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

Lambert conformal conic projection. More...

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

Lambert conformal conic projection.

Implementation taken from the report,

• J. P. Snyder, Map Projections: A Working Manual, USGS Professional Paper 1395 (1987), pp. 107–109.

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.

This class also returns the meridian convergence gamma and scale k. The meridian convergence is the bearing of grid north (the y axis) measured clockwise from true north.

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:

#include

#include

using namespace std;

try {

const double

a = Constants::WGS84_a(),

f = 1/298.257222101,

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

k1 = 1,

lat0 = 39 + 20/60.0, lon0 =-77 - 45/60.0,

fe = 600000, fn = 0;

double x0, y0;

PASouth.Forward(lon0, lat0, lon0, x0, y0);

x0 -= fe; y0 -= fn;

{

double lat = 39.95, lon = -75.17;

double x, y;

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

x -= x0; y -= y0;

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

}

{

double x = 820e3, y = 72e3;

double lat, lon;

x += x0; y += y0;

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

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

}

}

catch (const exception& e) {

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

return 1;

}

}

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

Header for GeographicLib::LambertConformalConic class.

Lambert conformal conic projection.

Namespace for GeographicLib.

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

Definition at line 63 of file LambertConformalConic.hpp.

Constructor with a single standard parallel.

Parameters

Exceptions

Definition at line 16 of file LambertConformalConic.cpp.

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

◆ LambertConformalConic() [2/3]

Constructor with two standard parallels.

Parameters

Exceptions

Definition at line 41 of file LambertConformalConic.cpp.

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

◆ LambertConformalConic() [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 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) ≤ 160° and max(abs(lat1), abs(lat2)) ≤ 90 − min(0.0002, 2.2 × 10−6(180 − dlat), 6 &times 10−8 _dlat_2) (in degrees), then the error in the latitude of origin is less than 4.5 × 10−14d and the relative error in the scale is less than 7 × 10−15.

Definition at line 73 of file LambertConformalConic.cpp.

References GeographicLib::Math::qd.

◆ SetScale()

◆ Forward() [1/2]

Forward projection, from geographic to Lambert conformal conic.

Parameters

The latitude origin is given by LambertConformalConic::LatitudeOrigin(). No false easting or northing is added and lat should be in the range [−90°, 90°]. 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 340 of file LambertConformalConic.cpp.

References GeographicLib::Math::AngDiff(), GeographicLib::Math::degree(), GeographicLib::Math::eatanhe(), 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 LambertConformalConic::LatitudeOrigin(). No false easting or northing is added. 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 382 of file LambertConformalConic.cpp.

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

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 290 of file LambertConformalConic.hpp.

◆ Flattening()

Returns

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

Definition at line 296 of file LambertConformalConic.hpp.

◆ OriginLatitude()

Returns

latitude of the origin for the projection (degrees).

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 305 of file LambertConformalConic.hpp.

◆ CentralScale()

Returns

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

Definition at line 311 of file LambertConformalConic.hpp.

◆ Mercator()

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

• LambertConformalConic.hpp
• LambertConformalConic.cpp