211 lines
9.2 KiB
C++
211 lines
9.2 KiB
C++
/**
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* \file CassiniSoldner.hpp
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* \brief Header for GeographicLib::CassiniSoldner class
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*
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* Copyright (c) Charles Karney (2009-2020) <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_CASSINISOLDNER_HPP)
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#define GEOGRAPHICLIB_CASSINISOLDNER_HPP 1
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#include <GeographicLib/Geodesic.hpp>
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#include <GeographicLib/GeodesicLine.hpp>
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#include <GeographicLib/Constants.hpp>
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namespace GeographicLib {
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/**
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* \brief Cassini-Soldner projection
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*
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* Cassini-Soldner projection centered at an arbitrary position, \e lat0, \e
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* lon0, on the ellipsoid. This projection is a transverse cylindrical
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* equidistant projection. The projection from (\e lat, \e lon) to easting
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* and northing (\e x, \e y) is defined by geodesics as follows. Go north
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* along a geodesic a distance \e y from the central point; then turn
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* clockwise 90° and go a distance \e x along a geodesic.
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* (Although the initial heading is north, this changes to south if the pole
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* is crossed.) This procedure uniquely defines the reverse projection. The
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* forward projection is constructed as follows. Find the point (\e lat1, \e
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* lon1) on the meridian closest to (\e lat, \e lon). Here we consider the
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* full meridian so that \e lon1 may be either \e lon0 or \e lon0 +
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* 180°. \e x is the geodesic distance from (\e lat1, \e lon1) to
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* (\e lat, \e lon), appropriately signed according to which side of the
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* central meridian (\e lat, \e lon) lies. \e y is the shortest distance
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* along the meridian from (\e lat0, \e lon0) to (\e lat1, \e lon1), again,
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* appropriately signed according to the initial heading. [Note that, in the
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* case of prolate ellipsoids, the shortest meridional path from (\e lat0, \e
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* lon0) to (\e lat1, \e lon1) may not be the shortest path.] This procedure
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* uniquely defines the forward projection except for a small class of points
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* for which there may be two equally short routes for either leg of the
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* path.
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*
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* Because of the properties of geodesics, the (\e x, \e y) grid is
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* orthogonal. The scale in the easting direction is unity. The scale, \e
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* k, in the northing direction is unity on the central meridian and
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* increases away from the central meridian. The projection routines return
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* \e azi, the true bearing of the easting direction, and \e rk = 1/\e k, the
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* reciprocal of the scale in the northing direction.
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*
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* The conversions all take place using a Geodesic object (by default
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* Geodesic::WGS84()). For more information on geodesics see \ref geodesic.
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* The determination of (\e lat1, \e lon1) in the forward projection is by
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* solving the inverse geodesic problem for (\e lat, \e lon) and its twin
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* obtained by reflection in the meridional plane. The scale is found by
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* determining where two neighboring geodesics intersecting the central
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* meridian at \e lat1 and \e lat1 + \e dlat1 intersect and taking the ratio
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* of the reduced lengths for the two geodesics between that point and,
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* respectively, (\e lat1, \e lon1) and (\e lat, \e lon).
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*
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* Example of use:
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* \include example-CassiniSoldner.cpp
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*
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* <a href="GeodesicProj.1.html">GeodesicProj</a> is a command-line utility
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* providing access to the functionality of AzimuthalEquidistant, Gnomonic,
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* and CassiniSoldner.
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**********************************************************************/
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class GEOGRAPHICLIB_EXPORT CassiniSoldner {
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private:
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typedef Math::real real;
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Geodesic _earth;
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GeodesicLine _meridian;
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real _sbet0, _cbet0;
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static const unsigned maxit_ = 10;
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public:
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/**
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* Constructor for CassiniSoldner.
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*
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* @param[in] earth the Geodesic object to use for geodesic calculations.
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* By default this uses the WGS84 ellipsoid.
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*
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* This constructor makes an "uninitialized" object. Call Reset to set the
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* central latitude and longitude, prior to calling Forward and Reverse.
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**********************************************************************/
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explicit CassiniSoldner(const Geodesic& earth = Geodesic::WGS84());
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/**
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* Constructor for CassiniSoldner specifying a center point.
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*
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* @param[in] lat0 latitude of center point of projection (degrees).
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* @param[in] lon0 longitude of center point of projection (degrees).
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* @param[in] earth the Geodesic object to use for geodesic calculations.
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* By default this uses the WGS84 ellipsoid.
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*
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* \e lat0 should be in the range [−90°, 90°].
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**********************************************************************/
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CassiniSoldner(real lat0, real lon0,
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const Geodesic& earth = Geodesic::WGS84());
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/**
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* Set the central point of the projection
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*
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* @param[in] lat0 latitude of center point of projection (degrees).
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* @param[in] lon0 longitude of center point of projection (degrees).
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*
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* \e lat0 should be in the range [−90°, 90°].
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**********************************************************************/
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void Reset(real lat0, real lon0);
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/**
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* Forward projection, from geographic to Cassini-Soldner.
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*
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* @param[in] lat latitude of point (degrees).
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* @param[in] lon longitude of point (degrees).
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* @param[out] x easting of point (meters).
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* @param[out] y northing of point (meters).
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* @param[out] azi azimuth of easting direction at point (degrees).
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* @param[out] rk reciprocal of azimuthal northing scale at point.
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*
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* \e lat should be in the range [−90°, 90°]. A call to
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* Forward followed by a call to Reverse will return the original (\e lat,
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* \e lon) (to within roundoff). The routine does nothing if the origin
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* has not been set.
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**********************************************************************/
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void Forward(real lat, real lon,
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real& x, real& y, real& azi, real& rk) const;
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/**
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* Reverse projection, from Cassini-Soldner to geographic.
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*
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* @param[in] x easting of point (meters).
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* @param[in] y northing of point (meters).
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* @param[out] lat latitude of point (degrees).
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* @param[out] lon longitude of point (degrees).
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* @param[out] azi azimuth of easting direction at point (degrees).
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* @param[out] rk reciprocal of azimuthal northing scale at point.
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*
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* A call to Reverse followed by a call to Forward will return the original
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* (\e x, \e y) (to within roundoff), provided that \e x and \e y are
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* sufficiently small not to "wrap around" the earth. The routine does
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* nothing if the origin has not been set.
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**********************************************************************/
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void Reverse(real x, real y,
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real& lat, real& lon, real& azi, real& rk) const;
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/**
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* CassiniSoldner::Forward without returning the azimuth and scale.
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**********************************************************************/
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void Forward(real lat, real lon,
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real& x, real& y) const {
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real azi, rk;
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Forward(lat, lon, x, y, azi, rk);
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}
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/**
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* CassiniSoldner::Reverse without returning the azimuth and scale.
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**********************************************************************/
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void Reverse(real x, real y,
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real& lat, real& lon) const {
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real azi, rk;
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Reverse(x, y, lat, lon, azi, rk);
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}
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/** \name Inspector functions
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**********************************************************************/
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///@{
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/**
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* @return true if the object has been initialized.
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**********************************************************************/
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bool Init() const { return _meridian.Init(); }
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/**
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* @return \e lat0 the latitude of origin (degrees).
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**********************************************************************/
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Math::real LatitudeOrigin() const
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{ return _meridian.Latitude(); }
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/**
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* @return \e lon0 the longitude of origin (degrees).
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**********************************************************************/
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Math::real LongitudeOrigin() const
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{ return _meridian.Longitude(); }
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/**
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* @return \e a the equatorial radius of the ellipsoid (meters). This is
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* the value inherited from the Geodesic object used in the constructor.
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**********************************************************************/
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Math::real EquatorialRadius() const { return _earth.EquatorialRadius(); }
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/**
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* @return \e f the flattening of the ellipsoid. This is the value
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* inherited from the Geodesic object used in the constructor.
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**********************************************************************/
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Math::real Flattening() const { return _earth.Flattening(); }
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/**
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* \deprecated An old name for EquatorialRadius().
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**********************************************************************/
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GEOGRAPHICLIB_DEPRECATED("Use EquatorialRadius()")
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Math::real MajorRadius() const { return EquatorialRadius(); }
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///@}
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};
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} // namespace GeographicLib
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#endif // GEOGRAPHICLIB_CASSINISOLDNER_HPP
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