Lambert conformal conic projection. More...

#include <LambertConformalConic.hpp>

Public Member Functions
void	Forward (real lon0, real lat, real lon, real &x, real &y, real &gamma, real &k) const

void	Forward (real lon0, real lat, real lon, real &x, real &y) const

	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	Reverse (real lon0, real x, real y, real &lat, real &lon, real &gamma, real &k) const

void	Reverse (real lon0, real x, real y, real &lat, real &lon) const

void	SetScale (real lat, real k=real(1))

Inspector functions
Math::real	MajorRadius () const

Math::real	Flattening () const

Math::real	OriginLatitude () const

Math::real	CentralScale () const

Static Public Member Functions
static const LambertConformalConic &	Mercator ()

Private Types
typedef Math::real	real

Private Member Functions
real	Deatanhe (real x, real y) const

void	Init (real sphi1, real cphi1, real sphi2, real cphi2, real k1)

Static Private Member Functions
static real	Dasinh (real x, real y, real hx, real hy)

static real	Dexp (real x, real y)

static real	Dhyp (real x, real y, real hx, real hy)

static real	Dlog1p (real x, real y)

static real	Dsinh (real x, real y, real sx, real sy, real cx, real cy)

static real	Dsn (real x, real y, real sx, real sy)

static real	hyp (real x)

Private Attributes
real	_a

real	_drhomax

real	_e2

real	_es

real	_f

real	_fm

real	_k0

real	_lat0

real	_n

real	_nc

real	_nrho0

real	_psi0

real	_scale

real	_scbet0

real	_scchi0

real	_sign

real	_t0nm1

real	_tchi0

real	ahypover_

real	eps_

real	epsx_

Static Private Attributes
static const int	numit_ = 5

Detailed Description

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:

// Example of using the GeographicLib::LambertConformalConic class
#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
    // http://www.spatialreference.org/ref/epsg/3364/
    const double
      a = Constants::WGS84_a(),
      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;
      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);
      cout << lat << " " << lon << "\n";
    }
  }
  catch (const exception& e) {
    cerr << "Caught exception: " << e.what() << "\n";
    return 1;
  }
}

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

Definition at line 63 of file LambertConformalConic.hpp.

Member Typedef Documentation

◆ real

typedef Math::real GeographicLib::LambertConformalConic::real

private

Definition at line 65 of file LambertConformalConic.hpp.

Constructor & Destructor Documentation

◆ LambertConformalConic() [1/3]

GeographicLib::LambertConformalConic::LambertConformalConic	(	real	a,
		real	f,
		real	stdlat,
		real	k0
	)

Constructor with a single standard parallel.

Parameters

[in]	a	equatorial radius of ellipsoid (meters).
[in]	f	flattening of ellipsoid. Setting f = 0 gives a sphere. Negative f gives a prolate ellipsoid.
[in]	stdlat	standard parallel (degrees), the circle of tangency.
[in]	k0	scale on the standard parallel.

Exceptions

GeographicErr	if a, (1 − f) a, or k0 is not positive.
GeographicErr	if stdlat is not in [−90°, 90°].

Definition at line 16 of file src/LambertConformalConic.cpp.

◆ LambertConformalConic() [2/3]

GeographicLib::LambertConformalConic::LambertConformalConic	(	real	a,
		real	f,
		real	stdlat1,
		real	stdlat2,
		real	k1
	)

Constructor with two standard parallels.

Parameters

[in]	a	equatorial radius of ellipsoid (meters).
[in]	f	flattening of ellipsoid. Setting f = 0 gives a sphere. Negative f gives a prolate ellipsoid.
[in]	stdlat1	first standard parallel (degrees).
[in]	stdlat2	second standard parallel (degrees).
[in]	k1	scale on the standard parallels.

Exceptions

GeographicErr	if a, (1 − f) a, or k1 is not positive.
GeographicErr	if stdlat1 or stdlat2 is not in [−90°, 90°], or if either stdlat1 or stdlat2 is a pole and stdlat1 is not equal stdlat2.

Definition at line 40 of file src/LambertConformalConic.cpp.

◆ LambertConformalConic() [3/3]

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.

Parameters

[in]	a	equatorial radius of ellipsoid (meters).
[in]	f	flattening of ellipsoid. Setting f = 0 gives a sphere. Negative f gives 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	scale on the standard parallels.

Exceptions

GeographicErr	if a, (1 − f) a, or k1 is not positive.
GeographicErr	if stdlat1 or stdlat2 is not in [−90°, 90°], or if either stdlat1 or stdlat2 is a pole and stdlat1 is not equal stdlat2.

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 dlat²) (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 68 of file src/LambertConformalConic.cpp.

Member Function Documentation

◆ CentralScale()

Math::real GeographicLib::LambertConformalConic::CentralScale ( ) const

inline

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

Definition at line 306 of file LambertConformalConic.hpp.

◆ Dasinh()

static real GeographicLib::LambertConformalConic::Dasinh	(	real	x,
		real	y,
		real	hx,
		real	hy
	)

inlinestaticprivate

Definition at line 125 of file LambertConformalConic.hpp.

◆ Deatanhe()

real GeographicLib::LambertConformalConic::Deatanhe	(	real	x,
		real	y
	)		const

inlineprivate

Definition at line 133 of file LambertConformalConic.hpp.

◆ Dexp()

static real GeographicLib::LambertConformalConic::Dexp	(	real	x,
		real	y
	)

inlinestaticprivate

Definition at line 105 of file LambertConformalConic.hpp.

◆ Dhyp()

static real GeographicLib::LambertConformalConic::Dhyp	(	real	x,
		real	y,
		real	hx,
		real	hy
	)

inlinestaticprivate

Definition at line 89 of file LambertConformalConic.hpp.

◆ Dlog1p()

static real GeographicLib::LambertConformalConic::Dlog1p	(	real	x,
		real	y
	)

inlinestaticprivate

Definition at line 100 of file LambertConformalConic.hpp.

◆ Dsinh()

static real GeographicLib::LambertConformalConic::Dsinh	(	real	x,
		real	y,
		real	sx,
		real	sy,
		real	cx,
		real	cy
	)

inlinestaticprivate

Definition at line 114 of file LambertConformalConic.hpp.

◆ Dsn()

static real GeographicLib::LambertConformalConic::Dsn	(	real	x,
		real	y,
		real	sx,
		real	sy
	)

inlinestaticprivate

Definition at line 93 of file LambertConformalConic.hpp.

◆ Flattening()

Math::real GeographicLib::LambertConformalConic::Flattening ( ) const

inline

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

Definition at line 291 of file LambertConformalConic.hpp.

◆ Forward() [1/2]

void GeographicLib::LambertConformalConic::Forward	(	real	lon0,
		real	lat,
		real	lon,
		real &	x,
		real &	y,
		real &	gamma,
		real &	k
	)		const

Forward projection, from geographic to Lambert conformal conic.

Parameters

[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°]. 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 331 of file src/LambertConformalConic.cpp.

◆ Forward() [2/2]

void GeographicLib::LambertConformalConic::Forward	(	real	lon0,
		real	lat,
		real	lon,
		real &	x,
		real &	y
	)		const

inline

LambertConformalConic::Forward without returning the convergence and scale.

Definition at line 262 of file LambertConformalConic.hpp.

◆ hyp()

static real GeographicLib::LambertConformalConic::hyp ( real x )

inlinestaticprivate

Definition at line 71 of file LambertConformalConic.hpp.

◆ Init()

void GeographicLib::LambertConformalConic::Init	(	real	sphi1,
		real	cphi1,
		real	sphi2,
		real	cphi2,
		real	k1
	)

private

Definition at line 102 of file src/LambertConformalConic.cpp.

◆ MajorRadius()

Math::real GeographicLib::LambertConformalConic::MajorRadius ( ) const

inline

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

Definition at line 285 of file LambertConformalConic.hpp.

◆ Mercator()

const LambertConformalConic & GeographicLib::LambertConformalConic::Mercator ( )

static

A global instantiation of LambertConformalConic with the WGS84 ellipsoid, stdlat = 0, and k0 = 1. This degenerates to the Mercator projection.

Definition at line 324 of file src/LambertConformalConic.cpp.

◆ OriginLatitude()

Math::real GeographicLib::LambertConformalConic::OriginLatitude ( ) const

inline

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 300 of file LambertConformalConic.hpp.

◆ Reverse() [1/2]

void GeographicLib::LambertConformalConic::Reverse	(	real	lon0,
		real	x,
		real	y,
		real &	lat,
		real &	lon,
		real &	gamma,
		real &	k
	)		const

Reverse projection, from Lambert conformal conic to geographic.

Parameters

[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. 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 373 of file src/LambertConformalConic.cpp.

◆ Reverse() [2/2]

void GeographicLib::LambertConformalConic::Reverse	(	real	lon0,
		real	x,
		real	y,
		real &	lat,
		real &	lon
	)		const

inline

LambertConformalConic::Reverse without returning the convergence and scale.

Definition at line 272 of file LambertConformalConic.hpp.

◆ SetScale()

void GeographicLib::LambertConformalConic::SetScale	(	real	lat,
		real	k = `real(1)`
	)

Set the scale for the projection.

Parameters

[in]	lat	(degrees).
[in]	k	scale at latitude lat (default 1).

Exceptions

GeographicErr	k is not positive.
GeographicErr	if lat is not in [−90°, 90°].

Definition at line 441 of file src/LambertConformalConic.cpp.

Member Data Documentation

◆ _a

real GeographicLib::LambertConformalConic::_a

private

Definition at line 67 of file LambertConformalConic.hpp.

◆ _drhomax

real GeographicLib::LambertConformalConic::_drhomax

private

Definition at line 69 of file LambertConformalConic.hpp.

◆ _e2

real GeographicLib::LambertConformalConic::_e2

private

Definition at line 67 of file LambertConformalConic.hpp.

◆ _es

real GeographicLib::LambertConformalConic::_es

private

Definition at line 67 of file LambertConformalConic.hpp.

◆ _f

real GeographicLib::LambertConformalConic::_f

private

Definition at line 67 of file LambertConformalConic.hpp.

◆ _fm

real GeographicLib::LambertConformalConic::_fm

private

Definition at line 67 of file LambertConformalConic.hpp.

◆ _k0

real GeographicLib::LambertConformalConic::_k0

private

Definition at line 68 of file LambertConformalConic.hpp.

◆ _lat0

real GeographicLib::LambertConformalConic::_lat0

private

Definition at line 68 of file LambertConformalConic.hpp.

◆ _n

real GeographicLib::LambertConformalConic::_n

private

Definition at line 68 of file LambertConformalConic.hpp.

◆ _nc

real GeographicLib::LambertConformalConic::_nc

private

Definition at line 68 of file LambertConformalConic.hpp.

◆ _nrho0

real GeographicLib::LambertConformalConic::_nrho0

private

Definition at line 69 of file LambertConformalConic.hpp.

◆ _psi0

real GeographicLib::LambertConformalConic::_psi0

private

Definition at line 69 of file LambertConformalConic.hpp.

◆ _scale

real GeographicLib::LambertConformalConic::_scale

private

Definition at line 68 of file LambertConformalConic.hpp.

◆ _scbet0

real GeographicLib::LambertConformalConic::_scbet0

private

Definition at line 69 of file LambertConformalConic.hpp.

◆ _scchi0

real GeographicLib::LambertConformalConic::_scchi0

private

Definition at line 69 of file LambertConformalConic.hpp.

◆ _sign

real GeographicLib::LambertConformalConic::_sign

private

Definition at line 68 of file LambertConformalConic.hpp.

◆ _t0nm1

real GeographicLib::LambertConformalConic::_t0nm1

private

Definition at line 68 of file LambertConformalConic.hpp.

◆ _tchi0

real GeographicLib::LambertConformalConic::_tchi0

private

Definition at line 69 of file LambertConformalConic.hpp.

◆ ahypover_

real GeographicLib::LambertConformalConic::ahypover_

private

Definition at line 66 of file LambertConformalConic.hpp.

◆ eps_

real GeographicLib::LambertConformalConic::eps_

private

Definition at line 66 of file LambertConformalConic.hpp.

◆ epsx_

real GeographicLib::LambertConformalConic::epsx_

private

Definition at line 66 of file LambertConformalConic.hpp.

◆ numit_

const int GeographicLib::LambertConformalConic::numit_ = 5

staticprivate

Definition at line 70 of file LambertConformalConic.hpp.

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

Public Member Functions

Static Public Member Functions

Private Types

Private Member Functions

Static Private Member Functions

Private Attributes

Static Private Attributes

Detailed Description

Member Typedef Documentation

◆ real

Constructor & Destructor Documentation

◆ LambertConformalConic() [1/3]

◆ LambertConformalConic() [2/3]

◆ LambertConformalConic() [3/3]

Member Function Documentation

◆ CentralScale()

◆ Dasinh()

◆ Deatanhe()

◆ Dexp()

◆ Dhyp()

◆ Dlog1p()

◆ Dsinh()

◆ Dsn()

◆ Flattening()

◆ Forward() [1/2]

◆ Forward() [2/2]

◆ hyp()

◆ Init()

◆ MajorRadius()

◆ Mercator()

◆ OriginLatitude()

◆ Reverse() [1/2]

◆ Reverse() [2/2]

◆ SetScale()

Member Data Documentation

◆ _a

◆ _drhomax

◆ _e2

◆ _es

◆ _f

◆ _fm

◆ _k0

◆ _lat0

◆ _n

◆ _nc

◆ _nrho0

◆ _psi0

◆ _scale

◆ _scbet0

◆ _scchi0

◆ _sign

◆ _t0nm1

◆ _tchi0

◆ ahypover_

◆ eps_

◆ epsx_

◆ numit_