Azimuthal equidistant projection. More...

#include <AzimuthalEquidistant.hpp>

Public Member Functions
	AzimuthalEquidistant (const Geodesic &earth=Geodesic::WGS84())

void	Forward (real lat0, real lon0, real lat, real lon, real &x, real &y, real &azi, real &rk) const

void	Forward (real lat0, real lon0, real lat, real lon, real &x, real &y) const

void	Reverse (real lat0, real lon0, real x, real y, real &lat, real &lon, real &azi, real &rk) const

void	Reverse (real lat0, real lon0, real x, real y, real &lat, real &lon) const

Inspector functions
Math::real	MajorRadius () const

Math::real	Flattening () const

Private Types
typedef Math::real	real

Private Attributes
Geodesic	_earth

real	eps_

Detailed Description

Azimuthal equidistant projection.

Azimuthal equidistant projection centered at an arbitrary position on the ellipsoid. For a point in projected space (x, y), the geodesic distance from the center position is hypot(x, y) and the azimuth of the geodesic from the center point is atan2(x, y). The Forward and Reverse methods also return the azimuth azi of the geodesic at (x, y) and reciprocal scale rk in the azimuthal direction which, together with the basic properties of the projection, serve to specify completely the local affine transformation between geographic and projected coordinates.

The conversions all take place using a Geodesic object (by default Geodesic::WGS84()). For more information on geodesics see geodesic.

Example of use:

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

GeodesicProj is a command-line utility providing access to the functionality of AzimuthalEquidistant, Gnomonic, and CassiniSoldner.

Definition at line 42 of file AzimuthalEquidistant.hpp.

Member Typedef Documentation

◆ real

typedef Math::real GeographicLib::AzimuthalEquidistant::real

private

Definition at line 44 of file AzimuthalEquidistant.hpp.

Constructor & Destructor Documentation

◆ AzimuthalEquidistant()

GeographicLib::AzimuthalEquidistant::AzimuthalEquidistant ( const Geodesic & earth = Geodesic::WGS84() )

explicit

Constructor for AzimuthalEquidistant.

Parameters

[in] earth the Geodesic object to use for geodesic calculations. By default this uses the WGS84 ellipsoid.

Definition at line 16 of file src/AzimuthalEquidistant.cpp.

Member Function Documentation

◆ Flattening()

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

inline

Returns: f the flattening of the ellipsoid. This is the value inherited from the Geodesic object used in the constructor.

Definition at line 132 of file AzimuthalEquidistant.hpp.

◆ Forward() [1/2]

void GeographicLib::AzimuthalEquidistant::Forward	(	real	lat0,
		real	lon0,
		real	lat,
		real	lon,
		real &	x,
		real &	y,
		real &	azi,
		real &	rk
	)		const

Forward projection, from geographic to azimuthal equidistant.

Parameters

[in]	lat0	latitude of center point of projection (degrees).
[in]	lon0	longitude of center point of projection (degrees).
[in]	lat	latitude of point (degrees).
[in]	lon	longitude of point (degrees).
[out]	x	easting of point (meters).
[out]	y	northing of point (meters).
[out]	azi	azimuth of geodesic at point (degrees).
[out]	rk	reciprocal of azimuthal scale at point.

lat0 and lat should be in the range [−90°, 90°]. The scale of the projection is 1 in the "radial" direction, azi clockwise from true north, and is 1/rk in the direction perpendicular to this. A call to Forward followed by a call to Reverse will return the original (lat, lon) (to within roundoff).

Definition at line 20 of file src/AzimuthalEquidistant.cpp.

◆ Forward() [2/2]

void GeographicLib::AzimuthalEquidistant::Forward	(	real	lat0,
		real	lon0,
		real	lat,
		real	lon,
		real &	x,
		real &	y
	)		const

inline

AzimuthalEquidistant::Forward without returning the azimuth and scale.

Definition at line 104 of file AzimuthalEquidistant.hpp.

◆ MajorRadius()

Math::real GeographicLib::AzimuthalEquidistant::MajorRadius ( ) const

inline

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

Definition at line 126 of file AzimuthalEquidistant.hpp.

◆ Reverse() [1/2]

void GeographicLib::AzimuthalEquidistant::Reverse	(	real	lat0,
		real	lon0,
		real	x,
		real	y,
		real &	lat,
		real &	lon,
		real &	azi,
		real &	rk
	)		const

Reverse projection, from azimuthal equidistant to geographic.

Parameters

[in]	lat0	latitude of center point of projection (degrees).
[in]	lon0	longitude of center point of projection (degrees).
[in]	x	easting of point (meters).
[in]	y	northing of point (meters).
[out]	lat	latitude of point (degrees).
[out]	lon	longitude of point (degrees).
[out]	azi	azimuth of geodesic at point (degrees).
[out]	rk	reciprocal of azimuthal scale at point.

lat0 should be in the range [−90°, 90°]. lat will be in the range [−90°, 90°] and lon will be in the range [−180°, 180°]. The scale of the projection is 1 in the "radial" direction, azi clockwise from true north, and is 1/rk in the direction perpendicular to this. A call to Reverse followed by a call to Forward will return the original (x, y) (to roundoff) only if the geodesic to (x, y) is a shortest path.

Definition at line 30 of file src/AzimuthalEquidistant.cpp.

◆ Reverse() [2/2]

void GeographicLib::AzimuthalEquidistant::Reverse	(	real	lat0,
		real	lon0,
		real	x,
		real	y,
		real &	lat,
		real &	lon
	)		const

inline

AzimuthalEquidistant::Reverse without returning the azimuth and scale.

Definition at line 113 of file AzimuthalEquidistant.hpp.

Member Data Documentation

◆ _earth

Geodesic GeographicLib::AzimuthalEquidistant::_earth

private

Definition at line 46 of file AzimuthalEquidistant.hpp.

◆ eps_

real GeographicLib::AzimuthalEquidistant::eps_

private

Definition at line 45 of file AzimuthalEquidistant.hpp.

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

Public Member Functions

Private Types

Private Attributes

Detailed Description

Member Typedef Documentation

◆ real

Constructor & Destructor Documentation

◆ AzimuthalEquidistant()

Member Function Documentation

◆ Flattening()

◆ Forward() [1/2]

◆ Forward() [2/2]

◆ MajorRadius()

◆ Reverse() [1/2]

◆ Reverse() [2/2]

Member Data Documentation

◆ _earth

◆ eps_