GeographicLib::Geocentric Class Reference

Geocentric coordinates More...

#include <GeographicLib/Geocentric.hpp>

List of all members.

Public Member Functions

 Geocentric (real a, real f)
 Geocentric ()
void Forward (real lat, real lon, real h, real &X, real &Y, real &Z) const
void Forward (real lat, real lon, real h, real &X, real &Y, real &Z, std::vector< real > &M) const
void Reverse (real X, real Y, real Z, real &lat, real &lon, real &h) const
void Reverse (real X, real Y, real Z, real &lat, real &lon, real &h, std::vector< real > &M) const
Inspector functions



bool Init () const
Math::real MajorRadius () const
Math::real Flattening () const

Static Public Member Functions

static const GeocentricWGS84 ()

Friends

class LocalCartesian
class MagneticCircle
class MagneticModel
class GravityCircle
class GravityModel
class NormalGravity
class SphericalHarmonic
class SphericalHarmonic1
class SphericalHarmonic2

Detailed Description

Geocentric coordinates

Convert between geodetic coordinates latitude = lat, longitude = lon, height = h (measured vertically from the surface of the ellipsoid) to geocentric coordinates (X, Y, Z). The origin of geocentric coordinates is at the center of the earth. The Z axis goes thru the north pole, lat = 90. The X axis goes thru lat = 0, 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

Several changes have been made to ensure that the method returns accurate results for all finite inputs (even if h is infinite). The changes are described in Appendix B of

Vermeille similarly updated his method in

See Geocentric coordinates 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 Geocentric coordinates for further information on the errors.

Example of use:

// Example of using the GeographicLib::Geocentric class

#include <iostream>
#include <exception>
#include <cmath>
#include <GeographicLib/Geocentric.hpp>

using namespace std;
using namespace GeographicLib;

int main() {
  try {
    Geocentric earth(Constants::WGS84_a(), Constants::WGS84_f());
    // Alternatively: const Geocentric& earth = Geocentric::WGS84();
    {
      // Sample forward calculation
      double lat = 27.99, lon = 86.93, h = 8820; // Mt Everest
      double X, Y, Z;
      earth.Forward(lat, lon, h, X, Y, Z);
      cout << floor(X / 1000 + 0.5) << " "
           << floor(Y / 1000 + 0.5) << " "
           << floor(Z / 1000 + 0.5) << "\n";
    }
    {
      // Sample reverse calculation
      double X = 302e3, Y = 5636e3, Z = 2980e3;
      double lat, lon, h;
      earth.Reverse(X, Y, Z, lat, lon, h);
      cout << lat << " " << lon << " " << h << "\n";
    }
  }
  catch (const exception& e) {
    cerr << "Caught exception: " << e.what() << "\n";
    return 1;
  }
  return 0;
}

CartConvert is a command-line utility providing access to the functionality of Geocentric and LocalCartesian.

Definition at line 67 of file Geocentric.hpp.


Constructor & Destructor Documentation

GeographicLib::Geocentric::Geocentric ( real  a,
real  f 
)

Constructor for a ellipsoid with

Parameters:
[in] a equatorial radius (meters).
[in] f flattening of ellipsoid. Setting f = 0 gives a sphere. Negative f gives a prolate ellipsoid. If f > 1, set flattening to 1/f.
Exceptions:
GeographicErr if a or (1 f) a is not positive.

Definition at line 16 of file Geocentric.cpp.

References GeographicLib::Math::isfinite().

GeographicLib::Geocentric::Geocentric (  )  [inline]

A default constructor (for use by NormalGravity).

Definition at line 122 of file Geocentric.hpp.


Member Function Documentation

void GeographicLib::Geocentric::Forward ( real  lat,
real  lon,
real  h,
real &  X,
real &  Y,
real &  Z 
) const [inline]

Convert from geodetic to geocentric coordinates.

Parameters:
[in] lat latitude of point (degrees).
[in] lon longitude of point (degrees).
[in] h height of point above the ellipsoid (meters).
[out] X geocentric coordinate (meters).
[out] Y geocentric coordinate (meters).
[out] Z geocentric coordinate (meters).

lat should be in the range [90, 90]; lon should be in the range [540, 540).

Definition at line 137 of file Geocentric.hpp.

Referenced by GeographicLib::LocalCartesian::Reset().

void GeographicLib::Geocentric::Forward ( real  lat,
real  lon,
real  h,
real &  X,
real &  Y,
real &  Z,
std::vector< real > &  M 
) const [inline]

Convert from geodetic to geocentric coordinates and return rotation matrix.

Parameters:
[in] lat latitude of point (degrees).
[in] lon longitude of point (degrees).
[in] h height of point above the ellipsoid (meters).
[out] X geocentric coordinate (meters).
[out] Y geocentric coordinate (meters).
[out] Z geocentric coordinate (meters).
[out] M if the length of the vector is 9, fill with the rotation matrix in row-major order.

Let v be a unit vector located at (lat, lon, h). We can express v as column vectors in one of two ways

  • in east, north, up coordinates (where the components are relative to a local coordinate system at (lat, lon, h)); call this representation v1.
  • in geocentric X, Y, Z coordinates; call this representation v0.

Then we have v0 = M v1.

Definition at line 166 of file Geocentric.hpp.

void GeographicLib::Geocentric::Reverse ( real  X,
real  Y,
real  Z,
real &  lat,
real &  lon,
real &  h 
) const [inline]

Convert from geocentric to geodetic to coordinates.

Parameters:
[in] X geocentric coordinate (meters).
[in] Y geocentric coordinate (meters).
[in] Z geocentric coordinate (meters).
[out] lat latitude of point (degrees).
[out] lon longitude of point (degrees).
[out] h height of point above the ellipsoid (meters).

In general there are multiple solutions and the result which maximizes h is returned. If there are still multiple solutions with different latitudes (applies only if Z = 0), then the solution with lat > 0 is returned. If there are still multiple solutions with different longitudes (applies only if X = Y = 0) then lon = 0 is returned. The value of h returned satisfies h a (1 e2) / sqrt(1 e2 sin2lat). The value of lon returned is in the range [180, 180).

Definition at line 199 of file Geocentric.hpp.

void GeographicLib::Geocentric::Reverse ( real  X,
real  Y,
real  Z,
real &  lat,
real &  lon,
real &  h,
std::vector< real > &  M 
) const [inline]

Convert from geocentric to geodetic to coordinates.

Parameters:
[in] X geocentric coordinate (meters).
[in] Y geocentric coordinate (meters).
[in] Z geocentric coordinate (meters).
[out] lat latitude of point (degrees).
[out] lon longitude of point (degrees).
[out] h height of point above the ellipsoid (meters).
[out] M if the length of the vector is 9, fill with the rotation matrix in row-major order.

Let v be a unit vector located at (lat, lon, h). We can express v as column vectors in one of two ways

  • in east, north, up coordinates (where the components are relative to a local coordinate system at (lat, lon, h)); call this representation v1.
  • in geocentric X, Y, Z coordinates; call this representation v0.

Then we have v1 = MT v0, where MT is the transpose of M.

Definition at line 228 of file Geocentric.hpp.

bool GeographicLib::Geocentric::Init (  )  const [inline]
Returns:
true if the object has been initialized.

Definition at line 247 of file Geocentric.hpp.

Math::real GeographicLib::Geocentric::MajorRadius (  )  const [inline]
Returns:
a the equatorial radius of the ellipsoid (meters). This is the value used in the constructor.

Definition at line 252 of file Geocentric.hpp.

References GeographicLib::Math::NaN().

Math::real GeographicLib::Geocentric::Flattening (  )  const [inline]
Returns:
f the flattening of the ellipsoid. This is the value used in the constructor.

Definition at line 259 of file Geocentric.hpp.

References GeographicLib::Math::NaN().

const Geocentric & GeographicLib::Geocentric::WGS84 (  )  [static]

A global instantiation of Geocentric with the parameters for the WGS84 ellipsoid.

Definition at line 31 of file Geocentric.cpp.

References GeographicLib::Constants::WGS84_a(), and GeographicLib::Constants::WGS84_f().


Friends And Related Function Documentation

friend class LocalCartesian [friend]

Definition at line 70 of file Geocentric.hpp.

friend class MagneticCircle [friend]

Definition at line 71 of file Geocentric.hpp.

friend class MagneticModel [friend]

Definition at line 72 of file Geocentric.hpp.

friend class GravityCircle [friend]

Definition at line 73 of file Geocentric.hpp.

friend class GravityModel [friend]

Definition at line 74 of file Geocentric.hpp.

friend class NormalGravity [friend]

Definition at line 75 of file Geocentric.hpp.

friend class SphericalHarmonic [friend]

Definition at line 76 of file Geocentric.hpp.

friend class SphericalHarmonic1 [friend]

Definition at line 77 of file Geocentric.hpp.

friend class SphericalHarmonic2 [friend]

Definition at line 78 of file Geocentric.hpp.


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