LocalCartesian.hpp
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/**
* \file LocalCartesian.hpp
* \brief Header for GeographicLib::LocalCartesian class
*
* Copyright (c) Charles Karney (2008-2022) <karney@alum.mit.edu> and licensed
* under the MIT/X11 License. For more information, see
* https://geographiclib.sourceforge.io/
**********************************************************************/
#if !defined(GEOGRAPHICLIB_LOCALCARTESIAN_HPP)
#define GEOGRAPHICLIB_LOCALCARTESIAN_HPP 1
#include <GeographicLib/Geocentric.hpp>
#include <GeographicLib/Constants.hpp>
namespace GeographicLib {
/**
* \brief Local cartesian coordinates
*
* Convert between geodetic coordinates latitude = \e lat, longitude = \e
* lon, height = \e h (measured vertically from the surface of the ellipsoid)
* to local cartesian coordinates (\e x, \e y, \e z). The origin of local
* cartesian coordinate system is at \e lat = \e lat0, \e lon = \e lon0, \e h
* = \e h0. The \e z axis is normal to the ellipsoid; the \e y axis points
* due north. The plane \e z = - \e h0 is tangent to the ellipsoid.
*
* The conversions all take place via geocentric coordinates using a
* Geocentric object (by default Geocentric::WGS84()).
*
* Example of use:
* \include example-LocalCartesian.cpp
*
* <a href="CartConvert.1.html">CartConvert</a> is a command-line utility
* providing access to the functionality of Geocentric and LocalCartesian.
**********************************************************************/
class GEOGRAPHICLIB_EXPORT LocalCartesian {
private:
typedef Math::real real;
static const size_t dim_ = 3;
static const size_t dim2_ = dim_ * dim_;
Geocentric _earth;
real _lat0, _lon0, _h0;
real _x0, _y0, _z0, _r[dim2_];
void IntForward(real lat, real lon, real h, real& x, real& y, real& z,
real M[dim2_]) const;
void IntReverse(real x, real y, real z, real& lat, real& lon, real& h,
real M[dim2_]) const;
void MatrixMultiply(real M[dim2_]) const;
public:
/**
* Constructor setting the origin.
*
* @param[in] lat0 latitude at origin (degrees).
* @param[in] lon0 longitude at origin (degrees).
* @param[in] h0 height above ellipsoid at origin (meters); default 0.
* @param[in] earth Geocentric object for the transformation; default
* Geocentric::WGS84().
*
* \e lat0 should be in the range [&minus;90&deg;, 90&deg;].
**********************************************************************/
LocalCartesian(real lat0, real lon0, real h0 = 0,
const Geocentric& earth = Geocentric::WGS84())
: _earth(earth)
{ Reset(lat0, lon0, h0); }
/**
* Default constructor.
*
* @param[in] earth Geocentric object for the transformation; default
* Geocentric::WGS84().
*
* Sets \e lat0 = 0, \e lon0 = 0, \e h0 = 0.
**********************************************************************/
explicit LocalCartesian(const Geocentric& earth = Geocentric::WGS84())
: _earth(earth)
{ Reset(real(0), real(0), real(0)); }
/**
* Reset the origin.
*
* @param[in] lat0 latitude at origin (degrees).
* @param[in] lon0 longitude at origin (degrees).
* @param[in] h0 height above ellipsoid at origin (meters); default 0.
*
* \e lat0 should be in the range [&minus;90&deg;, 90&deg;].
**********************************************************************/
void Reset(real lat0, real lon0, real h0 = 0);
/**
* Convert from geodetic to local cartesian coordinates.
*
* @param[in] lat latitude of point (degrees).
* @param[in] lon longitude of point (degrees).
* @param[in] h height of point above the ellipsoid (meters).
* @param[out] x local cartesian coordinate (meters).
* @param[out] y local cartesian coordinate (meters).
* @param[out] z local cartesian coordinate (meters).
*
* \e lat should be in the range [&minus;90&deg;, 90&deg;].
**********************************************************************/
void Forward(real lat, real lon, real h, real& x, real& y, real& z)
const {
IntForward(lat, lon, h, x, y, z, NULL);
}
/**
* Convert from geodetic to local cartesian coordinates and return rotation
* matrix.
*
* @param[in] lat latitude of point (degrees).
* @param[in] lon longitude of point (degrees).
* @param[in] h height of point above the ellipsoid (meters).
* @param[out] x local cartesian coordinate (meters).
* @param[out] y local cartesian coordinate (meters).
* @param[out] z local cartesian coordinate (meters).
* @param[out] M if the length of the vector is 9, fill with the rotation
* matrix in row-major order.
*
* \e lat should be in the range [&minus;90&deg;, 90&deg;].
*
* Let \e v be a unit vector located at (\e lat, \e lon, \e h). We can
* express \e v as \e column vectors in one of two ways
* - in east, north, up coordinates (where the components are relative to a
* local coordinate system at (\e lat, \e lon, \e h)); call this
* representation \e v1.
* - in \e x, \e y, \e z coordinates (where the components are relative to
* the local coordinate system at (\e lat0, \e lon0, \e h0)); call this
* representation \e v0.
* .
* Then we have \e v0 = \e M &sdot; \e v1.
**********************************************************************/
void Forward(real lat, real lon, real h, real& x, real& y, real& z,
std::vector<real>& M)
const {
if (M.end() == M.begin() + dim2_) {
real t[dim2_];
IntForward(lat, lon, h, x, y, z, t);
std::copy(t, t + dim2_, M.begin());
} else
IntForward(lat, lon, h, x, y, z, NULL);
}
/**
* Convert from local cartesian to geodetic coordinates.
*
* @param[in] x local cartesian coordinate (meters).
* @param[in] y local cartesian coordinate (meters).
* @param[in] z local cartesian coordinate (meters).
* @param[out] lat latitude of point (degrees).
* @param[out] lon longitude of point (degrees).
* @param[out] h height of point above the ellipsoid (meters).
*
* In general, there are multiple solutions and the result which minimizes
* |<i>h</i> |is returned, i.e., (<i>lat</i>, <i>lon</i>) corresponds to
* the closest point on the ellipsoid. The value of \e lon returned is in
* the range [&minus;180&deg;, 180&deg;].
**********************************************************************/
void Reverse(real x, real y, real z, real& lat, real& lon, real& h)
const {
IntReverse(x, y, z, lat, lon, h, NULL);
}
/**
* Convert from local cartesian to geodetic coordinates and return rotation
* matrix.
*
* @param[in] x local cartesian coordinate (meters).
* @param[in] y local cartesian coordinate (meters).
* @param[in] z local cartesian coordinate (meters).
* @param[out] lat latitude of point (degrees).
* @param[out] lon longitude of point (degrees).
* @param[out] h height of point above the ellipsoid (meters).
* @param[out] M if the length of the vector is 9, fill with the rotation
* matrix in row-major order.
*
* Let \e v be a unit vector located at (\e lat, \e lon, \e h). We can
* express \e v as \e column vectors in one of two ways
* - in east, north, up coordinates (where the components are relative to a
* local coordinate system at (\e lat, \e lon, \e h)); call this
* representation \e v1.
* - in \e x, \e y, \e z coordinates (where the components are relative to
* the local coordinate system at (\e lat0, \e lon0, \e h0)); call this
* representation \e v0.
* .
* Then we have \e v1 = <i>M</i><sup>T</sup> &sdot; \e v0, where
* <i>M</i><sup>T</sup> is the transpose of \e M.
**********************************************************************/
void Reverse(real x, real y, real z, real& lat, real& lon, real& h,
std::vector<real>& M)
const {
if (M.end() == M.begin() + dim2_) {
real t[dim2_];
IntReverse(x, y, z, lat, lon, h, t);
std::copy(t, t + dim2_, M.begin());
} else
IntReverse(x, y, z, lat, lon, h, NULL);
}
/** \name Inspector functions
**********************************************************************/
///@{
/**
* @return latitude of the origin (degrees).
**********************************************************************/
Math::real LatitudeOrigin() const { return _lat0; }
/**
* @return longitude of the origin (degrees).
**********************************************************************/
Math::real LongitudeOrigin() const { return _lon0; }
/**
* @return height of the origin (meters).
**********************************************************************/
Math::real HeightOrigin() const { return _h0; }
/**
* @return \e a the equatorial radius of the ellipsoid (meters). This is
* the value of \e a inherited from the Geocentric 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 Geocentric object used in the constructor.
**********************************************************************/
Math::real Flattening() const { return _earth.Flattening(); }
///@}
};
} // namespace GeographicLib
#endif // GEOGRAPHICLIB_LOCALCARTESIAN_HPP
Constants.hpp
Header for GeographicLib::Constants class.
GEOGRAPHICLIB_EXPORT
#define GEOGRAPHICLIB_EXPORT
Definition: Constants.hpp:67
Geocentric.hpp
Header for GeographicLib::Geocentric class.
real
GeographicLib::Math::real real
Definition: GeodSolve.cpp:29
GeographicLib::Geocentric
Geocentric coordinates
Definition: Geocentric.hpp:67
GeographicLib::Geocentric::Flattening
Math::real Flattening() const
Definition: Geocentric.hpp:255
GeographicLib::Geocentric::EquatorialRadius
Math::real EquatorialRadius() const
Definition: Geocentric.hpp:248
GeographicLib::Geocentric::WGS84
static const Geocentric & WGS84()
Definition: Geocentric.cpp:31
GeographicLib::LocalCartesian
Local cartesian coordinates.
Definition: LocalCartesian.hpp:38
GeographicLib::LocalCartesian::Reverse
void Reverse(real x, real y, real z, real &lat, real &lon, real &h) const
Definition: LocalCartesian.hpp:161
GeographicLib::LocalCartesian::Forward
void Forward(real lat, real lon, real h, real &x, real &y, real &z, std::vector< real > &M) const
Definition: LocalCartesian.hpp:135
GeographicLib::LocalCartesian::HeightOrigin
Math::real HeightOrigin() const
Definition: LocalCartesian.hpp:218
GeographicLib::LocalCartesian::LatitudeOrigin
Math::real LatitudeOrigin() const
Definition: LocalCartesian.hpp:208
GeographicLib::LocalCartesian::Reverse
void Reverse(real x, real y, real z, real &lat, real &lon, real &h, std::vector< real > &M) const
Definition: LocalCartesian.hpp:191
GeographicLib::LocalCartesian::Forward
void Forward(real lat, real lon, real h, real &x, real &y, real &z) const
Definition: LocalCartesian.hpp:104
GeographicLib::LocalCartesian::LocalCartesian
LocalCartesian(real lat0, real lon0, real h0=0, const Geocentric &earth=Geocentric::WGS84())
Definition: LocalCartesian.hpp:64
GeographicLib::LocalCartesian::LongitudeOrigin
Math::real LongitudeOrigin() const
Definition: LocalCartesian.hpp:213
GeographicLib::LocalCartesian::EquatorialRadius
Math::real EquatorialRadius() const
Definition: LocalCartesian.hpp:225
GeographicLib::LocalCartesian::Flattening
Math::real Flattening() const
Definition: LocalCartesian.hpp:231
GeographicLib::LocalCartesian::LocalCartesian
LocalCartesian(const Geocentric &earth=Geocentric::WGS84())
Definition: LocalCartesian.hpp:77
GeographicLib::Math::real
double real
Definition: Math.hpp:100
GeographicLib
Namespace for GeographicLib.
Definition: Accumulator.cpp:12