Cassini-Soldner projection. More...

#include <CassiniSoldner.hpp>

Public Member Functions
	CassiniSoldner (const Geodesic &earth=Geodesic::WGS84())

	CassiniSoldner (real lat0, real lon0, const Geodesic &earth=Geodesic::WGS84())

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

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

void	Reset (real lat0, real lon0)

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

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

Inspector functions
bool	Init () const

Math::real	LatitudeOrigin () const

Math::real	LongitudeOrigin () const

Math::real	MajorRadius () const

Math::real	Flattening () const

Private Types
typedef Math::real	real

Private Attributes
real	_cbet0

Geodesic	_earth

GeodesicLine	_meridian

real	_sbet0

Static Private Attributes
static const unsigned	maxit_ = 10

Detailed Description

Cassini-Soldner projection.

Cassini-Soldner projection centered at an arbitrary position, lat0, lon0, on the ellipsoid. This projection is a transverse cylindrical equidistant projection. The projection from (lat, lon) to easting and northing (x, y) is defined by geodesics as follows. Go north along a geodesic a distance y from the central point; then turn clockwise 90° and go a distance x along a geodesic. (Although the initial heading is north, this changes to south if the pole is crossed.) This procedure uniquely defines the reverse projection. The forward projection is constructed as follows. Find the point (lat1, lon1) on the meridian closest to (lat, lon). Here we consider the full meridian so that lon1 may be either lon0 or lon0 + 180°. x is the geodesic distance from (lat1, lon1) to (lat, lon), appropriately signed according to which side of the central meridian (lat, lon) lies. y is the shortest distance along the meridian from (lat0, lon0) to (lat1, lon1), again, appropriately signed according to the initial heading. [Note that, in the case of prolate ellipsoids, the shortest meridional path from (lat0, lon0) to (lat1, lon1) may not be the shortest path.] This procedure uniquely defines the forward projection except for a small class of points for which there may be two equally short routes for either leg of the path.

Because of the properties of geodesics, the (x, y) grid is orthogonal. The scale in the easting direction is unity. The scale, k, in the northing direction is unity on the central meridian and increases away from the central meridian. The projection routines return azi, the true bearing of the easting direction, and rk = 1/k, the reciprocal of the scale in the northing direction.

The conversions all take place using a Geodesic object (by default Geodesic::WGS84()). For more information on geodesics see geodesic. The determination of (lat1, lon1) in the forward projection is by solving the inverse geodesic problem for (lat, lon) and its twin obtained by reflection in the meridional plane. The scale is found by determining where two neighboring geodesics intersecting the central meridian at lat1 and lat1 + dlat1 intersect and taking the ratio of the reduced lengths for the two geodesics between that point and, respectively, (lat1, lon1) and (lat, lon).

Example of use:

// Example of using the GeographicLib::CassiniSoldner class
 
#include <iostream>
#include <exception>
#include <GeographicLib/Geodesic.hpp>
#include <GeographicLib/CassiniSoldner.hpp>
 
using namespace std;
using namespace GeographicLib;
 
int main() {
  try {
    Geodesic geod(Constants::WGS84_a(), Constants::WGS84_f());
    // Alternatively: const Geodesic& geod = Geodesic::WGS84();
    const double lat0 = 48 + 50/60.0, lon0 = 2 + 20/60.0; // Paris
    CassiniSoldner proj(lat0, lon0, geod);
    {
      // Sample forward calculation
      double lat = 50.9, lon = 1.8; // Calais
      double x, y;
      proj.Forward(lat, lon, x, y);
      cout << x << " " << y << "\n";
    }
    {
      // Sample reverse calculation
      double x = -38e3, y = 230e3;
      double lat, lon;
      proj.Reverse(x, y, lat, lon);
      cout << lat << " " << lon << "\n";
    }
  }
  catch (const exception& e) {
    cerr << "Caught exception: " << e.what() << "\n";
    return 1;
  }
}

GeodesicProj is a command-line utility providing access to the functionality of AzimuthalEquidistant, Gnomonic, and CassiniSoldner.

Definition at line 69 of file CassiniSoldner.hpp.

Member Typedef Documentation

◆ real

typedef Math::real GeographicLib::CassiniSoldner::real

private

Definition at line 71 of file CassiniSoldner.hpp.

Constructor & Destructor Documentation

◆ CassiniSoldner() [1/2]

GeographicLib::CassiniSoldner::CassiniSoldner ( const Geodesic & earth = Geodesic::WGS84() )

explicit

Constructor for CassiniSoldner.

Parameters

[in] earth the Geodesic object to use for geodesic calculations. By default this uses the WGS84 ellipsoid.

This constructor makes an "uninitialized" object. Call Reset to set the central latitude and longitude, prior to calling Forward and Reverse.

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

◆ CassiniSoldner() [2/2]

GeographicLib::CassiniSoldner::CassiniSoldner	(	real	lat0,
		real	lon0,
		const Geodesic &	earth = `Geodesic::WGS84()`
	)

Constructor for CassiniSoldner specifying a center point.

Parameters

[in]	lat0	latitude of center point of projection (degrees).
[in]	lon0	longitude of center point of projection (degrees).
[in]	earth	the Geodesic object to use for geodesic calculations. By default this uses the WGS84 ellipsoid.

lat0 should be in the range [−90°, 90°].

Definition at line 19 of file src/CassiniSoldner.cpp.

Member Function Documentation

◆ Flattening()

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

inline

Returns: f the flattening of the ellipsoid. This is the value inherited from the Geodesic object used in the constructor.

Definition at line 197 of file CassiniSoldner.hpp.

◆ Forward() [1/2]

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

inline

CassiniSoldner::Forward without returning the azimuth and scale.

Definition at line 152 of file CassiniSoldner.hpp.

◆ Forward() [2/2]

void GeographicLib::CassiniSoldner::Forward	(	real	lat,
		real	lon,
		real &	x,
		real &	y,
		real &	azi,
		real &	rk
	)		const

Forward projection, from geographic to Cassini-Soldner.

Parameters

[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]	azi	azimuth of easting direction at point (degrees).
[out]	rk	reciprocal of azimuthal northing scale at point.

lat should be in the range [−90°, 90°]. A call to Forward followed by a call to Reverse will return the original (lat, lon) (to within roundoff). The routine does nothing if the origin has not been set.

Definition at line 34 of file src/CassiniSoldner.cpp.

◆ Init()

bool GeographicLib::CassiniSoldner::Init ( ) const

inline

Returns: true if the object has been initialized.

Definition at line 173 of file CassiniSoldner.hpp.

◆ LatitudeOrigin()

Math::real GeographicLib::CassiniSoldner::LatitudeOrigin ( ) const

inline

Returns: lat0 the latitude of origin (degrees).

Definition at line 178 of file CassiniSoldner.hpp.

◆ LongitudeOrigin()

Math::real GeographicLib::CassiniSoldner::LongitudeOrigin ( ) const

inline

Returns: lon0 the longitude of origin (degrees).

Definition at line 184 of file CassiniSoldner.hpp.

◆ MajorRadius()

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

inline

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

Definition at line 191 of file CassiniSoldner.hpp.

◆ Reset()

void GeographicLib::CassiniSoldner::Reset	(	real	lat0,
		real	lon0
	)

Set the central point of the projection

Parameters

[in]	lat0	latitude of center point of projection (degrees).
[in]	lon0	longitude of center point of projection (degrees).

lat0 should be in the range [−90°, 90°].

Definition at line 23 of file src/CassiniSoldner.cpp.

◆ Reverse() [1/2]

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

inline

CassiniSoldner::Reverse without returning the azimuth and scale.

Definition at line 161 of file CassiniSoldner.hpp.

◆ Reverse() [2/2]

void GeographicLib::CassiniSoldner::Reverse	(	real	x,
		real	y,
		real &	lat,
		real &	lon,
		real &	azi,
		real &	rk
	)		const

Reverse projection, from Cassini-Soldner to geographic.

Parameters

[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]	azi	azimuth of easting direction at point (degrees).
[out]	rk	reciprocal of azimuthal northing scale at point.

A call to Reverse followed by a call to Forward will return the original (x, y) (to within roundoff), provided that x and y are sufficiently small not to "wrap around" the earth. The routine does nothing if the origin has not been set.

Definition at line 79 of file src/CassiniSoldner.cpp.

Member Data Documentation

◆ _cbet0

real GeographicLib::CassiniSoldner::_cbet0

private

Definition at line 74 of file CassiniSoldner.hpp.

◆ _earth

Geodesic GeographicLib::CassiniSoldner::_earth

private

Definition at line 72 of file CassiniSoldner.hpp.

◆ _meridian

GeodesicLine GeographicLib::CassiniSoldner::_meridian

private

Definition at line 73 of file CassiniSoldner.hpp.

◆ _sbet0

real GeographicLib::CassiniSoldner::_sbet0

private

Definition at line 74 of file CassiniSoldner.hpp.

◆ maxit_

const unsigned GeographicLib::CassiniSoldner::maxit_ = 10

staticprivate

Definition at line 75 of file CassiniSoldner.hpp.

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

Public Member Functions

Private Types

Private Attributes

Static Private Attributes

Detailed Description

Member Typedef Documentation

◆ real

Constructor & Destructor Documentation

◆ CassiniSoldner() [1/2]

◆ CassiniSoldner() [2/2]

Member Function Documentation

◆ Flattening()

◆ Forward() [1/2]

◆ Forward() [2/2]

◆ Init()

◆ LatitudeOrigin()

◆ LongitudeOrigin()

◆ MajorRadius()

◆ Reset()

◆ Reverse() [1/2]

◆ Reverse() [2/2]

Member Data Documentation

◆ _cbet0

◆ _earth

◆ _meridian

◆ _sbet0

◆ maxit_