GeographicLib  1.38
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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 MajorRadius () 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>
using namespace std;
using namespace GeographicLib;
int main() {
try {
// 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;
}
return 0;
}

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

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

Constructor setting the origin.

Parameters
[in]lat0latitude at origin (degrees).
[in]lon0longitude at origin (degrees).
[in]h0height above ellipsoid at origin (meters); default 0.
[in]earthGeocentric object for the transformation; default Geocentric::WGS84().

lat0 should be in the range [−90°, 90°]; lon0 should be in the range [−540°, 540°).

Definition at line 65 of file LocalCartesian.hpp.

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

Default constructor.

Parameters
[in]earthGeocentric object for the transformation; default Geocentric::WGS84().

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

Definition at line 78 of file LocalCartesian.hpp.

Member Function Documentation

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

Reset the origin.

Parameters
[in]lat0latitude at origin (degrees).
[in]lon0longitude at origin (degrees).
[in]h0height above ellipsoid at origin (meters); default 0.

lat0 should be in the range [−90°, 90°]; lon0 should be in the range [−540°, 540°).

Definition at line 16 of file LocalCartesian.cpp.

References GeographicLib::Math::AngNormalize(), and GeographicLib::Math::degree().

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]latlatitude of point (degrees).
[in]lonlongitude of point (degrees).
[in]hheight of point above the ellipsoid (meters).
[out]xlocal cartesian coordinate (meters).
[out]ylocal cartesian coordinate (meters).
[out]zlocal cartesian coordinate (meters).

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

Definition at line 107 of file LocalCartesian.hpp.

Referenced by main().

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]latlatitude of point (degrees).
[in]lonlongitude of point (degrees).
[in]hheight of point above the ellipsoid (meters).
[out]xlocal cartesian coordinate (meters).
[out]ylocal cartesian coordinate (meters).
[out]zlocal cartesian coordinate (meters).
[out]Mif the length of the vector is 9, fill with the rotation matrix in row-major order.

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

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 = Mv1.

Definition at line 139 of file LocalCartesian.hpp.

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]xlocal cartesian coordinate (meters).
[in]ylocal cartesian coordinate (meters).
[in]zlocal cartesian coordinate (meters).
[out]latlatitude of point (degrees).
[out]lonlongitude of point (degrees).
[out]hheight of point above the ellipsoid (meters).

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

Definition at line 163 of file LocalCartesian.hpp.

Referenced by main().

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]xlocal cartesian coordinate (meters).
[in]ylocal cartesian coordinate (meters).
[in]zlocal cartesian 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 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 = MTv0, where MT is the transpose of M.

Definition at line 193 of file LocalCartesian.hpp.

Math::real GeographicLib::LocalCartesian::LatitudeOrigin ( ) const
inline
Returns
latitude of the origin (degrees).

Definition at line 210 of file LocalCartesian.hpp.

Math::real GeographicLib::LocalCartesian::LongitudeOrigin ( ) const
inline
Returns
longitude of the origin (degrees).

Definition at line 215 of file LocalCartesian.hpp.

Math::real GeographicLib::LocalCartesian::HeightOrigin ( ) const
inline
Returns
height of the origin (meters).

Definition at line 220 of file LocalCartesian.hpp.

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 227 of file LocalCartesian.hpp.

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 233 of file LocalCartesian.hpp.


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