GeographicLib 2.5.2

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GeographicLib::GeodesicLineExact Class Reference

An exact geodesic line. More...

`#include <GeographicLib/GeodesicLineExact.hpp>`

## Public Types
enum | mask { NONE , LATITUDE , LONGITUDE , AZIMUTH , DISTANCE , STANDARD , DISTANCE_IN , REDUCEDLENGTH , GEODESICSCALE , AREA , LONG_UNROLL , ALL }
typedef GeodesicExact | BaseClass

## Public Member Functions
Constructors
| GeodesicLineExact (const GeodesicExact &g, real lat1, real lon1, real azi1, unsigned caps=ALL)
| GeodesicLineExact ()
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 | EquatorialRadius () 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

## Friends
class | GeodesicExact
class | GeodesicLine

## Detailed Description

An exact geodesic line.

GeodesicLineExact facilitates the determination of a series of points on a single geodesic. This is a companion to the GeodesicExact class. For additional information on this class see the documentation on the GeodesicLine class.

Example of use:

// Example of using the GeographicLib::GeodesicLineExact class
#include <iostream>
#include <iomanip>
#include <exception>
#include <cmath>
#include <GeographicLib/GeodesicExact.hpp>
#include <GeographicLib/GeodesicLineExact.hpp>
#include <GeographicLib/Constants.hpp>
using namespace std;
using namespace GeographicLib;
int main() {
try {
// Print waypoints between JFK and SIN
GeodesicExact geod(Constants::WGS84_a(), Constants::WGS84_f());
// Alternatively: const GeodesicExact& geod = GeodesicExact::WGS84();
double
lat1 = 40.640, lon1 = -73.779, // JFK
lat2 = 1.359, lon2 = 103.989; // SIN
GeodesicLineExact 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;
}
}
main
int main(int argc, const char *const argv[])
Definition CartConvert.cpp:28
Constants.hpp
Header for GeographicLib::Constants class.
GeodesicExact.hpp
Header for GeographicLib::GeodesicExact class.
GeodesicLineExact.hpp
Header for GeographicLib::GeodesicLineExact class.
GeographicLib::GeodesicExact
Exact geodesic calculations.
Definition GeodesicExact.hpp:85
GeographicLib::GeodesicLineExact
An exact geodesic line.
Definition GeodesicLineExact.hpp:42
GeographicLib::GeodesicLineExact::Arc
Math::real Arc() const
Definition GeodesicLineExact.hpp:671
GeographicLib::GeodesicLineExact::Position
Math::real Position(real s12, real &lat2, real &lon2, real &azi2, real &m12, real &M12, real &M21, real &S12) const
Definition GeodesicLineExact.hpp:263
GeographicLib::GeodesicLineExact::ArcPosition
void ArcPosition(real a12, real &lat2, real &lon2, real &azi2, real &s12, real &m12, real &M12, real &M21, real &S12) const
Definition GeodesicLineExact.hpp:371
GeographicLib::GeodesicLineExact::Distance
Math::real Distance() const
Definition GeodesicLineExact.hpp:665
GeographicLib
Namespace for GeographicLib.
Definition Accumulator.cpp:12
std
Definition NearestNeighbor.hpp:806

GeodSolve is a command-line utility providing access to the functionality of GeodesicExact and GeodesicLineExact (via the -E option).

Definition at line 42 of file GeodesicLineExact.hpp.

## Member Typedef Documentation

## ◆ BaseClass

typedef GeodesicExact GeographicLib::GeodesicLineExact::BaseClass

Typedef for the base class implementing geodesics.

Definition at line 162 of file GeodesicLineExact.hpp.

## Member Enumeration Documentation

## ◆ mask

enum GeographicLib::GeodesicLineExact::mask

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

Enumerator
NONE | No capabilities, no output.
LATITUDE | Calculate latitude lat2. (It's not necessary to include this as a capability to GeodesicLineExact 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 GeodesicLineExact because this is included by default.)
DISTANCE | Calculate distance s12.
STANDARD | A combination of the common capabilities: GeodesicLineExact::LATITUDE, GeodesicLineExact::LONGITUDE, GeodesicLineExact::AZIMUTH, GeodesicLineExact::DISTANCE.
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 89 of file GeodesicLineExact.hpp.

## Constructor & Destructor Documentation

## ◆ GeodesicLineExact() [1/2]

GeographicLib::GeodesicLineExact::GeodesicLineExact | ( | const GeodesicExact & | 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 GeodesicExact object used to compute the necessary information about the GeodesicLineExact.
  [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 GeodesicLineExact::mask values specifying the capabilities the GeodesicLineExact object should possess, i.e., which quantities can be returned in calls to GeodesicLine::Position.

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

The GeodesicLineExact::mask values are

- caps |= GeodesicLineExact::LATITUDE for the latitude lat2; this is added automatically;
- caps |= GeodesicLineExact::LONGITUDE for the latitude lon2;
- caps |= GeodesicLineExact::AZIMUTH for the latitude azi2; this is added automatically;
- caps |= GeodesicLineExact::DISTANCE for the distance s12;
- caps |= GeodesicLineExact::REDUCEDLENGTH for the reduced length m12;
- caps |= GeodesicLineExact::GEODESICSCALE for the geodesic scales M12 and M21;
- caps |= GeodesicLineExact::AREA for the area S12;
- caps |= GeodesicLineExact::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 |= GeodesicLineExact::ALL for all of the above.

The default value of caps is GeodesicLineExact::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 124 of file GeodesicLineExact.cpp.

References GeographicLib::Math::AngNormalize(), GeographicLib::Math::AngRound(), and GeographicLib::Math::sincosd().

## ◆ GeodesicLineExact() [2/2]

GeographicLib::GeodesicLineExact::GeodesicLineExact | ( |  | ) |
| inline

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

Definition at line 217 of file GeodesicLineExact.hpp.

## Member Function Documentation

## ◆ Position() [1/6]

Math::real GeographicLib::GeodesicLineExact::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 signed.
  [out] | lat2 | latitude of point 2 (degrees).
  [out] | lon2 | longitude of point 2 (degrees); requires that the GeodesicLineExact object was constructed with caps |= GeodesicLineExact::LONGITUDE.
  [out] | azi2 | (forward) azimuth at point 2 (degrees).
  [out] | m12 | reduced length of geodesic (meters); requires that the GeodesicLineExact object was constructed with caps |= GeodesicLineExact::REDUCEDLENGTH.
  [out] | M12 | geodesic scale of point 2 relative to point 1 (dimensionless); requires that the GeodesicLineExact object was constructed with caps |= GeodesicLineExact::GEODESICSCALE.
  [out] | M21 | geodesic scale of point 1 relative to point 2 (dimensionless); requires that the GeodesicLineExact object was constructed with caps |= GeodesicLineExact::GEODESICSCALE.
  [out] | S12 | area under the geodesic (meters2); requires that the GeodesicLineExact object was constructed with caps |= GeodesicLineExact::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 GeodesicLineExact object must have been constructed with caps |= GeodesicLineExact::DISTANCE_IN; otherwise Math::NaN() is returned and no parameters are set. Requesting a value which the GeodesicLineExact object is not capable of computing is not an error; the corresponding argument will not be altered.

The following functions are overloaded versions of GeodesicLineExact::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 263 of file GeodesicLineExact.hpp.

## ◆ Position() [2/6]

Math::real GeographicLib::GeodesicLineExact::Position | ( | real | s12,
|  | real & | lat2,
|  | real & | lon2 ) const
| inline

See the documentation for GeodesicLineExact::Position.

Definition at line 275 of file GeodesicLineExact.hpp.

## ◆ Position() [3/6]

Math::real GeographicLib::GeodesicLineExact::Position | ( | real | s12,
|  | real & | lat2,
|  | real & | lon2,
|  | real & | azi2 ) const
| inline

See the documentation for GeodesicLineExact::Position.

Definition at line 286 of file GeodesicLineExact.hpp.

## ◆ Position() [4/6]

Math::real GeographicLib::GeodesicLineExact::Position | ( | real | s12,
|  | real & | lat2,
|  | real & | lon2,
|  | real & | azi2,
|  | real & | m12 ) const
| inline

See the documentation for GeodesicLineExact::Position.

Definition at line 296 of file GeodesicLineExact.hpp.

## ◆ Position() [5/6]

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

See the documentation for GeodesicLineExact::Position.

Definition at line 308 of file GeodesicLineExact.hpp.

## ◆ Position() [6/6]

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

See the documentation for GeodesicLineExact::Position.

Definition at line 320 of file GeodesicLineExact.hpp.

## ◆ ArcPosition() [1/7]

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

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

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

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

Definition at line 371 of file GeodesicLineExact.hpp.

## ◆ ArcPosition() [2/7]

void GeographicLib::GeodesicLineExact::ArcPosition | ( | real | a12,
|  | real & | lat2,
|  | real & | lon2 ) const
| inline

See the documentation for GeodesicLineExact::ArcPosition.

Definition at line 383 of file GeodesicLineExact.hpp.

## ◆ ArcPosition() [3/7]

void GeographicLib::GeodesicLineExact::ArcPosition | ( | real | a12,
|  | real & | lat2,
|  | real & | lon2,
|  | real & | azi2 ) const
| inline

See the documentation for GeodesicLineExact::ArcPosition.

Definition at line 393 of file GeodesicLineExact.hpp.

## ◆ ArcPosition() [4/7]

void GeographicLib::GeodesicLineExact::ArcPosition | ( | real | a12,
|  | real & | lat2,
|  | real & | lon2,
|  | real & | azi2,
|  | real & | s12 ) const
| inline

See the documentation for GeodesicLineExact::ArcPosition.

Definition at line 403 of file GeodesicLineExact.hpp.

## ◆ ArcPosition() [5/7]

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

See the documentation for GeodesicLineExact::ArcPosition.

Definition at line 414 of file GeodesicLineExact.hpp.

## ◆ ArcPosition() [6/7]

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

See the documentation for GeodesicLineExact::ArcPosition.

Definition at line 426 of file GeodesicLineExact.hpp.

## ◆ ArcPosition() [7/7]

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

See the documentation for GeodesicLineExact::ArcPosition.

Definition at line 438 of file GeodesicLineExact.hpp.

## ◆ GenPosition()

Math::real GeographicLib::GeodesicLineExact::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. GeodesicLineExact::Position and GeodesicLineExact::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 GeodesicLineExact object must have been constructed with caps |= GeodesicLineExact::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 signed.
  [in] | outmask | a bitor'ed combination of GeodesicLineExact::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 GeodesicLineExact object was constructed with caps |= GeodesicLineExact::LONGITUDE.
  [out] | azi2 | (forward) azimuth at point 2 (degrees).
  [out] | s12 | distance from point 1 to point 2 (meters); requires that the GeodesicLineExact object was constructed with caps |= GeodesicLineExact::DISTANCE.
  [out] | m12 | reduced length of geodesic (meters); requires that the GeodesicLineExact object was constructed with caps |= GeodesicLineExact::REDUCEDLENGTH.
  [out] | M12 | geodesic scale of point 2 relative to point 1 (dimensionless); requires that the GeodesicLineExact object was constructed with caps |= GeodesicLineExact::GEODESICSCALE.
  [out] | M21 | geodesic scale of point 1 relative to point 2 (dimensionless); requires that the GeodesicLineExact object was constructed with caps |= GeodesicLineExact::GEODESICSCALE.
  [out] | S12 | area under the geodesic (meters2); requires that the GeodesicLineExact object was constructed with caps |= GeodesicLineExact::AREA.

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

The GeodesicLineExact::mask values possible for outmask are

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

Requesting a value which the GeodesicLineExact 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 GeodesicLineExact::LONG_UNROLL bit set, the quantity lon2 − lon1 indicates how many times and in what sense the geodesic encircles the ellipsoid.

Definition at line 143 of file GeodesicLineExact.cpp.

References GeographicLib::Math::AngNormalize(), AREA, GeographicLib::Math::atan2d(), AZIMUTH, GeographicLib::Math::degree(), GeographicLib::EllipticFunction::Delta(), GeographicLib::EllipticFunction::deltaD(), GeographicLib::EllipticFunction::deltaE(), GeographicLib::EllipticFunction::deltaEinv(), GeographicLib::EllipticFunction::deltaH(), DISTANCE, DISTANCE_IN, GEODESICSCALE, Init(), GeographicLib::DST::integral(), LATITUDE, LONG_UNROLL, LONGITUDE, GeographicLib::Math::NaN(), REDUCEDLENGTH, GeographicLib::Math::sincosd(), and GeographicLib::Math::sq().

Referenced by GeographicLib::GeodesicLine::GenPosition(), SetArc(), and SetDistance().

## ◆ SetDistance()

void GeographicLib::GeodesicLineExact::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 GeodesicLineExact object has been constructed with caps |= GeodesicLineExact::DISTANCE_IN.

Definition at line 272 of file GeodesicLineExact.cpp.

References GenPosition().

Referenced by GenSetDistance().

## ◆ SetArc()

void GeographicLib::GeodesicLineExact::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 GeodesicLineExact object has been constructed with caps |= GeodesicLineExact::DISTANCE.

Definition at line 280 of file GeodesicLineExact.cpp.

References DISTANCE, GenPosition(), and GeographicLib::Math::NaN().

Referenced by GenSetDistance().

## ◆ GenSetDistance()

void GeographicLib::GeodesicLineExact::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 GeodesicLineExact object must have been constructed with caps |= GeodesicLineExact::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 288 of file GeodesicLineExact.cpp.

References SetArc(), and SetDistance().

## ◆ Init()

bool GeographicLib::GeodesicLineExact::Init | ( |  | ) | const
| inline

Returns
  true if the object has been initialized.

Definition at line 562 of file GeodesicLineExact.hpp.

Referenced by GenPosition().

## ◆ Latitude()

Math::real GeographicLib::GeodesicLineExact::Latitude | ( |  | ) | const
| inline

Returns
  lat1 the latitude of point 1 (degrees).

Definition at line 567 of file GeodesicLineExact.hpp.

## ◆ Longitude()

Math::real GeographicLib::GeodesicLineExact::Longitude | ( |  | ) | const
| inline

Returns
  lon1 the longitude of point 1 (degrees).

Definition at line 573 of file GeodesicLineExact.hpp.

## ◆ Azimuth() [1/2]

Math::real GeographicLib::GeodesicLineExact::Azimuth | ( |  | ) | const
| inline

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

Definition at line 579 of file GeodesicLineExact.hpp.

## ◆ Azimuth() [2/2]

void GeographicLib::GeodesicLineExact::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 588 of file GeodesicLineExact.hpp.

## ◆ EquatorialAzimuth() [1/2]

Math::real GeographicLib::GeodesicLineExact::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 597 of file GeodesicLineExact.hpp.

## ◆ EquatorialAzimuth() [2/2]

void GeographicLib::GeodesicLineExact::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 606 of file GeodesicLineExact.hpp.

## ◆ EquatorialArc()

Math::real GeographicLib::GeodesicLineExact::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 615 of file GeodesicLineExact.hpp.

## ◆ EquatorialRadius()

Math::real GeographicLib::GeodesicLineExact::EquatorialRadius | ( |  | ) | const
| inline

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

Definition at line 625 of file GeodesicLineExact.hpp.

## ◆ Flattening()

Math::real GeographicLib::GeodesicLineExact::Flattening | ( |  | ) | const
| inline

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

Definition at line 632 of file GeodesicLineExact.hpp.

## ◆ Capabilities() [1/2]

unsigned GeographicLib::GeodesicLineExact::Capabilities | ( |  | ) | const
| inline

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

Definition at line 639 of file GeodesicLineExact.hpp.

## ◆ Capabilities() [2/2]

bool GeographicLib::GeodesicLineExact::Capabilities | ( | unsigned | testcaps | ) | const
| inline

Test what capabilities are available.

Parameters

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

Returns
  true if the GeodesicLineExact object has all these capabilities.

Definition at line 647 of file GeodesicLineExact.hpp.

## ◆ GenDistance()

Math::real GeographicLib::GeodesicLineExact::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 659 of file GeodesicLineExact.hpp.

## ◆ Distance()

Math::real GeographicLib::GeodesicLineExact::Distance | ( |  | ) | const
| inline

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

Definition at line 665 of file GeodesicLineExact.hpp.

## ◆ Arc()

Math::real GeographicLib::GeodesicLineExact::Arc | ( |  | ) | const
| inline

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

Definition at line 671 of file GeodesicLineExact.hpp.

## Friends And Related Symbol Documentation

## ◆ GeodesicExact

friend class GeodesicExact
| friend

Definition at line 45 of file GeodesicLineExact.hpp.

## ◆ GeodesicLine

friend class GeodesicLine
| friend

Definition at line 46 of file GeodesicLineExact.hpp.

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

- GeodesicLineExact.hpp
- GeodesicLineExact.cpp