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/**
* \file CassiniSoldner.hpp
* \brief Header for GeographicLib::CassiniSoldner 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_CASSINISOLDNER_HPP)
#define GEOGRAPHICLIB_CASSINISOLDNER_HPP 1
#include <GeographicLib/Geodesic.hpp>
#include <GeographicLib/GeodesicLine.hpp>
#include <GeographicLib/Constants.hpp>
namespace GeographicLib {
/**
* \brief Cassini-Soldner projection
*
* Cassini-Soldner projection centered at an arbitrary position, \e lat0, \e
* lon0, on the ellipsoid. This projection is a transverse cylindrical
* equidistant projection. The projection from (\e lat, \e lon) to easting
* and northing (\e x, \e y) is defined by geodesics as follows. Go north
* along a geodesic a distance \e y from the central point; then turn
* clockwise 90° and go a distance \e x along a geodesic.
* (Although the initial heading is north, this changes to south if the pole
* is crossed.) This procedure uniquely defines the reverse projection. The
* forward projection is constructed as follows. Find the point (\e lat1, \e
* lon1) on the meridian closest to (\e lat, \e lon). Here we consider the
* full meridian so that \e lon1 may be either \e lon0 or \e lon0 +
* 180°. \e x is the geodesic distance from (\e lat1, \e lon1) to
* (\e lat, \e lon), appropriately signed according to which side of the
* central meridian (\e lat, \e lon) lies. \e y is the shortest distance
* along the meridian from (\e lat0, \e lon0) to (\e lat1, \e lon1), again,
* appropriately signed according to the initial heading. [Note that, in the
* case of prolate ellipsoids, the shortest meridional path from (\e lat0, \e
* lon0) to (\e lat1, \e lon1) may not be the shortest path.] This procedure
* uniquely defines the forward projection except for a small class of points
* for which there may be two equally short routes for either leg of the
* path.
*
* Because of the properties of geodesics, the (\e x, \e y) grid is
* orthogonal. The scale in the easting direction is unity. The scale, \e
* k, in the northing direction is unity on the central meridian and
* increases away from the central meridian. The projection routines return
* \e azi, the true bearing of the easting direction, and \e rk = 1/\e k, the
* reciprocal of the scale in the northing direction.
*
* The conversions all take place using a Geodesic object (by default
* Geodesic::WGS84()). For more information on geodesics see \ref geodesic.
* The determination of (\e lat1, \e lon1) in the forward projection is by
* solving the inverse geodesic problem for (\e lat, \e lon) and its twin
* obtained by reflection in the meridional plane. The scale is found by
* determining where two neighboring geodesics intersecting the central
* meridian at \e lat1 and \e lat1 + \e dlat1 intersect and taking the ratio
* of the reduced lengths for the two geodesics between that point and,
* respectively, (\e lat1, \e lon1) and (\e lat, \e lon).
*
* Example of use:
* \include example-CassiniSoldner.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 CassiniSoldner {
private:
typedef Math::real real;
Geodesic _earth;
GeodesicLine _meridian;
real _sbet0, _cbet0;
static const unsigned maxit_ = 10;
public:
/**
* Constructor for CassiniSoldner.
*
* @param[in] earth the Geodesic object to use for geodesic calculations.
* By default this uses the WGS84 ellipsoid.
*
* This constructor makes an "uninitialized" object. Call Reset to set the
* central latitude and longitude, prior to calling Forward and Reverse.
**********************************************************************/
explicit CassiniSoldner(const Geodesic& earth = Geodesic::WGS84());
/**
* Constructor for CassiniSoldner specifying a center point.
*
* @param[in] lat0 latitude of center point of projection (degrees).
* @param[in] lon0 longitude of center point of projection (degrees).
* @param[in] earth the Geodesic object to use for geodesic calculations.
* By default this uses the WGS84 ellipsoid.
*
* \e lat0 should be in the range [−90°, 90°].
**********************************************************************/
CassiniSoldner(real lat0, real lon0,
const Geodesic& earth = Geodesic::WGS84());
/**
* Set the central point of the projection
*
* @param[in] lat0 latitude of center point of projection (degrees).
* @param[in] lon0 longitude of center point of projection (degrees).
*
* \e lat0 should be in the range [−90°, 90°].
**********************************************************************/
void Reset(real lat0, real lon0);
/**
* Forward projection, from geographic to Cassini-Soldner.
*
* @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 easting direction at point (degrees).
* @param[out] rk reciprocal of azimuthal northing scale at point.
*
* \e lat should be in the range [−90°, 90°]. A call to
* Forward followed by a call to Reverse will return the original (\e lat,
* \e lon) (to within roundoff). The routine does nothing if the origin
* has not been set.
**********************************************************************/
void Forward(real lat, real lon,
real& x, real& y, real& azi, real& rk) const;
/**
* Reverse projection, from Cassini-Soldner to geographic.
*
* @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 easting direction at point (degrees).
* @param[out] rk reciprocal of azimuthal northing scale at point.
*
* A call to Reverse followed by a call to Forward will return the original
* (\e x, \e y) (to within roundoff), provided that \e x and \e y are
* sufficiently small not to "wrap around" the earth. The routine does
* nothing if the origin has not been set.
**********************************************************************/
void Reverse(real x, real y,
real& lat, real& lon, real& azi, real& rk) const;
/**
* CassiniSoldner::Forward without returning the azimuth and scale.
**********************************************************************/
void Forward(real lat, real lon,
real& x, real& y) const {
real azi, rk;
Forward(lat, lon, x, y, azi, rk);
}
/**
* CassiniSoldner::Reverse without returning the azimuth and scale.
**********************************************************************/
void Reverse(real x, real y,
real& lat, real& lon) const {
real azi, rk;
Reverse(x, y, lat, lon, azi, rk);
}
/** \name Inspector functions
**********************************************************************/
///@{
/**
* @return true if the object has been initialized.
**********************************************************************/
bool Init() const { return _meridian.Init(); }
/**
* @return \e lat0 the latitude of origin (degrees).
**********************************************************************/
Math::real LatitudeOrigin() const
{ return _meridian.Latitude(); }
/**
* @return \e lon0 the longitude of origin (degrees).
**********************************************************************/
Math::real LongitudeOrigin() const
{ return _meridian.Longitude(); }
/**
* @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_CASSINISOLDNER_HPP