GeographicLib: GeographicLib::AlbersEqualArea Class Reference (original) (raw)

Albers equal area conic projection. More...

#include <[GeographicLib/AlbersEqualArea.hpp](AlbersEqualArea%5F8hpp%5Fsource.html)>

Albers equal area conic projection.

Implementation taken from the report,

• J. P. Snyder, Map Projections: A Working Manual, USGS Professional Paper 1395 (1987), pp. 101–102.

This is a implementation of the equations in Snyder except that divided differences will be [have been] used to transform the expressions into ones which may be evaluated accurately. [In this implementation, the projection correctly becomes the cylindrical equal area or the azimuthal equal area projection when the standard latitude is the equator or a pole.]

The ellipsoid parameters, the standard parallels, and the scale on the standard parallels are set in the constructor. Internally, the case with two standard parallels is converted into a single standard parallel, the latitude of minimum azimuthal scale, with an azimuthal scale specified on this parallel. This latitude is also used as the latitude of origin which is returned by AlbersEqualArea::OriginLatitude. The azimuthal scale on the latitude of origin is given by AlbersEqualArea::CentralScale. The case with two standard parallels at opposite poles is singular and is disallowed. The central meridian (which is a trivial shift of the longitude) is specified as the lon0 argument of the AlbersEqualArea::Forward and AlbersEqualArea::Reverse functions. AlbersEqualArea::Forward and AlbersEqualArea::Reverse also return the meridian convergence, γ, and azimuthal scale, k. A small square aligned with the cardinal directions is projected to a rectangle with dimensions k (in the E-W direction) and 1/k (in the N-S direction). The E-W sides of the rectangle are oriented γ degrees counter-clockwise from the x axis. There is no provision in this class for specifying a false easting or false northing or a different latitude of origin.

Example of use:

#include

#include

using namespace std;

try {

const double

a = Constants::WGS84_a(),

f = Constants::WGS84_f(),

lat1 = 40 + 58/60.0, lat2 = 39 + 56/60.0,

k1 = 1,

lon0 = -77 - 45/60.0;

{

double lat = 39.95, lon = -75.17;

double x, y;

albers.Forward(lon0, lat, lon, x, y);

cout << x << " " << y << "\n";

}

{

double x = 220e3, y = -53e3;

double lat, lon;

albers.Reverse(lon0, x, y, lat, lon);

cout << lat << " " << lon << "\n";

}

}

catch (const exception& e) {

cerr << "Caught exception: " << e.what() << "\n";

return 1;

}

}

Header for GeographicLib::AlbersEqualArea class.

int main(int argc, const char *const argv[])

Albers equal area conic projection.

Namespace for GeographicLib.

ConicProj is a command-line utility providing access to the functionality of LambertConformalConic and AlbersEqualArea.

Definition at line 60 of file AlbersEqualArea.hpp.

Constructor with a single standard parallel.

Parameters

Exceptions

Definition at line 16 of file AlbersEqualArea.cpp.

References GeographicLib::Math::qd, and GeographicLib::Math::sincosd().

◆ AlbersEqualArea() [2/3]

Constructor with two standard parallels.

Parameters

Exceptions

Definition at line 45 of file AlbersEqualArea.cpp.

References GeographicLib::Math::qd, and GeographicLib::Math::sincosd().

◆ AlbersEqualArea() [3/3]

Constructor with two standard parallels specified by sines and cosines.

Parameters

Exceptions

This allows parallels close to the poles to be specified accurately. This routine computes the latitude of origin and the azimuthal scale at this latitude. If dlat = abs(lat2 − lat1) ≤ 160°, then the error in the latitude of origin is less than 4.5 × 10−14d;.

Definition at line 81 of file AlbersEqualArea.cpp.

References GeographicLib::Math::qd.

◆ SetScale()

◆ Forward() [1/2]

Forward projection, from geographic to Lambert conformal conic.

Parameters

The latitude origin is given by AlbersEqualArea::LatitudeOrigin(). No false easting or northing is added and lat should be in the range [−90°, 90°]. The values of x and y returned for points which project to infinity (i.e., one or both of the poles) will be large but finite.

Definition at line 496 of file AlbersEqualArea.cpp.

References GeographicLib::Math::AngDiff(), GeographicLib::Math::degree(), GeographicLib::Math::LatFix(), GeographicLib::Math::sincosd(), and GeographicLib::Math::sq().

Referenced by main(), and SetScale().

◆ Reverse() [1/2]

Reverse projection, from Lambert conformal conic to geographic.

Parameters

The latitude origin is given by AlbersEqualArea::LatitudeOrigin(). No false easting or northing is added. The value of lon returned is in the range [−180°, 180°]. The value of lat returned is in the range [−90°, 90°]. If the input point is outside the legal projected space the nearest pole is returned.

Definition at line 521 of file AlbersEqualArea.cpp.

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

Referenced by main().

◆ Forward() [2/2]

◆ Reverse() [2/2]

◆ EquatorialRadius()

Returns

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

Definition at line 265 of file AlbersEqualArea.hpp.

◆ Flattening()

Returns

f the flattening of the ellipsoid. This is the value used in the constructor.

Definition at line 271 of file AlbersEqualArea.hpp.

◆ OriginLatitude()

Returns

latitude of the origin for the projection (degrees).

This is the latitude of minimum azimuthal scale and equals the stdlat in the 1-parallel constructor and lies between stdlat1 and stdlat2 in the 2-parallel constructors.

Definition at line 280 of file AlbersEqualArea.hpp.

◆ CentralScale()

Returns

central scale for the projection. This is the azimuthal scale on the latitude of origin.

Definition at line 286 of file AlbersEqualArea.hpp.

◆ CylindricalEqualArea()

◆ AzimuthalEqualAreaNorth()

◆ AzimuthalEqualAreaSouth()

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

• AlbersEqualArea.hpp
• AlbersEqualArea.cpp