594 lines
25 KiB
C++
594 lines
25 KiB
C++
/**
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* \file GeodesicLine30.hpp
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* \brief Header for GeographicLib::GeodesicLine30 class
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*
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* Copyright (c) Charles Karney (2009-2022) <charles@karney.com> and licensed
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* under the MIT/X11 License. For more information, see
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* https://geographiclib.sourceforge.io/
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**********************************************************************/
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#if !defined(GEOGRAPHICLIB_GEODESICLINEEXACT_HPP)
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#define GEOGRAPHICLIB_GEODESICLINEEXACT_HPP 1
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#include <GeographicLib/Constants.hpp>
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#include "Geodesic30.hpp"
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namespace GeographicLib {
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/**
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* \brief A geodesic line
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*
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* GeodesicLine30 facilitates the determination of a series of points on a
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* single geodesic. The starting point (\e lat1, \e lon1) and the azimuth \e
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* azi1 are specified in the constructor. GeodesicLine30.Position returns
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* the location of point 2 a distance \e s12 along the geodesic.
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* Alternatively GeodesicLine30.ArcPosition gives the position of point 2
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* an arc length \e a12 along the geodesic.
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*
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* The default copy constructor and assignment operators work with this
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* class. Similarly, a vector can be used to hold GeodesicLine30 objects.
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*
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* The calculations are accurate to better than 15 nm (15 nanometers). See
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* Sec. 9 of
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* <a href="https://arxiv.org/abs/1102.1215v1">arXiv:1102.1215v1</a> for
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* details.
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*
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* The algorithms are described in
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* - C. F. F. Karney,
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* <a href="https://doi.org/10.1007/s00190-012-0578-z">
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* Algorithms for geodesics</a>,
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* J. Geodesy <b>87</b>, 43--55 (2013);
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* DOI: <a href="https://doi.org/10.1007/s00190-012-0578-z">
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* 10.1007/s00190-012-0578-z</a>;
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* <a href="https://geographiclib.sourceforge.io/geod-addenda.html">
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* addenda</a>.
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* .
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* For more information on geodesics see \ref geodesic.
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**********************************************************************/
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template<typename real>
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class GeodesicLine30 {
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private:
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friend class Geodesic30<real>;
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static const int nC1_ = Geodesic30<real>::nC1_;
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static const int nC1p_ = Geodesic30<real>::nC1p_;
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static const int nC2_ = Geodesic30<real>::nC2_;
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static const int nC3_ = Geodesic30<real>::nC3_;
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static const int nC4_ = Geodesic30<real>::nC4_;
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real _lat1, _lon1, _azi1;
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real _a, _f, _b, _c2, _f1, _salp0, _calp0, _k2,
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_salp1, _calp1, _ssig1, _csig1, _stau1, _ctau1, _somg1, _comg1,
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_A1m1, _A2m1, _A3c, _B11, _B21, _B31, _A4, _B41;
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// index zero elements of _C1a, _C1pa, _C2a, _C3a are unused
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real _C1a[nC1_ + 1], _C1pa[nC1p_ + 1], _C2a[nC2_ + 1], _C3a[nC3_],
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_C4a[nC4_]; // all the elements of _C4a are used
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unsigned _caps;
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enum captype {
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CAP_NONE = Geodesic30<real>::CAP_NONE,
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CAP_C1 = Geodesic30<real>::CAP_C1,
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CAP_C1p = Geodesic30<real>::CAP_C1p,
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CAP_C2 = Geodesic30<real>::CAP_C2,
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CAP_C3 = Geodesic30<real>::CAP_C3,
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CAP_C4 = Geodesic30<real>::CAP_C4,
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CAP_ALL = Geodesic30<real>::CAP_ALL,
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OUT_ALL = Geodesic30<real>::OUT_ALL,
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};
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public:
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/**
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* Bit masks for what calculations to do. They signify to the
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* GeodesicLine30::GeodesicLine30 constructor and to
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* Geodesic30::Line what capabilities should be included in the
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* GeodesicLine30 object. This is merely a duplication of
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* Geodesic30::mask.
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**********************************************************************/
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enum mask {
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/**
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* No capabilities, no output.
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* @hideinitializer
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**********************************************************************/
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NONE = Geodesic30<real>::NONE,
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/**
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* Calculate latitude \e lat2. (It's not necessary to include this as a
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* capability to GeodesicLine30 because this is included by default.)
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* @hideinitializer
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**********************************************************************/
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LATITUDE = Geodesic30<real>::LATITUDE,
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/**
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* Calculate longitude \e lon2.
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* @hideinitializer
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**********************************************************************/
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LONGITUDE = Geodesic30<real>::LONGITUDE,
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/**
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* Calculate azimuths \e azi1 and \e azi2. (It's not necessary to
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* include this as a capability to GeodesicLine30 because this is
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* included by default.)
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* @hideinitializer
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**********************************************************************/
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AZIMUTH = Geodesic30<real>::AZIMUTH,
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/**
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* Calculate distance \e s12.
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* @hideinitializer
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**********************************************************************/
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DISTANCE = Geodesic30<real>::DISTANCE,
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/**
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* Allow distance \e s12 to be used as input in the direct geodesic
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* problem.
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* @hideinitializer
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**********************************************************************/
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DISTANCE_IN = Geodesic30<real>::DISTANCE_IN,
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/**
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* Calculate reduced length \e m12.
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* @hideinitializer
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**********************************************************************/
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REDUCEDLENGTH = Geodesic30<real>::REDUCEDLENGTH,
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/**
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* Calculate geodesic scales \e M12 and \e M21.
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* @hideinitializer
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**********************************************************************/
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GEODESICSCALE = Geodesic30<real>::GEODESICSCALE,
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/**
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* Calculate area \e S12.
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* @hideinitializer
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**********************************************************************/
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AREA = Geodesic30<real>::AREA,
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/**
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* All capabilities, calculate everything.
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* @hideinitializer
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**********************************************************************/
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ALL = Geodesic30<real>::ALL,
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};
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/** \name Constructors
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**********************************************************************/
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///@{
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/**
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* Constructor for a geodesic line staring at latitude \e lat1, longitude
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* \e lon1, and azimuth \e azi1 (all in degrees).
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*
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* @param[in] g A Geodesic30 object used to compute the necessary
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* information about the GeodesicLine30.
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* @param[in] lat1 latitude of point 1 (degrees).
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* @param[in] lon1 longitude of point 1 (degrees).
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* @param[in] azi1 azimuth at point 1 (degrees).
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* @param[in] caps bitor'ed combination of GeodesicLine30::mask values
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* specifying the capabilities the GeodesicLine30 object should
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* possess, i.e., which quantities can be returned in calls to
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* GeodesicLine::Position.
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*
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* \e lat1 should be in the range [−90°, 90°]; \e lon1 and \e
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* azi1 should be in the range [−540°, 540°).
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*
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* The GeodesicLine30::mask values are
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* - \e caps |= GeodesicLine30::LATITUDE for the latitude \e lat2; this
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* is added automatically
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* - \e caps |= GeodesicLine30::LONGITUDE for the latitude \e lon2
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* - \e caps |= GeodesicLine30::AZIMUTH for the latitude \e azi2; this is
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* added automatically
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* - \e caps |= GeodesicLine30::DISTANCE for the distance \e s12
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* - \e caps |= GeodesicLine30::REDUCEDLENGTH for the reduced length \e
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m12
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* - \e caps |= GeodesicLine30::GEODESICSCALE for the geodesic scales \e
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* M12 and \e M21
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* - \e caps |= GeodesicLine30::AREA for the area \e S12
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* - \e caps |= GeodesicLine30::DISTANCE_IN permits the length of the
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* geodesic to be given in terms of \e s12; without this capability the
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* length can only be specified in terms of arc length.
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* .
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* The default value of \e caps is GeodesicLine30::ALL which turns on
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* all the capabilities.
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*
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* If the point is at a pole, the azimuth is defined by keeping the \e lon1
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* fixed and writing \e lat1 = ±(90° − ε) and
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* taking the limit ε → 0+.
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**********************************************************************/
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GeodesicLine30(const Geodesic30<real>& g, real lat1, real lon1, real azi1,
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unsigned caps = ALL)
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;
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/**
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* A default constructor. If GeodesicLine30::Position is called on the
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* resulting object, it returns immediately (without doing any
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* calculations). The object can be set with a call to
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* Geodesic30::Line. Use Init() to test whether object is still in this
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* uninitialized state.
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**********************************************************************/
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GeodesicLine30() : _caps(0U) {}
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///@}
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/** \name Position in terms of distance
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**********************************************************************/
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///@{
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/**
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* Compute the position of point 2 which is a distance \e s12 (meters)
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* from point 1.
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*
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* @param[in] s12 distance between point 1 and point 2 (meters); it can be
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* signed.
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* @param[out] lat2 latitude of point 2 (degrees).
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* @param[out] lon2 longitude of point 2 (degrees); requires that the
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* GeodesicLine30 object was constructed with \e caps |=
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* GeodesicLine30::LONGITUDE.
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* @param[out] azi2 (forward) azimuth at point 2 (degrees).
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* @param[out] m12 reduced length of geodesic (meters); requires that the
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* GeodesicLine30 object was constructed with \e caps |=
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* GeodesicLine30::REDUCEDLENGTH.
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* @param[out] M12 geodesic scale of point 2 relative to point 1
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* (dimensionless); requires that the GeodesicLine30 object was
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* constructed with \e caps |= GeodesicLine30::GEODESICSCALE.
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* @param[out] M21 geodesic scale of point 1 relative to point 2
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* (dimensionless); requires that the GeodesicLine30 object was
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* constructed with \e caps |= GeodesicLine30::GEODESICSCALE.
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* @param[out] S12 area under the geodesic (meters<sup>2</sup>); requires
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* that the GeodesicLine30 object was constructed with \e caps |=
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* GeodesicLine30::AREA.
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* @return \e a12 arc length of between point 1 and point 2 (degrees).
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*
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* The values of \e lon2 and \e azi2 returned are in the range
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* [−180°, 180°).
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*
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* The GeodesicLine30 object \e must have been constructed with \e caps
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* |= GeodesicLine30::DISTANCE_IN; otherwise Math::NaN() is returned and
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* no parameters are set. Requesting a value which the GeodesicLine30
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* object is not capable of computing is not an error; the corresponding
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* argument will not be altered.
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*
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* The following functions are overloaded versions of
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* GeodesicLine30::Position which omit some of the output parameters.
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* Note, however, that the arc length is always computed and returned as
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* the function value.
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**********************************************************************/
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real Position(real s12,
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real& lat2, real& lon2, real& azi2,
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real& m12, real& M12, real& M21,
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real& S12) const {
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real t;
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return GenPosition(false, s12,
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LATITUDE | LONGITUDE | AZIMUTH |
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REDUCEDLENGTH | GEODESICSCALE | AREA,
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lat2, lon2, azi2, t, m12, M12, M21, S12);
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}
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/**
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* See the documentation for GeodesicLine30::Position.
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**********************************************************************/
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real Position(real s12, real& lat2, real& lon2) const {
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real t;
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return GenPosition(false, s12,
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LATITUDE | LONGITUDE,
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lat2, lon2, t, t, t, t, t, t);
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}
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/**
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* See the documentation for GeodesicLine30::Position.
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**********************************************************************/
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real Position(real s12, real& lat2, real& lon2,
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real& azi2) const {
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real t;
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return GenPosition(false, s12,
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LATITUDE | LONGITUDE | AZIMUTH,
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lat2, lon2, azi2, t, t, t, t, t);
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}
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/**
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* See the documentation for GeodesicLine30::Position.
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**********************************************************************/
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real Position(real s12, real& lat2, real& lon2,
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real& azi2, real& m12) const {
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real t;
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return GenPosition(false, s12,
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LATITUDE | LONGITUDE |
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AZIMUTH | REDUCEDLENGTH,
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lat2, lon2, azi2, t, m12, t, t, t);
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}
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/**
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* See the documentation for GeodesicLine30::Position.
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**********************************************************************/
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real Position(real s12, real& lat2, real& lon2,
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real& azi2, real& M12, real& M21)
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const {
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real t;
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return GenPosition(false, s12,
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LATITUDE | LONGITUDE |
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AZIMUTH | GEODESICSCALE,
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lat2, lon2, azi2, t, t, M12, M21, t);
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}
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/**
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* See the documentation for GeodesicLine30::Position.
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**********************************************************************/
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real Position(real s12,
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real& lat2, real& lon2, real& azi2,
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real& m12, real& M12, real& M21)
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const {
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real t;
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return GenPosition(false, s12,
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LATITUDE | LONGITUDE | AZIMUTH |
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REDUCEDLENGTH | GEODESICSCALE,
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lat2, lon2, azi2, t, m12, M12, M21, t);
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}
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///@}
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/** \name Position in terms of arc length
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**********************************************************************/
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///@{
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/**
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* Compute the position of point 2 which is an arc length \e a12 (degrees)
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* from point 1.
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*
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* @param[in] a12 arc length between point 1 and point 2 (degrees); it can
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* be signed.
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* @param[out] lat2 latitude of point 2 (degrees).
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* @param[out] lon2 longitude of point 2 (degrees); requires that the
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* GeodesicLine30 object was constructed with \e caps |=
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* GeodesicLine30::LONGITUDE.
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* @param[out] azi2 (forward) azimuth at point 2 (degrees).
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* @param[out] s12 distance between point 1 and point 2 (meters); requires
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* that the GeodesicLine30 object was constructed with \e caps |=
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* GeodesicLine30::DISTANCE.
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* @param[out] m12 reduced length of geodesic (meters); requires that the
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* GeodesicLine30 object was constructed with \e caps |=
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* GeodesicLine30::REDUCEDLENGTH.
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* @param[out] M12 geodesic scale of point 2 relative to point 1
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* (dimensionless); requires that the GeodesicLine30 object was
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* constructed with \e caps |= GeodesicLine30::GEODESICSCALE.
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* @param[out] M21 geodesic scale of point 1 relative to point 2
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* (dimensionless); requires that the GeodesicLine30 object was
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* constructed with \e caps |= GeodesicLine30::GEODESICSCALE.
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* @param[out] S12 area under the geodesic (meters<sup>2</sup>); requires
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* that the GeodesicLine30 object was constructed with \e caps |=
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* GeodesicLine30::AREA.
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*
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* The values of \e lon2 and \e azi2 returned are in the range
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* [−180°, 180°).
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*
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* Requesting a value which the GeodesicLine30 object is not capable of
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* computing is not an error; the corresponding argument will not be
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* altered.
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*
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* The following functions are overloaded versions of
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* GeodesicLine30::ArcPosition which omit some of the output parameters.
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**********************************************************************/
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void ArcPosition(real a12, real& lat2, real& lon2, real& azi2,
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real& s12, real& m12, real& M12, real& M21,
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real& S12) const {
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GenPosition(true, a12,
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LATITUDE | LONGITUDE | AZIMUTH | DISTANCE |
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REDUCEDLENGTH | GEODESICSCALE | AREA,
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lat2, lon2, azi2, s12, m12, M12, M21, S12);
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}
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/**
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* See the documentation for GeodesicLine30::ArcPosition.
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**********************************************************************/
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void ArcPosition(real a12, real& lat2, real& lon2)
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const {
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real t;
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GenPosition(true, a12,
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LATITUDE | LONGITUDE,
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lat2, lon2, t, t, t, t, t, t);
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}
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/**
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* See the documentation for GeodesicLine30::ArcPosition.
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**********************************************************************/
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void ArcPosition(real a12,
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real& lat2, real& lon2, real& azi2)
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const {
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real t;
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GenPosition(true, a12,
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LATITUDE | LONGITUDE | AZIMUTH,
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lat2, lon2, azi2, t, t, t, t, t);
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}
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/**
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* See the documentation for GeodesicLine30::ArcPosition.
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**********************************************************************/
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void ArcPosition(real a12, real& lat2, real& lon2, real& azi2,
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real& s12) const {
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real t;
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GenPosition(true, a12,
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LATITUDE | LONGITUDE | AZIMUTH | DISTANCE,
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lat2, lon2, azi2, s12, t, t, t, t);
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}
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/**
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* See the documentation for GeodesicLine30::ArcPosition.
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**********************************************************************/
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void ArcPosition(real a12, real& lat2, real& lon2, real& azi2,
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real& s12, real& m12) const {
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real t;
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GenPosition(true, a12,
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LATITUDE | LONGITUDE | AZIMUTH |
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DISTANCE | REDUCEDLENGTH,
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lat2, lon2, azi2, s12, m12, t, t, t);
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}
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/**
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* See the documentation for GeodesicLine30::ArcPosition.
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**********************************************************************/
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void ArcPosition(real a12, real& lat2, real& lon2, real& azi2,
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real& s12, real& M12, real& M21)
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const {
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real t;
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GenPosition(true, a12,
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LATITUDE | LONGITUDE | AZIMUTH |
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DISTANCE | GEODESICSCALE,
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lat2, lon2, azi2, s12, t, M12, M21, t);
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}
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/**
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* See the documentation for GeodesicLine30::ArcPosition.
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**********************************************************************/
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void ArcPosition(real a12, real& lat2, real& lon2, real& azi2,
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real& s12, real& m12, real& M12, real& M21)
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const {
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real t;
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GenPosition(true, a12,
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LATITUDE | LONGITUDE | AZIMUTH |
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DISTANCE | REDUCEDLENGTH | GEODESICSCALE,
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lat2, lon2, azi2, s12, m12, M12, M21, t);
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}
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///@}
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/** \name The general position function.
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**********************************************************************/
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///@{
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/**
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* The general position function. GeodesicLine30::Position and
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* GeodesicLine30::ArcPosition are defined in terms of this function.
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*
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* @param[in] arcmode boolean flag determining the meaning of the second
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* parameter; if arcmode is false, then the GeodesicLine30 object must
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* have been constructed with \e caps |= GeodesicLine30::DISTANCE_IN.
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* @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.
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* @param[in] outmask a bitor'ed combination of GeodesicLine30::mask
|
|
* values specifying which of the following parameters should be set.
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* @param[out] lat2 latitude of point 2 (degrees).
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* @param[out] lon2 longitude of point 2 (degrees); requires that the
|
|
* GeodesicLine30 object was constructed with \e caps |=
|
|
* GeodesicLine30::LONGITUDE.
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* @param[out] azi2 (forward) azimuth at point 2 (degrees).
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* @param[out] s12 distance between point 1 and point 2 (meters); requires
|
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* that the GeodesicLine30 object was constructed with \e caps |=
|
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* GeodesicLine30::DISTANCE.
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|
* @param[out] m12 reduced length of geodesic (meters); requires that the
|
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* GeodesicLine30 object was constructed with \e caps |=
|
|
* GeodesicLine30::REDUCEDLENGTH.
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|
* @param[out] M12 geodesic scale of point 2 relative to point 1
|
|
* (dimensionless); requires that the GeodesicLine30 object was
|
|
* constructed with \e caps |= GeodesicLine30::GEODESICSCALE.
|
|
* @param[out] M21 geodesic scale of point 1 relative to point 2
|
|
* (dimensionless); requires that the GeodesicLine30 object was
|
|
* constructed with \e caps |= GeodesicLine30::GEODESICSCALE.
|
|
* @param[out] S12 area under the geodesic (meters<sup>2</sup>); requires
|
|
* that the GeodesicLine30 object was constructed with \e caps |=
|
|
* GeodesicLine30::AREA.
|
|
* @return \e a12 arc length of between point 1 and point 2 (degrees).
|
|
*
|
|
* The GeodesicLine30::mask values possible for \e outmask are
|
|
* - \e outmask |= GeodesicLine30::LATITUDE for the latitude \e lat2.
|
|
* - \e outmask |= GeodesicLine30::LONGITUDE for the latitude \e lon2.
|
|
* - \e outmask |= GeodesicLine30::AZIMUTH for the latitude \e azi2.
|
|
* - \e outmask |= GeodesicLine30::DISTANCE for the distance \e s12.
|
|
* - \e outmask |= GeodesicLine30::REDUCEDLENGTH for the reduced length
|
|
* \e m12.
|
|
* - \e outmask |= GeodesicLine30::GEODESICSCALE for the geodesic scales
|
|
* \e M12 and \e M21.
|
|
* - \e outmask |= GeodesicLine30::AREA for the area \e S12.
|
|
* .
|
|
* Requesting a value which the GeodesicLine30 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.
|
|
**********************************************************************/
|
|
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 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).
|
|
**********************************************************************/
|
|
real Latitude() const
|
|
{ return Init() ? _lat1 : Math::NaN<real>(); }
|
|
|
|
/**
|
|
* @return \e lon1 the longitude of point 1 (degrees).
|
|
**********************************************************************/
|
|
real Longitude() const
|
|
{ return Init() ? _lon1 : Math::NaN<real>(); }
|
|
|
|
/**
|
|
* @return \e azi1 the azimuth (degrees) of the geodesic line at point 1.
|
|
**********************************************************************/
|
|
real Azimuth() const
|
|
{ return Init() ? _azi1 : Math::NaN<real>(); }
|
|
|
|
/**
|
|
* @return \e azi0 the azimuth (degrees) of the geodesic line as it crosses
|
|
* the equator in a northward direction.
|
|
**********************************************************************/
|
|
real EquatorialAzimuth() const {
|
|
using std::atan2;
|
|
return Init() ?
|
|
atan2(_salp0, _calp0) / Math::degree<real>() : Math::NaN<real>();
|
|
}
|
|
|
|
/**
|
|
* @return \e a1 the arc length (degrees) between the northward equatorial
|
|
* crossing and point 1.
|
|
**********************************************************************/
|
|
real EquatorialArc() const {
|
|
using std::atan2;
|
|
return Init() ?
|
|
atan2(_ssig1, _csig1) / Math::degree<real>() : Math::NaN<real>();
|
|
}
|
|
|
|
/**
|
|
* @return \e a the equatorial radius of the ellipsoid (meters). This is
|
|
* the value inherited from the Geodesic30 object used in the
|
|
* constructor.
|
|
**********************************************************************/
|
|
real EquatorialRadius() const
|
|
{ return Init() ? _a : Math::NaN<real>(); }
|
|
|
|
/**
|
|
* @return \e f the flattening of the ellipsoid. This is the value
|
|
* inherited from the Geodesic30 object used in the constructor.
|
|
**********************************************************************/
|
|
real Flattening() const
|
|
{ return Init() ? _f : Math::NaN<real>(); }
|
|
|
|
/// \cond SKIP
|
|
/**
|
|
* <b>DEPRECATED</b>
|
|
* @return \e r the inverse flattening of the ellipsoid.
|
|
**********************************************************************/
|
|
real InverseFlattening() const
|
|
{ return Init() ? 1/_f : Math::NaN<real>(); }
|
|
/// \endcond
|
|
|
|
/**
|
|
* @return \e caps the computational capabilities that this object was
|
|
* constructed with. LATITUDE and AZIMUTH are always included.
|
|
**********************************************************************/
|
|
unsigned Capabilities() const { return _caps; }
|
|
|
|
/**
|
|
* @param[in] testcaps a set of bitor'ed GeodesicLine30::mask values.
|
|
* @return true if the GeodesicLine30 object has all these capabilities.
|
|
**********************************************************************/
|
|
bool Capabilities(unsigned testcaps) const {
|
|
testcaps &= OUT_ALL;
|
|
return (_caps & testcaps) == testcaps;
|
|
}
|
|
///@}
|
|
|
|
};
|
|
|
|
} // namespace GeographicLib
|
|
|
|
#endif // GEOGRAPHICLIB_GEODESICLINEEXACT_HPP
|