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/**
* \file AzimuthalEquidistant.hpp
* \brief Header for GeographicLib::AzimuthalEquidistant class
*
* Copyright (c) Charles Karney (2009-2022) <karney@alum.mit.edu> and licensed
* under the MIT/X11 License. For more information, see
* https://geographiclib.sourceforge.io/
**********************************************************************/
#if !defined(GEOGRAPHICLIB_AZIMUTHALEQUIDISTANT_HPP)
#define GEOGRAPHICLIB_AZIMUTHALEQUIDISTANT_HPP 1
#include <GeographicLib/Geodesic.hpp>
#include <GeographicLib/Constants.hpp>
namespace GeographicLib {
/**
* \brief Azimuthal equidistant projection
*
* Azimuthal equidistant projection centered at an arbitrary position on the
* ellipsoid. For a point in projected space (\e x, \e y), the geodesic
* distance from the center position is hypot(\e x, \e y) and the azimuth of
* the geodesic from the center point is atan2(\e x, \e y). The Forward and
* Reverse methods also return the azimuth \e azi of the geodesic at (\e x,
* \e y) and reciprocal scale \e rk in the azimuthal direction which,
* together with the basic properties of the projection, serve to specify
* completely the local affine transformation between geographic and
* projected coordinates.
*
* The conversions all take place using a Geodesic object (by default
* Geodesic::WGS84()). For more information on geodesics see \ref geodesic.
*
* Example of use:
* \include example-AzimuthalEquidistant.cpp
*
* <a href="GeodesicProj.1.html">GeodesicProj</a> is a command-line utility
* providing access to the functionality of AzimuthalEquidistant, Gnomonic,
* and CassiniSoldner.
**********************************************************************/
class GEOGRAPHICLIB_EXPORT AzimuthalEquidistant {
private:
typedef Math::real real;
real eps_;
Geodesic _earth;
public:
/**
* Constructor for AzimuthalEquidistant.
*
* @param[in] earth the Geodesic object to use for geodesic calculations.
* By default this uses the WGS84 ellipsoid.
**********************************************************************/
explicit AzimuthalEquidistant(const Geodesic& earth = Geodesic::WGS84());
/**
* Forward projection, from geographic to azimuthal equidistant.
*
* @param[in] lat0 latitude of center point of projection (degrees).
* @param[in] lon0 longitude of center point of projection (degrees).
* @param[in] lat latitude of point (degrees).
* @param[in] lon longitude of point (degrees).
* @param[out] x easting of point (meters).
* @param[out] y northing of point (meters).
* @param[out] azi azimuth of geodesic at point (degrees).
* @param[out] rk reciprocal of azimuthal scale at point.
*
* \e lat0 and \e lat should be in the range [−90°, 90°].
* The scale of the projection is 1 in the "radial" direction, \e azi
* clockwise from true north, and is 1/\e rk in the direction perpendicular
* to this. A call to Forward followed by a call to Reverse will return
* the original (\e lat, \e lon) (to within roundoff).
**********************************************************************/
void Forward(real lat0, real lon0, real lat, real lon,
real& x, real& y, real& azi, real& rk) const;
/**
* Reverse projection, from azimuthal equidistant to geographic.
*
* @param[in] lat0 latitude of center point of projection (degrees).
* @param[in] lon0 longitude of center point of projection (degrees).
* @param[in] x easting of point (meters).
* @param[in] y northing of point (meters).
* @param[out] lat latitude of point (degrees).
* @param[out] lon longitude of point (degrees).
* @param[out] azi azimuth of geodesic at point (degrees).
* @param[out] rk reciprocal of azimuthal scale at point.
*
* \e lat0 should be in the range [−90°, 90°]. \e lat will
* be in the range [−90°, 90°] and \e lon will be in the
* range [−180°, 180°]. The scale of the projection is 1 in
* the "radial" direction, \e azi clockwise from true north, and is 1/\e rk
* in the direction perpendicular to this. A call to Reverse followed by a
* call to Forward will return the original (\e x, \e y) (to roundoff) only
* if the geodesic to (\e x, \e y) is a shortest path.
**********************************************************************/
void Reverse(real lat0, real lon0, real x, real y,
real& lat, real& lon, real& azi, real& rk) const;
/**
* AzimuthalEquidistant::Forward without returning the azimuth and scale.
**********************************************************************/
void Forward(real lat0, real lon0, real lat, real lon,
real& x, real& y) const {
real azi, rk;
Forward(lat0, lon0, lat, lon, x, y, azi, rk);
}
/**
* AzimuthalEquidistant::Reverse without returning the azimuth and scale.
**********************************************************************/
void Reverse(real lat0, real lon0, real x, real y,
real& lat, real& lon) const {
real azi, rk;
Reverse(lat0, lon0, x, y, lat, lon, azi, rk);
}
/** \name Inspector functions
**********************************************************************/
///@{
/**
* @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 _earth.EquatorialRadius(); }
/**
* @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 _earth.Flattening(); }
///@}
};
} // namespace GeographicLib
#endif // GEOGRAPHICLIB_AZIMUTHALEQUIDISTANT_HPP