GeographicLib
1.21
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Lambert Conformal Conic Projection. More...
#include <GeographicLib/LambertConformalConic.hpp>
Public Member Functions | |
LambertConformalConic (real a, real f, real stdlat, real k0) | |
LambertConformalConic (real a, real f, real stdlat1, real stdlat2, real k1) | |
LambertConformalConic (real a, real f, 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 | Flattening () const throw () |
Math::real | OriginLatitude () const throw () |
Math::real | CentralScale () const throw () |
Static Public Attributes | |
static const LambertConformalConic | Mercator |
Lambert Conformal Conic Projection.
Implementation taken from the report,
This is a implementation of the equations in Snyder except that divided differences have been used to transform the expressions into ones which may be evaluated accurately and that Newton's method is used to invert the projection. In this implementation, the projection correctly becomes the Mercator projection or the polar stereographic projection when the standard latitude is the equator or a pole. The accuracy of the projections is about 10 nm (10 nanometers).
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 tangency (also the latitude of minimum scale), with a scale specified on this parallel. This latitude is also used as the latitude of origin which is returned by LambertConformalConic::OriginLatitude. The scale on the latitude of origin is given by LambertConformalConic::CentralScale. The case with two distinct standard parallels where one is a pole is singular and is disallowed. The central meridian (which is a trivial shift of the longitude) is specified as the lon0 argument of the LambertConformalConic::Forward and LambertConformalConic::Reverse functions. There is no provision in this class for specifying a false easting or false northing or a different latitude of origin. However these are can be simply included by the calling function. For example the Pennsylvania South state coordinate system (EPSG:3364) is obtained by:
// Example of using the GeographicLib::LambertConformalConic class // $Id: 5cb2532e2709bcafee50974307836930069b0cff $ #include <iostream> #include <exception> #include <GeographicLib/LambertConformalConic.hpp> using namespace std; using namespace GeographicLib; int main() { try { // Define the Pennsylvania South state coordinate system EPSG:3364 const double a = Constants::WGS84_a<double>(), f = 1/298.257222101, // GRS80 lat1 = 40 + 58/60.0, lat2 = 39 + 56/60.0, // standard parallels k1 = 1, // scale lat0 = 39 + 20/60.0, lon0 =-77 - 45/60.0, // origin fe = 600000, fn = 0; // false easting and northing // Set up basic projection const LambertConformalConic PASouth(a, f, lat1, lat2, k1); double x0, y0; // Transform origin point PASouth.Forward(lon0, lat0, lon0, x0, y0); x0 -= fe; y0 -= fn; { // Sample conversion from geodetic to PASouth grid double lat = 39.95, lon = -75.17; // Philadelphia double x, y; PASouth.Forward(lon0, lat, lon, x, y); x -= x0; y -= y0; std::cout << x << " " << y << "\n"; } { // Sample conversion from PASouth grid to geodetic double x = 820e3, y = 72e3; double lat, lon; x += x0; y += y0; PASouth.Reverse(lon0, x, y, lat, lon); std::cout << lat << " " << lon << "\n"; } } catch (const exception& e) { cerr << "Caught exception: " << e.what() << "\n"; return 1; } return 0; }
ConicProj is a command-line utility providing access to the functionality of LambertConformalConic and AlbersEqualArea.
GeographicLib::LambertConformalConic::LambertConformalConic | ( | real | a, |
real | f, | ||
real | stdlat, | ||
real | k0 | ||
) |
Constructor with a single standard parallel.
[in] | a | equatorial radius of ellipsoid (meters). |
[in] | f | flattening of ellipsoid. Setting f = 0 gives a sphere. Negative f gives a prolate ellipsoid. If f > 1, set flattening to 1/f. |
[in] | stdlat | standard parallel (degrees), the circle of tangency. |
[in] | k0 | 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 LambertConformalConic.cpp.
References GeographicLib::Math::isfinite().
GeographicLib::LambertConformalConic::LambertConformalConic | ( | real | a, |
real | f, | ||
real | stdlat1, | ||
real | stdlat2, | ||
real | k1 | ||
) |
Constructor with two standard parallels.
[in] | a | equatorial radius of ellipsoid (meters). |
[in] | f | flattening of ellipsoid. Setting f = 0 gives a sphere. Negative f gives a prolate ellipsoid. If f > 1, set flattening to 1/f. |
[in] | stdlat1 | first standard parallel (degrees). |
[in] | stdlat2 | second standard parallel (degrees). |
[in] | k1 | 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, if either stdlat1 or stdlat2 is a pole, then an exception is thrown if stdlat1 is not equal stdlat2.
Definition at line 54 of file LambertConformalConic.cpp.
References GeographicLib::Math::isfinite().
GeographicLib::LambertConformalConic::LambertConformalConic | ( | real | a, |
real | f, | ||
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] | f | flattening of ellipsoid. Setting f = 0 gives a sphere. Negative f gives a prolate ellipsoid. If f > 1, set flattening to 1/f. |
[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 | 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 scale at this latitude. In the case where lat1 and lat2 are different, the errors in this routines are as follows: if dlat = abs(lat2 - lat1) <= 160o and max(abs(lat1), abs(lat2)) <= 90 - min(0.0002, 2.2e-6(180 - dlat), 6e-8 dlat2) (in degrees), then the error in the latitude of origin is less than 4.5e-14o and the relative error in the scale is less than 7e-15.
Definition at line 81 of file LambertConformalConic.cpp.
References GeographicLib::Math::isfinite().
void GeographicLib::LambertConformalConic::SetScale | ( | real | lat, |
real | k = real(1) |
||
) |
Set the scale for the projection.
[in] | lat | (degrees). |
[in] | k | scale at latitude lat (default 1). |
This allows a "latitude of true scale" to be specified. An exception is thrown if k is not positive or if stdlat is not in the range [-90, 90]
Definition at line 455 of file LambertConformalConic.cpp.
References GeographicLib::Math::isfinite(), and Forward().
void GeographicLib::LambertConformalConic::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 | scale of projection at point. |
The latitude origin is given by LambertConformalConic::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 error in the projection is less than about 10 nm (10 nanometers), true distance, and the errors in the meridian convergence and scale are consistent with this. 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 324 of file LambertConformalConic.cpp.
References GeographicLib::Math::asinh(), and GeographicLib::Math::sq().
Referenced by SetScale().
void GeographicLib::LambertConformalConic::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 | scale of projection at point. |
The latitude origin is given by LambertConformalConic::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 error in the projection is less than about 10 nm (10 nanometers), true distance, and the errors in the meridian convergence and scale are consistent with this.
Definition at line 371 of file LambertConformalConic.cpp.
References GeographicLib::Math::hypot(), GeographicLib::Math::sq(), and GeographicLib::Math::log1p().
void GeographicLib::LambertConformalConic::Forward | ( | real | lon0, |
real | lat, | ||
real | lon, | ||
real & | x, | ||
real & | y | ||
) | const throw () [inline] |
LambertConformalConic::Forward without returning the convergence and scale.
Definition at line 262 of file LambertConformalConic.hpp.
void GeographicLib::LambertConformalConic::Reverse | ( | real | lon0, |
real | x, | ||
real | y, | ||
real & | lat, | ||
real & | lon | ||
) | const throw () [inline] |
LambertConformalConic::Reverse without returning the convergence and scale.
Definition at line 272 of file LambertConformalConic.hpp.
Math::real GeographicLib::LambertConformalConic::MajorRadius | ( | ) | const throw () [inline] |
Definition at line 285 of file LambertConformalConic.hpp.
Math::real GeographicLib::LambertConformalConic::Flattening | ( | ) | const throw () [inline] |
Definition at line 291 of file LambertConformalConic.hpp.
Math::real GeographicLib::LambertConformalConic::OriginLatitude | ( | ) | const throw () [inline] |
This is the latitude of minimum scale and equals the stdlat in the 1-parallel constructor and lies between stdlat1 and stdlat2 in the 2-parallel constructors.
Definition at line 308 of file LambertConformalConic.hpp.
Math::real GeographicLib::LambertConformalConic::CentralScale | ( | ) | const throw () [inline] |
Definition at line 314 of file LambertConformalConic.hpp.
A global instantiation of LambertConformalConic with the WGS84 ellipsoid, stdlat = 0, and k0 = 1. This degenerates to the Mercator projection.
Definition at line 322 of file LambertConformalConic.hpp.