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GeographicLib::Geocentric Class Reference

Geocentric coordinates More...

#include <GeographicLib/Geocentric.hpp>

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>
using namespace std;
using namespace GeographicLib;
int main() {
try {
// 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]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.
Exceptions
GeographicErrif 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]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 should be in the range [−540°, 540°).

Definition at line 137 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
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 = Mv1.

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]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 199 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
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 = MTv0, 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.


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