GeographicLib::AzimuthalEquidistant Class Reference

Azimuthal equidistant projection. More...

#include <GeographicLib/AzimuthalEquidistant.hpp>

List of all members.

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



Math::real MajorRadius () const
Math::real Flattening () const

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 Geodesics on an ellipsoid of revolution.

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;
  }
  return 0;
}

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

Definition at line 42 of file AzimuthalEquidistant.hpp.


Constructor & Destructor Documentation

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 AzimuthalEquidistant.cpp.


Member Function Documentation

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] and lon0 and lon should be in the range [540, 540). 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 AzimuthalEquidistant.cpp.

References GeographicLib::Math::degree(), and GeographicLib::Geodesic::Inverse().

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] and lon0 should be in the range [540, 540). 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 31 of file AzimuthalEquidistant.cpp.

References GeographicLib::Math::degree(), GeographicLib::Geodesic::Direct(), and GeographicLib::Math::hypot().

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 108 of file AzimuthalEquidistant.hpp.

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 117 of file AzimuthalEquidistant.hpp.

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 130 of file AzimuthalEquidistant.hpp.

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 136 of file AzimuthalEquidistant.hpp.


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