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/**
* \file Geocentric.hpp
* \brief Header for GeographicLib::Geocentric 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_GEOCENTRIC_HPP)
#define GEOGRAPHICLIB_GEOCENTRIC_HPP 1
#include <vector>
#include <GeographicLib/Constants.hpp>
namespace GeographicLib {
/**
* \brief %Geocentric coordinates
*
* Convert between geodetic coordinates latitude = \e lat, longitude = \e
* lon, height = \e h (measured vertically from the surface of the ellipsoid)
* to geocentric coordinates (\e X, \e Y, \e Z). The origin of geocentric
* coordinates is at the center of the earth. The \e Z axis goes thru the
* north pole, \e lat = 90°. The \e X axis goes thru \e lat = 0,
* \e lon = 0. %Geocentric coordinates are also known as earth centered,
* earth fixed (ECEF) coordinates.
*
* The conversion from geographic to geocentric coordinates is
* straightforward. For the reverse transformation we use
* - H. Vermeille,
* <a href="https://doi.org/10.1007/s00190-002-0273-6"> Direct
* transformation from geocentric coordinates to geodetic coordinates</a>,
* J. Geodesy 76, 451--454 (2002).
* .
* Several changes have been made to ensure that the method returns accurate
* results for all finite inputs (even if \e h is infinite). The changes are
* described in Appendix B of
* - C. F. F. Karney,
* <a href="https://arxiv.org/abs/1102.1215v1">Geodesics
* on an ellipsoid of revolution</a>,
* Feb. 2011;
* preprint
* <a href="https://arxiv.org/abs/1102.1215v1">arxiv:1102.1215v1</a>.
* .
* Vermeille similarly updated his method in
* - H. Vermeille,
* <a href="https://doi.org/10.1007/s00190-010-0419-x">
* An analytical method to transform geocentric into
* geodetic coordinates</a>, J. Geodesy 85, 105--117 (2011).
* .
* See \ref geocentric for more information.
*
* The errors in these routines are close to round-off. Specifically, for
* points within 5000 km of the surface of the ellipsoid (either inside or
* outside the ellipsoid), the error is bounded by 7 nm (7 nanometers) for
* the WGS84 ellipsoid. See \ref geocentric for further information on the
* errors.
*
* Example of use:
* \include example-Geocentric.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 Geocentric {
private:
typedef Math::real real;
friend class LocalCartesian;
friend class MagneticCircle; // MagneticCircle uses Rotation
friend class MagneticModel; // MagneticModel uses IntForward
friend class GravityCircle; // GravityCircle uses Rotation
friend class GravityModel; // GravityModel uses IntForward
friend class NormalGravity; // NormalGravity uses IntForward
static const size_t dim_ = 3;
static const size_t dim2_ = dim_ * dim_;
real _a, _f, _e2, _e2m, _e2a, _e4a, _maxrad;
static void Rotation(real sphi, real cphi, real slam, real clam,
real M[dim2_]);
static void Rotate(const real M[dim2_], real x, real y, real z,
real& X, real& Y, real& Z) {
// Perform [X,Y,Z]^t = M.[x,y,z]^t
// (typically local cartesian to geocentric)
X = M[0] * x + M[1] * y + M[2] * z;
Y = M[3] * x + M[4] * y + M[5] * z;
Z = M[6] * x + M[7] * y + M[8] * z;
}
static void Unrotate(const real M[dim2_], real X, real Y, real Z,
real& x, real& y, real& z) {
// Perform [x,y,z]^t = M^t.[X,Y,Z]^t
// (typically geocentric to local cartesian)
x = M[0] * X + M[3] * Y + M[6] * Z;
y = M[1] * X + M[4] * Y + M[7] * Z;
z = M[2] * X + M[5] * Y + M[8] * Z;
}
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;
public:
/**
* Constructor for an ellipsoid with
*
* @param[in] a equatorial radius (meters).
* @param[in] f flattening of ellipsoid. Setting \e f = 0 gives a sphere.
* Negative \e f gives a prolate ellipsoid.
* @exception GeographicErr if \e a or (1 − \e f) \e a is not
* positive.
**********************************************************************/
Geocentric(real a, real f);
/**
* A default constructor (for use by NormalGravity).
**********************************************************************/
Geocentric() : _a(-1) {}
/**
* Convert from geodetic to geocentric 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 geocentric coordinate (meters).
* @param[out] Y geocentric coordinate (meters).
* @param[out] Z geocentric coordinate (meters).
*
* \e lat should be in the range [−90°, 90°].
**********************************************************************/
void Forward(real lat, real lon, real h, real& X, real& Y, real& Z)
const {
if (Init())
IntForward(lat, lon, h, X, Y, Z, NULL);
}
/**
* Convert from geodetic to geocentric 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 geocentric coordinate (meters).
* @param[out] Y geocentric coordinate (meters).
* @param[out] Z geocentric coordinate (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 geocentric \e X, \e Y, \e Z coordinates; call this representation
* \e v0.
* .
* Then we have \e v0 = \e M ⋅ \e v1.
**********************************************************************/
void Forward(real lat, real lon, real h, real& X, real& Y, real& Z,
std::vector<real>& M)
const {
if (!Init())
return;
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 geocentric to geodetic to coordinates.
*
* @param[in] X geocentric coordinate (meters).
* @param[in] Y geocentric coordinate (meters).
* @param[in] Z geocentric 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. If there are still multiple
* solutions with different latitudes (applies only if \e Z = 0), then the
* solution with \e lat > 0 is returned. If there are still multiple
* solutions with different longitudes (applies only if \e X = \e Y = 0)
* then \e lon = 0 is returned. The value of \e h returned satisfies \e h
* ≥ − \e a (1 − <i>e</i><sup>2</sup>) / sqrt(1 −
* <i>e</i><sup>2</sup> sin<sup>2</sup>\e lat). The value of \e lon
* returned is in the range [−180°, 180°].
**********************************************************************/
void Reverse(real X, real Y, real Z, real& lat, real& lon, real& h)
const {
if (Init())
IntReverse(X, Y, Z, lat, lon, h, NULL);
}
/**
* Convert from geocentric to geodetic to coordinates.
*
* @param[in] X geocentric coordinate (meters).
* @param[in] Y geocentric coordinate (meters).
* @param[in] Z geocentric 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 geocentric \e X, \e Y, \e Z coordinates; call this representation
* \e v0.
* .
* Then we have \e v1 = <i>M</i><sup>T</sup> ⋅ \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 (!Init())
return;
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 true if the object has been initialized.
**********************************************************************/
bool Init() const { return _a > 0; }
/**
* @return \e a the equatorial radius of the ellipsoid (meters). This is
* the value used in the constructor.
**********************************************************************/
Math::real EquatorialRadius() const
{ return Init() ? _a : Math::NaN(); }
/**
* @return \e f the flattening of the ellipsoid. This is the
* value used in the constructor.
**********************************************************************/
Math::real Flattening() const
{ return Init() ? _f : Math::NaN(); }
///@}
/**
* A global instantiation of Geocentric with the parameters for the WGS84
* ellipsoid.
**********************************************************************/
static const Geocentric& WGS84();
};
} // namespace GeographicLib
#endif // GEOGRAPHICLIB_GEOCENTRIC_HPP