GeographicLib  1.21
Public Member Functions | Static Public Attributes | Friends
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 throw ()
void Forward (real lat, real lon, real h, real &X, real &Y, real &Z, std::vector< real > &M) const throw ()
void Reverse (real X, real Y, real Z, real &lat, real &lon, real &h) const throw ()
void Reverse (real X, real Y, real Z, real &lat, real &lon, real &h, std::vector< real > &M) const throw ()
Inspector functions
bool Init () const throw ()
Math::real MajorRadius () const throw ()
Math::real Flattening () const throw ()

Static Public Attributes

static const Geocentric WGS84

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 = 90o. 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

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
// $Id: fea8cd4d5464b6029d6a135a25230892f52f318f $

#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.


Constructor & Destructor Documentation

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

Constructor for a ellipsoid with

Parameters:
[in]aequatorial radius (meters).
[in]fflattening of ellipsoid. Setting f = 0 gives a sphere. Negative f gives a prolate ellipsoid. If f > 1, set flattening to 1/f.

An exception is thrown if either of the axes of the ellipsoid is non-positive.

Definition at line 22 of file Geocentric.cpp.

References GeographicLib::Math::isfinite().

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

A default constructor (for use by NormalGravity).

Definition at line 119 of file Geocentric.hpp.


Member Function Documentation

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

Convert from geodetic to geocentric coordinates.

Parameters:
[in]latlatitude of point (degrees).
[in]lonlongitude of point (degrees).
[in]hheight of point above the ellipsoid (meters).
[out]Xgeocentric coordinate (meters).
[out]Ygeocentric coordinate (meters).
[out]Zgeocentric coordinate (meters).

lat should be in the range [-90, 90]; lon and lon0 should be in the range [-180, 360].

Definition at line 134 of file Geocentric.hpp.

Referenced by main().

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

Convert from geodetic to geocentric coordinates and return rotation matrix.

Parameters:
[in]latlatitude of point (degrees).
[in]lonlongitude of point (degrees).
[in]hheight of point above the ellipsoid (meters).
[out]Xgeocentric coordinate (meters).
[out]Ygeocentric coordinate (meters).
[out]Zgeocentric coordinate (meters).
[out]Mif 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 163 of file Geocentric.hpp.

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

Convert from geocentric to geodetic to coordinates.

Parameters:
[in]Xgeocentric coordinate (meters).
[in]Ygeocentric coordinate (meters).
[in]Zgeocentric coordinate (meters).
[out]latlatitude of point (degrees).
[out]lonlongitude of point (degrees).
[out]hheight 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 195 of file Geocentric.hpp.

Referenced by main().

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

Convert from geocentric to geodetic to coordinates.

Parameters:
[in]Xgeocentric coordinate (meters).
[in]Ygeocentric coordinate (meters).
[in]Zgeocentric coordinate (meters).
[out]latlatitude of point (degrees).
[out]lonlongitude of point (degrees).
[out]hheight of point above the ellipsoid (meters).
[out]Mif 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 = M^T . v0, where M^T is the transpose of M.

Definition at line 224 of file Geocentric.hpp.

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

Definition at line 243 of file Geocentric.hpp.

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

Definition at line 248 of file Geocentric.hpp.

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

Definition at line 255 of file Geocentric.hpp.


Friends And Related Function Documentation

friend class LocalCartesian [friend]

Definition at line 66 of file Geocentric.hpp.

friend class MagneticCircle [friend]

Definition at line 67 of file Geocentric.hpp.

friend class MagneticModel [friend]

Definition at line 68 of file Geocentric.hpp.

friend class GravityCircle [friend]

Definition at line 69 of file Geocentric.hpp.

friend class GravityModel [friend]

Definition at line 70 of file Geocentric.hpp.

friend class NormalGravity [friend]

Definition at line 71 of file Geocentric.hpp.

friend class SphericalHarmonic [friend]

Definition at line 72 of file Geocentric.hpp.

friend class SphericalHarmonic1 [friend]

Definition at line 73 of file Geocentric.hpp.

friend class SphericalHarmonic2 [friend]

Definition at line 74 of file Geocentric.hpp.


Member Data Documentation

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

Definition at line 272 of file Geocentric.hpp.


The documentation for this class was generated from the following files: