outmask |= GeodesicLine::AZIMUTH for the latitude \e azi2;
|
|
* - \e outmask |= GeodesicLine::DISTANCE for the distance \e s12;
|
|
* - \e outmask |= GeodesicLine::REDUCEDLENGTH for the reduced length \e
|
|
* m12;
|
|
* - \e outmask |= GeodesicLine::GEODESICSCALE for the geodesic scales \e
|
|
* M12 and \e M21;
|
|
* - \e outmask |= GeodesicLine::AREA for the area \e S12;
|
|
* - \e outmask |= GeodesicLine::ALL for all of the above;
|
|
* - \e outmask |= GeodesicLine::LONG_UNROLL to unroll \e lon2 instead of
|
|
* reducing it into the range [−180°, 180°].
|
|
* .
|
|
* Requesting a value which the GeodesicLine 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 GeodesicLine::LONG_UNROLL bit set, the quantity \e lon2 −
|
|
* \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 GeodesicLine object has been constructed
|
|
* with \e caps |= GeodesicLine::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 GeodesicLine object has been
|
|
* constructed with \e caps |= GeodesicLine::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 GeodesicLine object must
|
|
* have been constructed with \e caps |= GeodesicLine::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 [−90°, 90°].
|
|
**********************************************************************/
|
|
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 (−180°, 180°].
|
|
**********************************************************************/
|
|
Math::real EquatorialArc() const {
|
|
return Init() ? Math::atan2d(_ssig1, _csig1) : Math::NaN();
|
|
}
|
|
|
|
/**
|
|
* @return \e a the equatorial radius of the ellipsoid (meters). This is
|
|
* the value inherited from the Geodesic 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 Geodesic 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 GeodesicLine::mask values.
|
|
* @return true if the GeodesicLine 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); }
|
|
|
|
/**
|
|
* \deprecated An old name for EquatorialRadius().
|
|
**********************************************************************/
|
|
GEOGRAPHICLIB_DEPRECATED("Use EquatorialRadius()")
|
|
Math::real MajorRadius() const { return EquatorialRadius(); }
|
|
///@}
|
|
|
|
};
|
|
|
|
} // namespace GeographicLib
|
|
|
|
#endif // GEOGRAPHICLIB_GEODESICLINE_HPP
|