Albers Equal Area Conic Projection. More...
#include <GeographicLib/AlbersEqualArea.hpp>
Public Member Functions | |
AlbersEqualArea (real a, real r, real stdlat, real k0) | |
AlbersEqualArea (real a, real r, real stdlat1, real stdlat2, real k1) | |
AlbersEqualArea (real a, real r, real sinlat1, real coslat1, real sinlat2, real coslat2, real k1) | |
void | SetScale (real lat, real k=real(1)) |
void | Forward (real lon0, real lat, real lon, real &x, real &y, real &gamma, real &k) const throw () |
void | Reverse (real lon0, real x, real y, real &lat, real &lon, real &gamma, real &k) const throw () |
void | Forward (real lon0, real lat, real lon, real &x, real &y) const throw () |
void | Reverse (real lon0, real x, real y, real &lat, real &lon) const throw () |
Inspector functions | |
Math::real | MajorRadius () const throw () |
Math::real | InverseFlattening () const throw () |
Math::real | OriginLatitude () const throw () |
Math::real | CentralScale () const throw () |
Static Public Attributes | |
static const AlbersEqualArea | CylindricalEqualArea |
static const AlbersEqualArea | AzimuthalEqualAreaNorth |
static const AlbersEqualArea | AzimuthalEqualAreaSouth |
Albers Equal Area Conic Projection.
Implementation taken from the report,
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, gamma, 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 gamma 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.
Definition at line 53 of file AlbersEqualArea.hpp.
GeographicLib::AlbersEqualArea::AlbersEqualArea | ( | real | a, | |
real | r, | |||
real | stdlat, | |||
real | k0 | |||
) |
Constructor with a single standard parallel.
[in] | a | equatorial radius of ellipsoid (meters) |
[in] | r | reciprocal flattening of ellipsoid. Setting r = 0 implies r = inf or flattening = 0 (i.e., a sphere). Negative r indicates a prolate ellipsoid. |
[in] | stdlat | standard parallel (degrees), the circle of tangency. |
[in] | k0 | azimuthal scale on the standard parallel. |
An exception is thrown if a or k0 is not positive or if stdlat is not in the range [-90, 90].
Definition at line 30 of file AlbersEqualArea.cpp.
GeographicLib::AlbersEqualArea::AlbersEqualArea | ( | real | a, | |
real | r, | |||
real | stdlat1, | |||
real | stdlat2, | |||
real | k1 | |||
) |
Constructor with two standard parallels.
[in] | a | equatorial radius of ellipsoid (meters) |
[in] | r | reciprocal flattening of ellipsoid. Setting r = 0 implies r = inf or flattening = 0 (i.e., a sphere). Negative r indicates a prolate ellipsoid. |
[in] | stdlat1 | first standard parallel (degrees). |
[in] | stdlat2 | second standard parallel (degrees). |
[in] | k1 | azimuthal scale on the standard parallels. |
An exception is thrown if a or k0 is not positive or if stdlat1 or stdlat2 is not in the range [-90, 90]. In addition, an exception is thrown if stdlat1 and stdlat2 are opposite poles.
Definition at line 57 of file AlbersEqualArea.cpp.
GeographicLib::AlbersEqualArea::AlbersEqualArea | ( | real | a, | |
real | r, | |||
real | sinlat1, | |||
real | coslat1, | |||
real | sinlat2, | |||
real | coslat2, | |||
real | k1 | |||
) |
Constructor with two standard parallels specified by sines and cosines.
[in] | a | equatorial radius of ellipsoid (meters) |
[in] | r | reciprocal flattening of ellipsoid. Setting r = 0 implies r = inf or flattening = 0 (i.e., a sphere). Negative r indicates a prolate ellipsoid. |
[in] | sinlat1 | sine of first standard parallel. |
[in] | coslat1 | cosine of first standard parallel. |
[in] | sinlat2 | sine of second standard parallel. |
[in] | coslat2 | cosine of second standard parallel. |
[in] | k1 | azimuthal scale on the standard parallels. |
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) <= 160o, then the error in the latitude of origin is less than 4.5e-14o.
Definition at line 87 of file AlbersEqualArea.cpp.
void GeographicLib::AlbersEqualArea::SetScale | ( | real | lat, | |
real | k = real(1) | |||
) |
Set the azimuthal scale for the projection.
[in] | lat | (degrees). |
[in] | k | azimuthal scale at latitude lat (default 1). |
This allows a "latitude of conformality" to be specified. An exception is thrown if k is not positive or if lat is not in the range (-90, 90).
Definition at line 432 of file AlbersEqualArea.cpp.
References Forward().
void GeographicLib::AlbersEqualArea::Forward | ( | real | lon0, | |
real | lat, | |||
real | lon, | |||
real & | x, | |||
real & | y, | |||
real & | gamma, | |||
real & | k | |||
) | const throw () |
Forward projection, from geographic to Lambert conformal conic.
[in] | lon0 | central meridian longitude (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] | gamma | meridian convergence at point (degrees). |
[out] | k | azimuthal scale of projection at point; the radial scale is the 1/k. |
The latitude origin is given by AlbersEqualArea::LatitudeOrigin(). No false easting or northing is added and lat should be in the range [-90, 90]; lon and lon0 should be in the range [-180, 360]. 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 380 of file AlbersEqualArea.cpp.
Referenced by Forward(), and SetScale().
void GeographicLib::AlbersEqualArea::Reverse | ( | real | lon0, | |
real | x, | |||
real | y, | |||
real & | lat, | |||
real & | lon, | |||
real & | gamma, | |||
real & | k | |||
) | const throw () |
Reverse projection, from Lambert conformal conic to geographic.
[in] | lon0 | central meridian longitude (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] | gamma | meridian convergence at point (degrees). |
[out] | k | azimuthal scale of projection at point; the radial scale is the 1/k. |
The latitude origin is given by AlbersEqualArea::LatitudeOrigin(). No false easting or northing is added. lon0 should be in the range [-180, 360]. 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 410 of file AlbersEqualArea.cpp.
References GeographicLib::Math::hypot().
Referenced by Reverse().
void GeographicLib::AlbersEqualArea::Forward | ( | real | lon0, | |
real | lat, | |||
real | lon, | |||
real & | x, | |||
real & | y | |||
) | const throw () [inline] |
AlbersEqualArea::Forward without returning the convergence and scale.
Definition at line 220 of file AlbersEqualArea.hpp.
References Forward().
void GeographicLib::AlbersEqualArea::Reverse | ( | real | lon0, | |
real | x, | |||
real | y, | |||
real & | lat, | |||
real & | lon | |||
) | const throw () [inline] |
AlbersEqualArea::Reverse without returning the convergence and scale.
Definition at line 230 of file AlbersEqualArea.hpp.
References Reverse().
Math::real GeographicLib::AlbersEqualArea::MajorRadius | ( | ) | const throw () [inline] |
Definition at line 243 of file AlbersEqualArea.hpp.
Math::real GeographicLib::AlbersEqualArea::InverseFlattening | ( | ) | const throw () [inline] |
Definition at line 250 of file AlbersEqualArea.hpp.
Math::real GeographicLib::AlbersEqualArea::OriginLatitude | ( | ) | const throw () [inline] |
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 259 of file AlbersEqualArea.hpp.
Math::real GeographicLib::AlbersEqualArea::CentralScale | ( | ) | const throw () [inline] |
Definition at line 265 of file AlbersEqualArea.hpp.
A global instantiation of AlbersEqualArea with the WGS84 ellipsoid, stdlat = 0, and k0 = 1. This degenerates to the cylindrical equal area projection.
Definition at line 273 of file AlbersEqualArea.hpp.
A global instantiation of AlbersEqualArea with the WGS84 ellipsoid, stdlat = 90o, and k0 = 1. This degenerates to the Lambert azimuthal equal area projection.
Definition at line 280 of file AlbersEqualArea.hpp.
A global instantiation of AlbersEqualArea with the WGS84 ellipsoid, stdlat = -90o, and k0 = 1. This degenerates to the Lambert azimuthal equal area projection.
Definition at line 287 of file AlbersEqualArea.hpp.