GeographicLib::LocalCartesian Class Reference

Local cartesian coordinates. More...

#include <GeographicLib/LocalCartesian.hpp>

Public Member Functions
	LocalCartesian (real lat0, real lon0, real h0=0, const Geocentric &earth=Geocentric::WGS84())
	LocalCartesian (const Geocentric &earth=Geocentric::WGS84())
void	Reset (real lat0, real lon0, real h0=0)
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
Math::real	LatitudeOrigin () const
Math::real	LongitudeOrigin () const
Math::real	HeightOrigin () const
Math::real	EquatorialRadius () const
Math::real	Flattening () const

Detailed Description

Local cartesian coordinates.

Convert between geodetic coordinates latitude = lat, longitude = lon, height = h (measured vertically from the surface of the ellipsoid) to local cartesian coordinates (x, y, z). The origin of local cartesian coordinate system is at lat = lat0, lon = lon0, h = h0. The z axis is normal to the ellipsoid; the y axis points due north. The plane z = - 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:

// Example of using the GeographicLib::LocalCartesian class
 
#include <iostream>
#include <exception>
#include <cmath>
#include <GeographicLib/Geocentric.hpp>
#include <GeographicLib/LocalCartesian.hpp>
 
using namespace std;
using namespace GeographicLib;
 
int main() {
  try {
    Geocentric earth(Constants::WGS84_a(), Constants::WGS84_f());
    // Alternatively: const Geocentric& earth = Geocentric::WGS84();
    const double lat0 = 48 + 50/60.0, lon0 = 2 + 20/60.0; // Paris
    LocalCartesian proj(lat0, lon0, 0, earth);
    {
      // Sample forward calculation
      double lat = 50.9, lon = 1.8, h = 0; // Calais
      double x, y, z;
      proj.Forward(lat, lon, h, x, y, z);
      cout << x << " " << y << " " << z << "\n";
    }
    {
      // Sample reverse calculation
      double x = -38e3, y = 230e3, z = -4e3;
      double lat, lon, h;
      proj.Reverse(x, y, z, lat, lon, h);
      cout << lat << " " << lon << " " << h << "\n";
    }
  }
  catch (const exception& e) {
    cerr << "Caught exception: " << e.what() << "\n";
    return 1;
  }
}

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

Definition at line 38 of file LocalCartesian.hpp.

Constructor & Destructor Documentation

LocalCartesian() [1/2]

GeographicLib::LocalCartesian::LocalCartesian ( real  lat0, real  lon0, real  h0 = 0, const Geocentric &  earth = Geocentric::WGS84()  )

inline

Constructor setting the origin.

Parameters

[in]	lat0	latitude at origin (degrees).
[in]	lon0	longitude at origin (degrees).
[in]	h0	height above ellipsoid at origin (meters); default 0.
[in]	earth	Geocentric object for the transformation; default Geocentric::WGS84().

lat0 should be in the range [−90°, 90°].

Definition at line 64 of file LocalCartesian.hpp.

LocalCartesian() [2/2]

GeographicLib::LocalCartesian::LocalCartesian ( const Geocentric &  earth = Geocentric::WGS84() )

inlineexplicit

Default constructor.

Parameters

[in]

earth

Geocentric object for the transformation; default Geocentric::WGS84().

Sets lat0 = 0, lon0 = 0, h0 = 0.

Definition at line 77 of file LocalCartesian.hpp.

Member Function Documentation

Reset()

void GeographicLib::LocalCartesian::Reset	(	real	lat0,
		real	lon0,
		real	h0 = 0
	)

Reset the origin.

Parameters

[in]	lat0	latitude at origin (degrees).
[in]	lon0	longitude at origin (degrees).
[in]	h0	height above ellipsoid at origin (meters); default 0.

lat0 should be in the range [−90°, 90°].

Definition at line 16 of file LocalCartesian.cpp.

References GeographicLib::Math::AngNormalize(), GeographicLib::Geocentric::Forward(), GeographicLib::Math::LatFix(), and GeographicLib::Math::sincosd().

Forward() [1/2]

void GeographicLib::LocalCartesian::Forward ( real  lat, real  lon, real  h, real &  x, real &  y, real &  z  ) const

inline

Convert from geodetic to local cartesian 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	local cartesian coordinate (meters).
[out]	y	local cartesian coordinate (meters).
[out]	z	local cartesian coordinate (meters).

lat should be in the range [−90°, 90°].

Definition at line 104 of file LocalCartesian.hpp.

Referenced by main().

Forward() [2/2]

void GeographicLib::LocalCartesian::Forward ( real  lat, real  lon, real  h, real &  x, real &  y, real &  z, std::vector< real > &  M  ) const

inline

Convert from geodetic to local cartesian 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	local cartesian coordinate (meters).
[out]	y	local cartesian coordinate (meters).
[out]	z	local cartesian coordinate (meters).
[out]	M	if the length of the vector is 9, fill with the rotation matrix in row-major order.

lat should be in the range [−90°, 90°].

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 x, y, z coordinates (where the components are relative to the local coordinate system at (lat0, lon0, h0)); call this representation v0.

Then we have v0 = M ⋅ v1.

Definition at line 135 of file LocalCartesian.hpp.

Reverse() [1/2]

void GeographicLib::LocalCartesian::Reverse ( real  x, real  y, real  z, real &  lat, real &  lon, real &  h  ) const

inline

Convert from local cartesian to geodetic coordinates.

Parameters

[in]	x	local cartesian coordinate (meters).
[in]	y	local cartesian coordinate (meters).
[in]	z	local cartesian 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 minimizes |h |is returned, i.e., (lat, lon) corresponds to the closest point on the ellipsoid. The value of lon returned is in the range [−180°, 180°].

Definition at line 161 of file LocalCartesian.hpp.

Referenced by main().

Reverse() [2/2]

void GeographicLib::LocalCartesian::Reverse ( real  x, real  y, real  z, real &  lat, real &  lon, real &  h, std::vector< real > &  M  ) const

inline

Convert from local cartesian to geodetic coordinates and return rotation matrix.

Parameters

[in]	x	local cartesian coordinate (meters).
[in]	y	local cartesian coordinate (meters).
[in]	z	local cartesian 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 x, y, z coordinates (where the components are relative to the local coordinate system at (lat0, lon0, h0)); call this representation v0.

Then we have v1 = M^T ⋅ v0, where M^T is the transpose of M.

Definition at line 191 of file LocalCartesian.hpp.

LatitudeOrigin()

Math::real GeographicLib::LocalCartesian::LatitudeOrigin ( ) const

inline

Returns

latitude of the origin (degrees).

Definition at line 208 of file LocalCartesian.hpp.

LongitudeOrigin()

Math::real GeographicLib::LocalCartesian::LongitudeOrigin ( ) const

inline

Returns

longitude of the origin (degrees).

Definition at line 213 of file LocalCartesian.hpp.

HeightOrigin()

Math::real GeographicLib::LocalCartesian::HeightOrigin ( ) const

inline

Returns

height of the origin (meters).

Definition at line 218 of file LocalCartesian.hpp.

EquatorialRadius()

Math::real GeographicLib::LocalCartesian::EquatorialRadius ( ) const

inline

Returns

a the equatorial radius of the ellipsoid (meters). This is the value of a inherited from the Geocentric object used in the constructor.

Definition at line 225 of file LocalCartesian.hpp.

References GeographicLib::Geocentric::EquatorialRadius().

Flattening()

Math::real GeographicLib::LocalCartesian::Flattening ( ) const

inline

Returns

f the flattening of the ellipsoid. This is the value inherited from the Geocentric object used in the constructor.

Definition at line 231 of file LocalCartesian.hpp.

References GeographicLib::Geocentric::Flattening().

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

• LocalCartesian.hpp
• LocalCartesian.cpp