Local cartesian coordinates. More...

#include <LocalCartesian.hpp>

Public Member Functions
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

	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	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	MajorRadius () const

Math::real	Flattening () const

Private Types
typedef Math::real	real

Private Member Functions
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

void	MatrixMultiply (real M[dim2_]) const

Private Attributes
Geocentric	_earth

real	_h0

real	_lat0

real	_lon0

real	_r [dim2_]

real	_x0

real	_y0

real	_z0

Static Private Attributes
static const size_t	dim2_ = dim_ * dim_

static const size_t	dim_ = 3

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.

Member Typedef Documentation

◆ real

typedef Math::real GeographicLib::LocalCartesian::real

private

Definition at line 40 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

◆ 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 229 of file LocalCartesian.hpp.

◆ 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.

◆ 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.

◆ HeightOrigin()

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

inline

Returns: height of the origin (meters).

Definition at line 216 of file LocalCartesian.hpp.

◆ IntForward()

void GeographicLib::LocalCartesian::IntForward	(	real	lat,
		real	lon,
		real	h,
		real &	x,
		real &	y,
		real &	z,
		real	M[dim2_]
	)		const

private

Definition at line 37 of file src/LocalCartesian.cpp.

◆ IntReverse()

void GeographicLib::LocalCartesian::IntReverse	(	real	x,
		real	y,
		real	z,
		real &	lat,
		real &	lon,
		real &	h,
		real	M[dim2_]
	)		const

private

Definition at line 50 of file src/LocalCartesian.cpp.

◆ LatitudeOrigin()

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

inline

Returns: latitude of the origin (degrees).

Definition at line 206 of file LocalCartesian.hpp.

◆ LongitudeOrigin()

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

inline

Returns: longitude of the origin (degrees).

Definition at line 211 of file LocalCartesian.hpp.

◆ MajorRadius()

Math::real GeographicLib::LocalCartesian::MajorRadius ( ) 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 223 of file LocalCartesian.hpp.

◆ MatrixMultiply()

void GeographicLib::LocalCartesian::MatrixMultiply ( real M[dim2_] ) const

private

Definition at line 27 of file src/LocalCartesian.cpp.

◆ 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 src/LocalCartesian.cpp.

◆ 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).

The value of lon returned is in the range [−180°, 180°].

Definition at line 159 of file LocalCartesian.hpp.

◆ 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 189 of file LocalCartesian.hpp.

Member Data Documentation

◆ _earth

Geocentric GeographicLib::LocalCartesian::_earth

private

Definition at line 43 of file LocalCartesian.hpp.

◆ _h0

real GeographicLib::LocalCartesian::_h0

private

Definition at line 44 of file LocalCartesian.hpp.

◆ _lat0

real GeographicLib::LocalCartesian::_lat0

private

Definition at line 44 of file LocalCartesian.hpp.

◆ _lon0

real GeographicLib::LocalCartesian::_lon0

private

Definition at line 44 of file LocalCartesian.hpp.

◆ _r

real GeographicLib::LocalCartesian::_r[dim2_]

private

Definition at line 45 of file LocalCartesian.hpp.

◆ _x0

real GeographicLib::LocalCartesian::_x0

private

Definition at line 45 of file LocalCartesian.hpp.

◆ _y0

real GeographicLib::LocalCartesian::_y0

private

Definition at line 45 of file LocalCartesian.hpp.

◆ _z0

real GeographicLib::LocalCartesian::_z0

private

Definition at line 45 of file LocalCartesian.hpp.

◆ dim2_

const size_t GeographicLib::LocalCartesian::dim2_ = dim_ * dim_

staticprivate

Definition at line 42 of file LocalCartesian.hpp.

◆ dim_

const size_t GeographicLib::LocalCartesian::dim_ = 3

staticprivate

Definition at line 41 of file LocalCartesian.hpp.

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

Public Member Functions

Private Types

Private Member Functions

Private Attributes

Static Private Attributes

Detailed Description

Member Typedef Documentation

◆ real

Constructor & Destructor Documentation

◆ LocalCartesian() [1/2]

◆ LocalCartesian() [2/2]

Member Function Documentation

◆ Flattening()

◆ Forward() [1/2]

◆ Forward() [2/2]

◆ HeightOrigin()

◆ IntForward()

◆ IntReverse()

◆ LatitudeOrigin()

◆ LongitudeOrigin()

◆ MajorRadius()

◆ MatrixMultiply()

◆ Reset()

◆ Reverse() [1/2]

◆ Reverse() [2/2]

Member Data Documentation

◆ _earth

◆ _h0

◆ _lat0

◆ _lon0

◆ _r

◆ _x0

◆ _y0

◆ _z0

◆ dim2_

◆ dim_