A geodesic line. More...

#include <GeodesicLine.hpp>

Public Types
enum	mask { NONE, LATITUDE, LONGITUDE, AZIMUTH, DISTANCE, DISTANCE_IN, REDUCEDLENGTH, GEODESICSCALE, AREA, LONG_UNROLL, ALL }

Public Member Functions
Constructors
	GeodesicLine (const Geodesic &g, real lat1, real lon1, real azi1, unsigned caps=ALL)

	GeodesicLine ()

Position in terms of distance
Math::real	Position (real s12, real &lat2, real &lon2, real &azi2, real &m12, real &M12, real &M21, real &S12) const

Math::real	Position (real s12, real &lat2, real &lon2) const

Math::real	Position (real s12, real &lat2, real &lon2, real &azi2) const

Math::real	Position (real s12, real &lat2, real &lon2, real &azi2, real &m12) const

Math::real	Position (real s12, real &lat2, real &lon2, real &azi2, real &M12, real &M21) const

Math::real	Position (real s12, real &lat2, real &lon2, real &azi2, real &m12, real &M12, real &M21) const

Position in terms of arc length
void	ArcPosition (real a12, real &lat2, real &lon2, real &azi2, real &s12, real &m12, real &M12, real &M21, real &S12) const

void	ArcPosition (real a12, real &lat2, real &lon2) const

void	ArcPosition (real a12, real &lat2, real &lon2, real &azi2) const

void	ArcPosition (real a12, real &lat2, real &lon2, real &azi2, real &s12) const

void	ArcPosition (real a12, real &lat2, real &lon2, real &azi2, real &s12, real &m12) const

void	ArcPosition (real a12, real &lat2, real &lon2, real &azi2, real &s12, real &M12, real &M21) const

void	ArcPosition (real a12, real &lat2, real &lon2, real &azi2, real &s12, real &m12, real &M12, real &M21) const

The general position function.
Math::real	GenPosition (bool arcmode, real s12_a12, unsigned outmask, real &lat2, real &lon2, real &azi2, real &s12, real &m12, real &M12, real &M21, real &S12) const

Setting point 3
void	SetDistance (real s13)

void	SetArc (real a13)

void	GenSetDistance (bool arcmode, real s13_a13)

Inspector functions
bool	Init () const

Math::real	Latitude () const

Math::real	Longitude () const

Math::real	Azimuth () const

void	Azimuth (real &sazi1, real &cazi1) const

Math::real	EquatorialAzimuth () const

void	EquatorialAzimuth (real &sazi0, real &cazi0) const

Math::real	EquatorialArc () const

Math::real	MajorRadius () const

Math::real	Flattening () const

unsigned	Capabilities () const

bool	Capabilities (unsigned testcaps) const

Math::real	GenDistance (bool arcmode) const

Math::real	Distance () const

Math::real	Arc () const

Private Types
enum	captype { CAP_NONE = Geodesic::CAP_NONE, CAP_C1 = Geodesic::CAP_C1, CAP_C1p = Geodesic::CAP_C1p, CAP_C2 = Geodesic::CAP_C2, CAP_C3 = Geodesic::CAP_C3, CAP_C4 = Geodesic::CAP_C4, CAP_ALL = Geodesic::CAP_ALL, CAP_MASK = Geodesic::CAP_MASK, OUT_ALL = Geodesic::OUT_ALL, OUT_MASK = Geodesic::OUT_MASK }

typedef Math::real	real

Private Member Functions
	GeodesicLine (const Geodesic &g, real lat1, real lon1, real azi1, real salp1, real calp1, unsigned caps, bool arcmode, real s13_a13)

void	LineInit (const Geodesic &g, real lat1, real lon1, real azi1, real salp1, real calp1, unsigned caps)

Private Attributes
real	_a

real	_a13

real	_A1m1

real	_A2m1

real	_A3c

real	_A4

real	_azi1

real	_b

real	_B11

real	_B21

real	_B31

real	_B41

real	_C1a [nC1_+1]

real	_C1pa [nC1p_+1]

real	_c2

real	_C2a [nC2_+1]

real	_C3a [nC3_]

real	_C4a [nC4_]

real	_calp0

real	_calp1

unsigned	_caps

real	_comg1

real	_csig1

real	_ctau1

real	_dn1

real	_f

real	_f1

real	_k2

real	_lat1

real	_lon1

real	_s13

real	_salp0

real	_salp1

real	_somg1

real	_ssig1

real	_stau1

real	tiny_

Static Private Attributes
static const int	nC1_ = Geodesic::nC1_

static const int	nC1p_ = Geodesic::nC1p_

static const int	nC2_ = Geodesic::nC2_

static const int	nC3_ = Geodesic::nC3_

static const int	nC4_ = Geodesic::nC4_

Friends
class	Geodesic

Detailed Description

A geodesic line.

GeodesicLine facilitates the determination of a series of points on a single geodesic. The starting point (lat1, lon1) and the azimuth azi1 are specified in the constructor; alternatively, the Geodesic::Line method can be used to create a GeodesicLine. GeodesicLine.Position returns the location of point 2 a distance s12 along the geodesic. In addition, GeodesicLine.ArcPosition gives the position of point 2 an arc length a12 along the geodesic.

You can register the position of a reference point 3 a distance (arc length), s13 (a13) along the geodesic with the GeodesicLine.SetDistance (GeodesicLine.SetArc) functions. Points a fractional distance along the line can be found by providing, for example, 0.5 * Distance() as an argument to GeodesicLine.Position. The Geodesic::InverseLine or Geodesic::DirectLine methods return GeodesicLine objects with point 3 set to the point 2 of the corresponding geodesic problem. GeodesicLine objects created with the public constructor or with Geodesic::Line have s13 and a13 set to NaNs.

The default copy constructor and assignment operators work with this class. Similarly, a vector can be used to hold GeodesicLine objects.

The calculations are accurate to better than 15 nm (15 nanometers). See Sec. 9 of arXiv:1102.1215v1 for details. The algorithms used by this class are based on series expansions using the flattening f as a small parameter. These are only accurate for |f| < 0.02; however reasonably accurate results will be obtained for |f| < 0.2. For very eccentric ellipsoids, use GeodesicLineExact instead.

The algorithms are described in

C. F. F. Karney, Algorithms for geodesics, J. Geodesy 87, 43–55 (2013); DOI: 10.1007/s00190-012-0578-z; addenda: geod-addenda.html.

For more information on geodesics see geodesic.

Example of use:

// Example of using the GeographicLib::GeodesicLine class
#include <iostream>
#include <iomanip>
#include <exception>
#include <cmath>
#include <GeographicLib/Geodesic.hpp>
#include <GeographicLib/GeodesicLine.hpp>
#include <GeographicLib/Constants.hpp>
using namespace std;
using namespace GeographicLib;
int main() {
  try {
    // Print waypoints between JFK and SIN
    Geodesic geod(Constants::WGS84_a(), Constants::WGS84_f());
    // Alternatively: const Geodesic& geod = Geodesic::WGS84();
    double
      lat1 = 40.640, lon1 = -73.779, // JFK
      lat2 =  1.359, lon2 = 103.989; // SIN
    const GeographicLib::GeodesicLine line =
      geod.InverseLine(lat1, lon1, lat2, lon2);
    double ds0 = 500e3;             // Nominal distance between points = 500 km
    int num = int(ceil(line.Distance() / ds0)); // The number of intervals
    cout << fixed << setprecision(3);
    {
      // Use intervals of equal length
      double ds = line.Distance() / num;
      for (int i = 0; i <= num; ++i) {
        double lat, lon;
       line.Position(i * ds, lat, lon);
       cout << i << " " << lat << " " << lon << "\n";
      }
    }
    {
      // Slightly faster, use intervals of equal arc length
      double da = line.Arc() / num;
      for (int i = 0; i <= num; ++i) {
        double lat, lon;
       line.ArcPosition(i * da, lat, lon);
       cout << i << " " << lat << " " << lon << "\n";
      }
    }
  }
  catch (const exception& e) {
    cerr << "Caught exception: " << e.what() << "\n";
    return 1;
  }
}

GeodSolve is a command-line utility providing access to the functionality of Geodesic and GeodesicLine.

Definition at line 71 of file GeodesicLine.hpp.

Member Typedef Documentation

◆ real

typedef Math::real GeographicLib::GeodesicLine::real

private

Definition at line 73 of file GeodesicLine.hpp.

Member Enumeration Documentation

◆ captype

enum GeographicLib::GeodesicLine::captype

private

Enumerator
CAP_NONE
CAP_C1
CAP_C1p
CAP_C2
CAP_C3
CAP_C4
CAP_ALL
CAP_MASK
OUT_ALL
OUT_MASK

Definition at line 101 of file GeodesicLine.hpp.

◆ mask

enum GeographicLib::GeodesicLine::mask

Bit masks for what calculations to do. They signify to the GeodesicLine::GeodesicLine constructor and to Geodesic::Line what capabilities should be included in the GeodesicLine object. This is merely a duplication of Geodesic::mask.

Enumerator
NONE	No capabilities, no output.
LATITUDE	Calculate latitude lat2. (It's not necessary to include this as a capability to GeodesicLine because this is included by default.)
LONGITUDE	Calculate longitude lon2.
AZIMUTH	Calculate azimuths azi1 and azi2. (It's not necessary to include this as a capability to GeodesicLine because this is included by default.)
DISTANCE	Calculate distance s12.
DISTANCE_IN	Allow distance s12 to be used as input in the direct geodesic problem.
REDUCEDLENGTH	Calculate reduced length m12.
GEODESICSCALE	Calculate geodesic scales M12 and M21.
AREA	Calculate area S12.
LONG_UNROLL	Unroll lon2 in the direct calculation.
ALL	All capabilities, calculate everything. (LONG_UNROLL is not included in this mask.)

Definition at line 121 of file GeodesicLine.hpp.

Constructor & Destructor Documentation

◆ GeodesicLine() [1/3]

GeographicLib::GeodesicLine::GeodesicLine	(	const Geodesic &	g,
		real	lat1,
		real	lon1,
		real	azi1,
		real	salp1,
		real	calp1,
		unsigned	caps,
		bool	arcmode,
		real	s13_a13
	)

private

Definition at line 128 of file src/GeodesicLine.cpp.

◆ GeodesicLine() [2/3]

GeographicLib::GeodesicLine::GeodesicLine	(	const Geodesic &	g,
		real	lat1,
		real	lon1,
		real	azi1,
		unsigned	caps = `ALL`
	)

Constructor for a geodesic line staring at latitude lat1, longitude lon1, and azimuth azi1 (all in degrees).

Parameters

[in]	g	A Geodesic object used to compute the necessary information about the GeodesicLine.
[in]	lat1	latitude of point 1 (degrees).
[in]	lon1	longitude of point 1 (degrees).
[in]	azi1	azimuth at point 1 (degrees).
[in]	caps	bitor'ed combination of GeodesicLine::mask values specifying the capabilities the GeodesicLine object should possess, i.e., which quantities can be returned in calls to GeodesicLine::Position.

lat1 should be in the range [−90°, 90°].

The GeodesicLine::mask values are

caps |= GeodesicLine::LATITUDE for the latitude lat2; this is added automatically;
caps |= GeodesicLine::LONGITUDE for the latitude lon2;
caps |= GeodesicLine::AZIMUTH for the latitude azi2; this is added automatically;
caps |= GeodesicLine::DISTANCE for the distance s12;
caps |= GeodesicLine::REDUCEDLENGTH for the reduced length m12;
caps |= GeodesicLine::GEODESICSCALE for the geodesic scales M12 and M21;
caps |= GeodesicLine::AREA for the area S12;
caps |= GeodesicLine::DISTANCE_IN permits the length of the geodesic to be given in terms of s12; without this capability the length can only be specified in terms of arc length;
caps |= GeodesicLine::ALL for all of the above.

The default value of caps is GeodesicLine::ALL.

If the point is at a pole, the azimuth is defined by keeping lon1 fixed, writing lat1 = ±(90° − ε), and taking the limit ε → 0+.

Definition at line 118 of file src/GeodesicLine.cpp.

◆ GeodesicLine() [3/3]

GeographicLib::GeodesicLine::GeodesicLine ( )

inline

A default constructor. If GeodesicLine::Position is called on the resulting object, it returns immediately (without doing any calculations). The object can be set with a call to Geodesic::Line. Use Init() to test whether object is still in this uninitialized state.

Definition at line 235 of file GeodesicLine.hpp.

Member Function Documentation

◆ Arc()

Math::real GeographicLib::GeodesicLine::Arc ( ) const

inline

Returns: a13, the arc length to point 3 (degrees).

Definition at line 695 of file GeodesicLine.hpp.

◆ ArcPosition() [1/7]

void GeographicLib::GeodesicLine::ArcPosition	(	real	a12,
		real &	lat2,
		real &	lon2,
		real &	azi2,
		real &	s12,
		real &	m12,
		real &	M12,
		real &	M21,
		real &	S12
	)		const

inline

Compute the position of point 2 which is an arc length a12 (degrees) from point 1.

Parameters

[in]	a12	arc length from point 1 to point 2 (degrees); it can be negative.
[out]	lat2	latitude of point 2 (degrees).
[out]	lon2	longitude of point 2 (degrees); requires that the GeodesicLine object was constructed with caps \|= GeodesicLine::LONGITUDE.
[out]	azi2	(forward) azimuth at point 2 (degrees).
[out]	s12	distance from point 1 to point 2 (meters); requires that the GeodesicLine object was constructed with caps \|= GeodesicLine::DISTANCE.
[out]	m12	reduced length of geodesic (meters); requires that the GeodesicLine object was constructed with caps \|= GeodesicLine::REDUCEDLENGTH.
[out]	M12	geodesic scale of point 2 relative to point 1 (dimensionless); requires that the GeodesicLine object was constructed with caps \|= GeodesicLine::GEODESICSCALE.
[out]	M21	geodesic scale of point 1 relative to point 2 (dimensionless); requires that the GeodesicLine object was constructed with caps \|= GeodesicLine::GEODESICSCALE.
[out]	S12	area under the geodesic (meters²); requires that the GeodesicLine object was constructed with caps \|= GeodesicLine::AREA.

The values of lon2 and azi2 returned are in the range [−180°, 180°].

Requesting a value which the GeodesicLine object is not capable of computing is not an error; the corresponding argument will not be altered.

The following functions are overloaded versions of GeodesicLine::ArcPosition which omit some of the output parameters.

Definition at line 394 of file GeodesicLine.hpp.

◆ ArcPosition() [2/7]

void GeographicLib::GeodesicLine::ArcPosition	(	real	a12,
		real &	lat2,
		real &	lon2
	)		const

inline

See the documentation for GeodesicLine::ArcPosition.

Definition at line 406 of file GeodesicLine.hpp.

◆ ArcPosition() [3/7]

void GeographicLib::GeodesicLine::ArcPosition	(	real	a12,
		real &	lat2,
		real &	lon2,
		real &	azi2
	)		const

inline

See the documentation for GeodesicLine::ArcPosition.

Definition at line 417 of file GeodesicLine.hpp.

◆ ArcPosition() [4/7]

void GeographicLib::GeodesicLine::ArcPosition	(	real	a12,
		real &	lat2,
		real &	lon2,
		real &	azi2,
		real &	s12
	)		const

inline

See the documentation for GeodesicLine::ArcPosition.

Definition at line 429 of file GeodesicLine.hpp.

◆ ArcPosition() [5/7]

void GeographicLib::GeodesicLine::ArcPosition	(	real	a12,
		real &	lat2,
		real &	lon2,
		real &	azi2,
		real &	s12,
		real &	m12
	)		const

inline

See the documentation for GeodesicLine::ArcPosition.

Definition at line 440 of file GeodesicLine.hpp.

◆ ArcPosition() [6/7]

void GeographicLib::GeodesicLine::ArcPosition	(	real	a12,
		real &	lat2,
		real &	lon2,
		real &	azi2,
		real &	s12,
		real &	M12,
		real &	M21
	)		const

inline

See the documentation for GeodesicLine::ArcPosition.

Definition at line 452 of file GeodesicLine.hpp.

◆ ArcPosition() [7/7]

void GeographicLib::GeodesicLine::ArcPosition	(	real	a12,
		real &	lat2,
		real &	lon2,
		real &	azi2,
		real &	s12,
		real &	m12,
		real &	M12,
		real &	M21
	)		const

inline

See the documentation for GeodesicLine::ArcPosition.

Definition at line 465 of file GeodesicLine.hpp.

◆ Azimuth() [1/2]

Math::real GeographicLib::GeodesicLine::Azimuth ( ) const

inline

Returns: azi1 the azimuth (degrees) of the geodesic line at point 1.

Definition at line 606 of file GeodesicLine.hpp.

◆ Azimuth() [2/2]

void GeographicLib::GeodesicLine::Azimuth	(	real &	sazi1,
		real &	cazi1
	)		const

inline

The sine and cosine of azi1.

Parameters

[out]	sazi1	the sine of azi1.
[out]	cazi1	the cosine of azi1.

Definition at line 615 of file GeodesicLine.hpp.

◆ Capabilities() [1/2]

unsigned GeographicLib::GeodesicLine::Capabilities ( ) const

inline

Returns: caps the computational capabilities that this object was constructed with. LATITUDE and AZIMUTH are always included.

Definition at line 664 of file GeodesicLine.hpp.

◆ Capabilities() [2/2]

bool GeographicLib::GeodesicLine::Capabilities ( unsigned testcaps ) const

inline

Test what capabilities are available.

Parameters

[in] testcaps a set of bitor'ed GeodesicLine::mask values.

Returns: true if the GeodesicLine object has all these capabilities.

Definition at line 672 of file GeodesicLine.hpp.

◆ Distance()

Math::real GeographicLib::GeodesicLine::Distance ( ) const

inline

Returns: s13, the distance to point 3 (meters).

Definition at line 690 of file GeodesicLine.hpp.

◆ EquatorialArc()

Math::real GeographicLib::GeodesicLine::EquatorialArc ( ) const

inline

Returns: a1 the arc length (degrees) between the northward equatorial crossing and point 1.

The result lies in (−180°, 180°].

Definition at line 642 of file GeodesicLine.hpp.

◆ EquatorialAzimuth() [1/2]

Math::real GeographicLib::GeodesicLine::EquatorialAzimuth ( ) const

inline

Returns: azi0 the azimuth (degrees) of the geodesic line as it crosses the equator in a northward direction.

The result lies in [−90°, 90°].

Definition at line 624 of file GeodesicLine.hpp.

◆ EquatorialAzimuth() [2/2]

void GeographicLib::GeodesicLine::EquatorialAzimuth	(	real &	sazi0,
		real &	cazi0
	)		const

inline

The sine and cosine of azi0.

Parameters

[out]	sazi0	the sine of azi0.
[out]	cazi0	the cosine of azi0.

Definition at line 633 of file GeodesicLine.hpp.

◆ Flattening()

Math::real GeographicLib::GeodesicLine::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 657 of file GeodesicLine.hpp.

◆ GenDistance()

Math::real GeographicLib::GeodesicLine::GenDistance ( bool arcmode ) const

inline

The distance or arc length to point 3.

Parameters

[in] arcmode boolean flag determining the meaning of returned value.

Returns: s13 if arcmode is false; a13 if arcmode is true.

Definition at line 684 of file GeodesicLine.hpp.

◆ GenPosition()

Math::real GeographicLib::GeodesicLine::GenPosition	(	bool	arcmode,
		real	s12_a12,
		unsigned	outmask,
		real &	lat2,
		real &	lon2,
		real &	azi2,
		real &	s12,
		real &	m12,
		real &	M12,
		real &	M21,
		real &	S12
	)		const

The general position function. GeodesicLine::Position and GeodesicLine::ArcPosition are defined in terms of this function.

Parameters

[in]	arcmode	boolean flag determining the meaning of the second parameter; if arcmode is false, then the GeodesicLine object must have been constructed with caps \|= GeodesicLine::DISTANCE_IN.
[in]	s12_a12	if arcmode is false, this is the distance between point 1 and point 2 (meters); otherwise it is the arc length between point 1 and point 2 (degrees); it can be negative.
[in]	outmask	a bitor'ed combination of GeodesicLine::mask values specifying which of the following parameters should be set.
[out]	lat2	latitude of point 2 (degrees).
[out]	lon2	longitude of point 2 (degrees); requires that the GeodesicLine object was constructed with caps \|= GeodesicLine::LONGITUDE.
[out]	azi2	(forward) azimuth at point 2 (degrees).
[out]	s12	distance from point 1 to point 2 (meters); requires that the GeodesicLine object was constructed with caps \|= GeodesicLine::DISTANCE.
[out]	m12	reduced length of geodesic (meters); requires that the GeodesicLine object was constructed with caps \|= GeodesicLine::REDUCEDLENGTH.
[out]	M12	geodesic scale of point 2 relative to point 1 (dimensionless); requires that the GeodesicLine object was constructed with caps \|= GeodesicLine::GEODESICSCALE.
[out]	M21	geodesic scale of point 1 relative to point 2 (dimensionless); requires that the GeodesicLine object was constructed with caps \|= GeodesicLine::GEODESICSCALE.
[out]	S12	area under the geodesic (meters²); requires that the GeodesicLine object was constructed with caps \|= GeodesicLine::AREA.

Returns: a12 arc length from point 1 to point 2 (degrees).

The GeodesicLine::mask values possible for outmask are

outmask |= GeodesicLine::LATITUDE for the latitude lat2;
outmask |= GeodesicLine::LONGITUDE for the latitude lon2;
outmask |= GeodesicLine::AZIMUTH for the latitude azi2;
outmask |= GeodesicLine::DISTANCE for the distance s12;
outmask |= GeodesicLine::REDUCEDLENGTH for the reduced length m12;
outmask |= GeodesicLine::GEODESICSCALE for the geodesic scales M12 and M21;
outmask |= GeodesicLine::AREA for the area S12;
outmask |= GeodesicLine::ALL for all of the above;
outmask |= GeodesicLine::LONG_UNROLL to unroll lon2 instead of reducing it into the range [−180°, 180°].

Requesting a value which the GeodesicLine object is not capable of computing is not an error; the corresponding argument will not be altered. Note, however, that the arc length is always computed and returned as the function value.

With the GeodesicLine::LONG_UNROLL bit set, the quantity lon2 − lon1 indicates how many times and in what sense the geodesic encircles the ellipsoid.

Definition at line 136 of file src/GeodesicLine.cpp.

◆ GenSetDistance()

void GeographicLib::GeodesicLine::GenSetDistance	(	bool	arcmode,
		real	s13_a13
	)

Specify position of point 3 in terms of either distance or arc length.

Parameters

[in]	arcmode	boolean flag determining the meaning of the second parameter; if arcmode is false, then the GeodesicLine object must have been constructed with caps \|= GeodesicLine::DISTANCE_IN.
[in]	s13_a13	if arcmode is false, this is the distance from point 1 to point 3 (meters); otherwise it is the arc length from point 1 to point 3 (degrees); it can be negative.

Definition at line 317 of file src/GeodesicLine.cpp.

◆ Init()

bool GeographicLib::GeodesicLine::Init ( ) const

inline

Returns: true if the object has been initialized.

Definition at line 589 of file GeodesicLine.hpp.

◆ Latitude()

Math::real GeographicLib::GeodesicLine::Latitude ( ) const

inline

Returns: lat1 the latitude of point 1 (degrees).

Definition at line 594 of file GeodesicLine.hpp.

◆ LineInit()

void GeographicLib::GeodesicLine::LineInit	(	const Geodesic &	g,
		real	lat1,
		real	lon1,
		real	azi1,
		real	salp1,
		real	calp1,
		unsigned	caps
	)

private

Definition at line 35 of file src/GeodesicLine.cpp.

◆ Longitude()

Math::real GeographicLib::GeodesicLine::Longitude ( ) const

inline

Returns: lon1 the longitude of point 1 (degrees).

Definition at line 600 of file GeodesicLine.hpp.

◆ MajorRadius()

Math::real GeographicLib::GeodesicLine::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 650 of file GeodesicLine.hpp.

◆ Position() [1/6]

Math::real GeographicLib::GeodesicLine::Position	(	real	s12,
		real &	lat2,
		real &	lon2,
		real &	azi2,
		real &	m12,
		real &	M12,
		real &	M21,
		real &	S12
	)		const

inline

Compute the position of point 2 which is a distance s12 (meters) from point 1.

Parameters

[in]	s12	distance from point 1 to point 2 (meters); it can be negative.
[out]	lat2	latitude of point 2 (degrees).
[out]	lon2	longitude of point 2 (degrees); requires that the GeodesicLine object was constructed with caps \|= GeodesicLine::LONGITUDE.
[out]	azi2	(forward) azimuth at point 2 (degrees).
[out]	m12	reduced length of geodesic (meters); requires that the GeodesicLine object was constructed with caps \|= GeodesicLine::REDUCEDLENGTH.
[out]	M12	geodesic scale of point 2 relative to point 1 (dimensionless); requires that the GeodesicLine object was constructed with caps \|= GeodesicLine::GEODESICSCALE.
[out]	M21	geodesic scale of point 1 relative to point 2 (dimensionless); requires that the GeodesicLine object was constructed with caps \|= GeodesicLine::GEODESICSCALE.
[out]	S12	area under the geodesic (meters²); requires that the GeodesicLine object was constructed with caps \|= GeodesicLine::AREA.

Returns: a12 arc length from point 1 to point 2 (degrees).

The values of lon2 and azi2 returned are in the range [−180°, 180°].

The GeodesicLine object must have been constructed with caps |= GeodesicLine::DISTANCE_IN; otherwise Math::NaN() is returned and no parameters are set. Requesting a value which the GeodesicLine object is not capable of computing is not an error; the corresponding argument will not be altered.

The following functions are overloaded versions of GeodesicLine::Position which omit some of the output parameters. Note, however, that the arc length is always computed and returned as the function value.

Definition at line 281 of file GeodesicLine.hpp.

◆ Position() [2/6]

Math::real GeographicLib::GeodesicLine::Position	(	real	s12,
		real &	lat2,
		real &	lon2
	)		const

inline

See the documentation for GeodesicLine::Position.

Definition at line 295 of file GeodesicLine.hpp.

◆ Position() [3/6]

Math::real GeographicLib::GeodesicLine::Position	(	real	s12,
		real &	lat2,
		real &	lon2,
		real &	azi2
	)		const

inline

See the documentation for GeodesicLine::Position.

Definition at line 305 of file GeodesicLine.hpp.

◆ Position() [4/6]

Math::real GeographicLib::GeodesicLine::Position	(	real	s12,
		real &	lat2,
		real &	lon2,
		real &	azi2,
		real &	m12
	)		const

inline

See the documentation for GeodesicLine::Position.

Definition at line 316 of file GeodesicLine.hpp.

◆ Position() [5/6]

Math::real GeographicLib::GeodesicLine::Position	(	real	s12,
		real &	lat2,
		real &	lon2,
		real &	azi2,
		real &	M12,
		real &	M21
	)		const

inline

See the documentation for GeodesicLine::Position.

Definition at line 328 of file GeodesicLine.hpp.

◆ Position() [6/6]

Math::real GeographicLib::GeodesicLine::Position	(	real	s12,
		real &	lat2,
		real &	lon2,
		real &	azi2,
		real &	m12,
		real &	M12,
		real &	M21
	)		const

inline

See the documentation for GeodesicLine::Position.

Definition at line 341 of file GeodesicLine.hpp.

◆ SetArc()

void GeographicLib::GeodesicLine::SetArc ( real a13 )

Specify position of point 3 in terms of arc length.

Parameters

[in] a13 the arc length from point 1 to point 3 (degrees); it can be negative.

The distance s13 is only set if the GeodesicLine object has been constructed with caps |= GeodesicLine::DISTANCE.

Definition at line 309 of file src/GeodesicLine.cpp.

◆ SetDistance()

void GeographicLib::GeodesicLine::SetDistance ( real s13 )

Specify position of point 3 in terms of distance.

Parameters

[in] s13 the distance from point 1 to point 3 (meters); it can be negative.

This is only useful if the GeodesicLine object has been constructed with caps |= GeodesicLine::DISTANCE_IN.

Definition at line 301 of file src/GeodesicLine.cpp.

Friends And Related Function Documentation

◆ Geodesic

friend class Geodesic

friend

Definition at line 74 of file GeodesicLine.hpp.

Member Data Documentation

◆ _a

real GeographicLib::GeodesicLine::_a

private

Definition at line 83 of file GeodesicLine.hpp.

◆ _a13

real GeographicLib::GeodesicLine::_a13

private

Definition at line 86 of file GeodesicLine.hpp.

◆ _A1m1

real GeographicLib::GeodesicLine::_A1m1

private

Definition at line 83 of file GeodesicLine.hpp.

◆ _A2m1

real GeographicLib::GeodesicLine::_A2m1

private

Definition at line 83 of file GeodesicLine.hpp.

◆ _A3c

real GeographicLib::GeodesicLine::_A3c

private

Definition at line 83 of file GeodesicLine.hpp.

◆ _A4

real GeographicLib::GeodesicLine::_A4

private

Definition at line 83 of file GeodesicLine.hpp.

◆ _azi1

real GeographicLib::GeodesicLine::_azi1

private

Definition at line 82 of file GeodesicLine.hpp.

◆ _b

real GeographicLib::GeodesicLine::_b

private

Definition at line 83 of file GeodesicLine.hpp.

◆ _B11

real GeographicLib::GeodesicLine::_B11

private

Definition at line 83 of file GeodesicLine.hpp.

◆ _B21

real GeographicLib::GeodesicLine::_B21

private

Definition at line 83 of file GeodesicLine.hpp.

◆ _B31

real GeographicLib::GeodesicLine::_B31

private

Definition at line 83 of file GeodesicLine.hpp.

◆ _B41

real GeographicLib::GeodesicLine::_B41

private

Definition at line 83 of file GeodesicLine.hpp.

◆ _C1a

real GeographicLib::GeodesicLine::_C1a[nC1_+1]

private

Definition at line 88 of file GeodesicLine.hpp.

◆ _C1pa

real GeographicLib::GeodesicLine::_C1pa[nC1p_+1]

private

Definition at line 88 of file GeodesicLine.hpp.

◆ _c2

real GeographicLib::GeodesicLine::_c2

private

Definition at line 83 of file GeodesicLine.hpp.

◆ _C2a

real GeographicLib::GeodesicLine::_C2a[nC2_+1]

private

Definition at line 88 of file GeodesicLine.hpp.

◆ _C3a

real GeographicLib::GeodesicLine::_C3a[nC3_]

private

Definition at line 88 of file GeodesicLine.hpp.

◆ _C4a

real GeographicLib::GeodesicLine::_C4a[nC4_]

private

Definition at line 88 of file GeodesicLine.hpp.

◆ _calp0

real GeographicLib::GeodesicLine::_calp0

private

Definition at line 83 of file GeodesicLine.hpp.

◆ _calp1

real GeographicLib::GeodesicLine::_calp1

private

Definition at line 83 of file GeodesicLine.hpp.

◆ _caps

unsigned GeographicLib::GeodesicLine::_caps

private

Definition at line 90 of file GeodesicLine.hpp.

◆ _comg1

real GeographicLib::GeodesicLine::_comg1

private

Definition at line 83 of file GeodesicLine.hpp.

◆ _csig1

real GeographicLib::GeodesicLine::_csig1

private

Definition at line 83 of file GeodesicLine.hpp.

◆ _ctau1

real GeographicLib::GeodesicLine::_ctau1

private

Definition at line 83 of file GeodesicLine.hpp.

◆ _dn1

real GeographicLib::GeodesicLine::_dn1

private

Definition at line 83 of file GeodesicLine.hpp.

◆ _f

real GeographicLib::GeodesicLine::_f

private

Definition at line 83 of file GeodesicLine.hpp.

◆ _f1

real GeographicLib::GeodesicLine::_f1

private

Definition at line 83 of file GeodesicLine.hpp.

◆ _k2

real GeographicLib::GeodesicLine::_k2

private

Definition at line 83 of file GeodesicLine.hpp.

◆ _lat1

real GeographicLib::GeodesicLine::_lat1

private

Definition at line 82 of file GeodesicLine.hpp.

◆ _lon1

real GeographicLib::GeodesicLine::_lon1

private

Definition at line 82 of file GeodesicLine.hpp.

◆ _s13

real GeographicLib::GeodesicLine::_s13

private

Definition at line 86 of file GeodesicLine.hpp.

◆ _salp0

real GeographicLib::GeodesicLine::_salp0

private

Definition at line 83 of file GeodesicLine.hpp.

◆ _salp1

real GeographicLib::GeodesicLine::_salp1

private

Definition at line 83 of file GeodesicLine.hpp.

◆ _somg1

real GeographicLib::GeodesicLine::_somg1

private

Definition at line 83 of file GeodesicLine.hpp.

◆ _ssig1

real GeographicLib::GeodesicLine::_ssig1

private

Definition at line 83 of file GeodesicLine.hpp.

◆ _stau1

real GeographicLib::GeodesicLine::_stau1

private

Definition at line 83 of file GeodesicLine.hpp.

◆ nC1_

const int GeographicLib::GeodesicLine::nC1_ = Geodesic::nC1_

staticprivate

Definition at line 75 of file GeodesicLine.hpp.

◆ nC1p_

const int GeographicLib::GeodesicLine::nC1p_ = Geodesic::nC1p_

staticprivate

Definition at line 76 of file GeodesicLine.hpp.

◆ nC2_

const int GeographicLib::GeodesicLine::nC2_ = Geodesic::nC2_

staticprivate

Definition at line 77 of file GeodesicLine.hpp.

◆ nC3_

const int GeographicLib::GeodesicLine::nC3_ = Geodesic::nC3_

staticprivate

Definition at line 78 of file GeodesicLine.hpp.

◆ nC4_

const int GeographicLib::GeodesicLine::nC4_ = Geodesic::nC4_

staticprivate

Definition at line 79 of file GeodesicLine.hpp.

◆ tiny_

real GeographicLib::GeodesicLine::tiny_

private

Definition at line 81 of file GeodesicLine.hpp.

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

Public Types

Public Member Functions

Private Types

Private Member Functions

Private Attributes

Static Private Attributes

Friends

Detailed Description

Member Typedef Documentation

◆ real

Member Enumeration Documentation

◆ captype

◆ mask

Constructor & Destructor Documentation

◆ GeodesicLine() [1/3]

◆ GeodesicLine() [2/3]

◆ GeodesicLine() [3/3]

Member Function Documentation

◆ Arc()

◆ ArcPosition() [1/7]

◆ ArcPosition() [2/7]

◆ ArcPosition() [3/7]

◆ ArcPosition() [4/7]

◆ ArcPosition() [5/7]

◆ ArcPosition() [6/7]

◆ ArcPosition() [7/7]

◆ Azimuth() [1/2]

◆ Azimuth() [2/2]

◆ Capabilities() [1/2]

◆ Capabilities() [2/2]

◆ Distance()

◆ EquatorialArc()

◆ EquatorialAzimuth() [1/2]

◆ EquatorialAzimuth() [2/2]

◆ Flattening()

◆ GenDistance()

◆ GenPosition()

◆ GenSetDistance()

◆ Init()

◆ Latitude()

◆ LineInit()

◆ Longitude()

◆ MajorRadius()

◆ Position() [1/6]

◆ Position() [2/6]

◆ Position() [3/6]

◆ Position() [4/6]

◆ Position() [5/6]

◆ Position() [6/6]

◆ SetArc()

◆ SetDistance()

Friends And Related Function Documentation

◆ Geodesic

Member Data Documentation

◆ _a

◆ _a13

◆ _A1m1

◆ _A2m1

◆ _A3c

◆ _A4

◆ _azi1

◆ _b

◆ _B11

◆ _B21

◆ _B31

◆ _B41

◆ _C1a

◆ _C1pa

◆ _c2

◆ _C2a

◆ _C3a

◆ _C4a

◆ _calp0

◆ _calp1

◆ _caps

◆ _comg1

◆ _csig1

◆ _ctau1

◆ _dn1

◆ _f