GeographicLib  1.48
GeographicLib::GeodesicLine Class Reference

A geodesic line. More...

#include <GeographicLib/GeodesicLine.hpp>

## Public Types

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 Flattening () const

unsigned Capabilities () const

bool Capabilities (unsigned testcaps) const

Math::real GenDistance (bool arcmode) const

Math::real Distance () const

Math::real Arc () const

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

For more information on geodesics see Geodesics on an ellipsoid of revolution.

Example of use:

// Example of using the GeographicLib::GeodesicLine class
#include <iostream>
#include <exception>
#include <cmath>
#include <iomanip>
using namespace std;
using namespace GeographicLib;
int main() {
try {
// Print waypoints between JFK and SIN
// Alternatively: const Geodesic& geod = Geodesic::WGS84();
double
lat1 = 40.640, lon1 = -73.779, // JFK
lat2 = 1.359, lon2 = 103.989; // SIN
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 Enumeration Documentation

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.

## ◆ GeodesicLine() [1/2]

 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 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 GeodesicLine.cpp.

## ◆ GeodesicLine() [2/2]

 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.

Referenced by GeodesicLine().

## ◆ 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.

Referenced by GeographicLib::CassiniSoldner::Reverse().

## ◆ 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.

## ◆ 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.

## ◆ 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).

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 lon2lon1 indicates how many times and in what sense the geodesic encircles the ellipsoid.

Definition at line 136 of file GeodesicLine.cpp.

Referenced by GeographicLib::CassiniSoldner::Forward(), and main().

## ◆ 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 GeodesicLine.cpp.

## ◆ 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 GeodesicLine.cpp.

References GeographicLib::Math::NaN().

## ◆ 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 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.

Referenced by GeographicLib::CassiniSoldner::Init().

## ◆ Latitude()

 Math::real GeographicLib::GeodesicLine::Latitude ( ) const
inline
Returns
lat1 the latitude of point 1 (degrees).

Definition at line 594 of file GeodesicLine.hpp.

References GeographicLib::Math::NaN().

Referenced by GeographicLib::CassiniSoldner::LatitudeOrigin().

## ◆ Longitude()

 Math::real GeographicLib::GeodesicLine::Longitude ( ) const
inline
Returns
lon1 the longitude of point 1 (degrees).

Definition at line 600 of file GeodesicLine.hpp.

References GeographicLib::Math::NaN().

Referenced by GeographicLib::CassiniSoldner::LongitudeOrigin().

## ◆ 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.

References GeographicLib::Math::NaN().

Referenced by main().

## ◆ 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.

## ◆ 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.

References GeographicLib::Math::atan2d(), and GeographicLib::Math::NaN().

## ◆ 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.

## ◆ 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.

References GeographicLib::Math::atan2d(), and GeographicLib::Math::NaN().

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.

References GeographicLib::Math::NaN().

## ◆ 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.

References GeographicLib::Math::NaN().

## ◆ 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.

## ◆ 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.

References GeographicLib::Math::NaN().

Referenced by main().

## ◆ Distance()

 Math::real GeographicLib::GeodesicLine::Distance ( ) const
inline
Returns
s13, the distance to point 3 (meters).

Definition at line 690 of file GeodesicLine.hpp.

## ◆ 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.

## ◆ Geodesic

 friend class Geodesic
friend

Definition at line 74 of file GeodesicLine.hpp.

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