GeographicLib  1.48
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GeographicLib::GeodesicExact Class Reference

Exact geodesic calculations. More...

#include <GeographicLib/GeodesicExact.hpp>

Public Types

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

Public Member Functions

Constructor
 GeodesicExact (real a, real f)
 
Direct geodesic problem specified in terms of distance.
Math::real Direct (real lat1, real lon1, real azi1, real s12, real &lat2, real &lon2, real &azi2, real &m12, real &M12, real &M21, real &S12) const
 
Math::real Direct (real lat1, real lon1, real azi1, real s12, real &lat2, real &lon2) const
 
Math::real Direct (real lat1, real lon1, real azi1, real s12, real &lat2, real &lon2, real &azi2) const
 
Math::real Direct (real lat1, real lon1, real azi1, real s12, real &lat2, real &lon2, real &azi2, real &m12) const
 
Math::real Direct (real lat1, real lon1, real azi1, real s12, real &lat2, real &lon2, real &azi2, real &M12, real &M21) const
 
Math::real Direct (real lat1, real lon1, real azi1, real s12, real &lat2, real &lon2, real &azi2, real &m12, real &M12, real &M21) const
 
Direct geodesic problem specified in terms of arc length.
void ArcDirect (real lat1, real lon1, real azi1, real a12, real &lat2, real &lon2, real &azi2, real &s12, real &m12, real &M12, real &M21, real &S12) const
 
void ArcDirect (real lat1, real lon1, real azi1, real a12, real &lat2, real &lon2) const
 
void ArcDirect (real lat1, real lon1, real azi1, real a12, real &lat2, real &lon2, real &azi2) const
 
void ArcDirect (real lat1, real lon1, real azi1, real a12, real &lat2, real &lon2, real &azi2, real &s12) const
 
void ArcDirect (real lat1, real lon1, real azi1, real a12, real &lat2, real &lon2, real &azi2, real &s12, real &m12) const
 
void ArcDirect (real lat1, real lon1, real azi1, real a12, real &lat2, real &lon2, real &azi2, real &s12, real &M12, real &M21) const
 
void ArcDirect (real lat1, real lon1, real azi1, real a12, real &lat2, real &lon2, real &azi2, real &s12, real &m12, real &M12, real &M21) const
 
General version of the direct geodesic solution.
Math::real GenDirect (real lat1, real lon1, real azi1, bool arcmode, real s12_a12, unsigned outmask, real &lat2, real &lon2, real &azi2, real &s12, real &m12, real &M12, real &M21, real &S12) const
 
Inverse geodesic problem.
Math::real Inverse (real lat1, real lon1, real lat2, real lon2, real &s12, real &azi1, real &azi2, real &m12, real &M12, real &M21, real &S12) const
 
Math::real Inverse (real lat1, real lon1, real lat2, real lon2, real &s12) const
 
Math::real Inverse (real lat1, real lon1, real lat2, real lon2, real &azi1, real &azi2) const
 
Math::real Inverse (real lat1, real lon1, real lat2, real lon2, real &s12, real &azi1, real &azi2) const
 
Math::real Inverse (real lat1, real lon1, real lat2, real lon2, real &s12, real &azi1, real &azi2, real &m12) const
 
Math::real Inverse (real lat1, real lon1, real lat2, real lon2, real &s12, real &azi1, real &azi2, real &M12, real &M21) const
 
Math::real Inverse (real lat1, real lon1, real lat2, real lon2, real &s12, real &azi1, real &azi2, real &m12, real &M12, real &M21) const
 
General version of inverse geodesic solution.
Math::real GenInverse (real lat1, real lon1, real lat2, real lon2, unsigned outmask, real &s12, real &azi1, real &azi2, real &m12, real &M12, real &M21, real &S12) const
 
Interface to GeodesicLineExact.
GeodesicLineExact Line (real lat1, real lon1, real azi1, unsigned caps=ALL) const
 
GeodesicLineExact InverseLine (real lat1, real lon1, real lat2, real lon2, unsigned caps=ALL) const
 
GeodesicLineExact DirectLine (real lat1, real lon1, real azi1, real s12, unsigned caps=ALL) const
 
GeodesicLineExact ArcDirectLine (real lat1, real lon1, real azi1, real a12, unsigned caps=ALL) const
 
GeodesicLineExact GenDirectLine (real lat1, real lon1, real azi1, bool arcmode, real s12_a12, unsigned caps=ALL) const
 
Inspector functions.
Math::real MajorRadius () const
 
Math::real Flattening () const
 
Math::real EllipsoidArea () const
 

Static Public Member Functions

static const GeodesicExactWGS84 ()
 

Friends

class GeodesicLineExact
 

Detailed Description

Exact geodesic calculations.

The equations for geodesics on an ellipsoid can be expressed in terms of incomplete elliptic integrals. The Geodesic class expands these integrals in a series in the flattening f and this provides an accurate solution for f ∈ [-0.01, 0.01]. The GeodesicExact class computes the ellitpic integrals directly and so provides a solution which is valid for all f. However, in practice, its use should be limited to about b/a ∈ [0.01, 100] or f ∈ [−99, 0.99].

For the WGS84 ellipsoid, these classes are 2–3 times slower than the series solution and 2–3 times less accurate (because it's less easy to control round-off errors with the elliptic integral formulation); i.e., the error is about 40 nm (40 nanometers) instead of 15 nm. However the error in the series solution scales as f7 while the error in the elliptic integral solution depends weakly on f. If the quarter meridian distance is 10000 km and the ratio b/a = 1 − f is varied then the approximate maximum error (expressed as a distance) is

      1 - f  error (nm)
      1/128     387
      1/64      345
      1/32      269
      1/16      210
      1/8       115
      1/4        69
      1/2        36
        1        15
        2        25
        4        96
        8       318
       16       985
       32      2352
       64      6008
      128     19024

The computation of the area in these classes is via a 30th order series. This gives accurate results for b/a ∈ [1/2, 2]; the accuracy is about 8 decimal digits for b/a ∈ [1/4, 4].

See Geodesics in terms of elliptic integrals for the formulation. See the documentation on the Geodesic class for additional information on the geodesic problems.

Example of use:

// Example of using the GeographicLib::GeodesicExact class
#include <iostream>
#include <exception>
using namespace std;
using namespace GeographicLib;
int main() {
try {
// Alternatively: const GeodesicExact& geod = GeodesicExact::WGS84();
{
// Sample direct calculation, travelling about NE from JFK
double lat1 = 40.6, lon1 = -73.8, s12 = 5.5e6, azi1 = 51;
double lat2, lon2;
geod.Direct(lat1, lon1, azi1, s12, lat2, lon2);
cout << lat2 << " " << lon2 << "\n";
}
{
// Sample inverse calculation, JFK to LHR
double
lat1 = 40.6, lon1 = -73.8, // JFK Airport
lat2 = 51.6, lon2 = -0.5; // LHR Airport
double s12;
geod.Inverse(lat1, lon1, lat2, lon2, s12);
cout << s12 << "\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 GeodesicExact and GeodesicLineExact (via the -E option).

Definition at line 80 of file GeodesicExact.hpp.

Member Enumeration Documentation

◆ mask

Bit masks for what calculations to do. These masks do double duty. They signify to the GeodesicLineExact::GeodesicLineExact constructor and to GeodesicExact::Line what capabilities should be included in the GeodesicLineExact object. They also specify which results to return in the general routines GeodesicExact::GenDirect and GeodesicExact::GenInverse routines. GeodesicLineExact::mask is a duplication of this enum.

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.

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 158 of file GeodesicExact.hpp.

Constructor & Destructor Documentation

◆ GeodesicExact()

GeographicLib::GeodesicExact::GeodesicExact ( real  a,
real  f 
)

Constructor for a ellipsoid with

Parameters
[in]aequatorial radius (meters).
[in]fflattening of ellipsoid. Setting f = 0 gives a sphere. Negative f gives a prolate ellipsoid.
Exceptions
GeographicErrif a or (1 − f) a is not positive.

Definition at line 42 of file GeodesicExact.cpp.

References GeographicLib::Math::isfinite().

Member Function Documentation

◆ Direct() [1/6]

Math::real GeographicLib::GeodesicExact::Direct ( real  lat1,
real  lon1,
real  azi1,
real  s12,
real &  lat2,
real &  lon2,
real &  azi2,
real &  m12,
real &  M12,
real &  M21,
real &  S12 
) const
inline

Perform the direct geodesic calculation where the length of the geodesic is specified in terms of distance.

Parameters
[in]lat1latitude of point 1 (degrees).
[in]lon1longitude of point 1 (degrees).
[in]azi1azimuth at point 1 (degrees).
[in]s12distance between point 1 and point 2 (meters); it can be signed.
[out]lat2latitude of point 2 (degrees).
[out]lon2longitude of point 2 (degrees).
[out]azi2(forward) azimuth at point 2 (degrees).
[out]m12reduced length of geodesic (meters).
[out]M12geodesic scale of point 2 relative to point 1 (dimensionless).
[out]M21geodesic scale of point 1 relative to point 2 (dimensionless).
[out]S12area under the geodesic (meters2).
Returns
a12 arc length of between point 1 and point 2 (degrees).

lat1 should be in the range [−90°, 90°]. The values of lon2 and azi2 returned are in the range [−180°, 180°].

If either point is at a pole, the azimuth is defined by keeping the longitude fixed, writing lat = ±(90° − ε), and taking the limit ε → 0+. An arc length greater that 180° signifies a geodesic which is not a shortest path. (For a prolate ellipsoid, an additional condition is necessary for a shortest path: the longitudinal extent must not exceed of 180°.)

The following functions are overloaded versions of GeodesicExact::Direct 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 274 of file GeodesicExact.hpp.

◆ Direct() [2/6]

Math::real GeographicLib::GeodesicExact::Direct ( real  lat1,
real  lon1,
real  azi1,
real  s12,
real &  lat2,
real &  lon2 
) const
inline

See the documentation for GeodesicExact::Direct.

Definition at line 288 of file GeodesicExact.hpp.

◆ Direct() [3/6]

Math::real GeographicLib::GeodesicExact::Direct ( real  lat1,
real  lon1,
real  azi1,
real  s12,
real &  lat2,
real &  lon2,
real &  azi2 
) const
inline

See the documentation for GeodesicExact::Direct.

Definition at line 300 of file GeodesicExact.hpp.

◆ Direct() [4/6]

Math::real GeographicLib::GeodesicExact::Direct ( real  lat1,
real  lon1,
real  azi1,
real  s12,
real &  lat2,
real &  lon2,
real &  azi2,
real &  m12 
) const
inline

See the documentation for GeodesicExact::Direct.

Definition at line 312 of file GeodesicExact.hpp.

◆ Direct() [5/6]

Math::real GeographicLib::GeodesicExact::Direct ( real  lat1,
real  lon1,
real  azi1,
real  s12,
real &  lat2,
real &  lon2,
real &  azi2,
real &  M12,
real &  M21 
) const
inline

See the documentation for GeodesicExact::Direct.

Definition at line 324 of file GeodesicExact.hpp.

◆ Direct() [6/6]

Math::real GeographicLib::GeodesicExact::Direct ( real  lat1,
real  lon1,
real  azi1,
real  s12,
real &  lat2,
real &  lon2,
real &  azi2,
real &  m12,
real &  M12,
real &  M21 
) const
inline

See the documentation for GeodesicExact::Direct.

Definition at line 337 of file GeodesicExact.hpp.

◆ ArcDirect() [1/7]

void GeographicLib::GeodesicExact::ArcDirect ( real  lat1,
real  lon1,
real  azi1,
real  a12,
real &  lat2,
real &  lon2,
real &  azi2,
real &  s12,
real &  m12,
real &  M12,
real &  M21,
real &  S12 
) const
inline

Perform the direct geodesic calculation where the length of the geodesic is specified in terms of arc length.

Parameters
[in]lat1latitude of point 1 (degrees).
[in]lon1longitude of point 1 (degrees).
[in]azi1azimuth at point 1 (degrees).
[in]a12arc length between point 1 and point 2 (degrees); it can be signed.
[out]lat2latitude of point 2 (degrees).
[out]lon2longitude of point 2 (degrees).
[out]azi2(forward) azimuth at point 2 (degrees).
[out]s12distance between point 1 and point 2 (meters).
[out]m12reduced length of geodesic (meters).
[out]M12geodesic scale of point 2 relative to point 1 (dimensionless).
[out]M21geodesic scale of point 1 relative to point 2 (dimensionless).
[out]S12area under the geodesic (meters2).

lat1 should be in the range [−90°, 90°]. The values of lon2 and azi2 returned are in the range [−180°, 180°].

If either point is at a pole, the azimuth is defined by keeping the longitude fixed, writing lat = ±(90° − ε), and taking the limit ε → 0+. An arc length greater that 180° signifies a geodesic which is not a shortest path. (For a prolate ellipsoid, an additional condition is necessary for a shortest path: the longitudinal extent must not exceed of 180°.)

The following functions are overloaded versions of GeodesicExact::Direct which omit some of the output parameters.

Definition at line 386 of file GeodesicExact.hpp.

◆ ArcDirect() [2/7]

void GeographicLib::GeodesicExact::ArcDirect ( real  lat1,
real  lon1,
real  azi1,
real  a12,
real &  lat2,
real &  lon2 
) const
inline

See the documentation for GeodesicExact::ArcDirect.

Definition at line 399 of file GeodesicExact.hpp.

◆ ArcDirect() [3/7]

void GeographicLib::GeodesicExact::ArcDirect ( real  lat1,
real  lon1,
real  azi1,
real  a12,
real &  lat2,
real &  lon2,
real &  azi2 
) const
inline

See the documentation for GeodesicExact::ArcDirect.

Definition at line 410 of file GeodesicExact.hpp.

◆ ArcDirect() [4/7]

void GeographicLib::GeodesicExact::ArcDirect ( real  lat1,
real  lon1,
real  azi1,
real  a12,
real &  lat2,
real &  lon2,
real &  azi2,
real &  s12 
) const
inline

See the documentation for GeodesicExact::ArcDirect.

Definition at line 421 of file GeodesicExact.hpp.

◆ ArcDirect() [5/7]

void GeographicLib::GeodesicExact::ArcDirect ( real  lat1,
real  lon1,
real  azi1,
real  a12,
real &  lat2,
real &  lon2,
real &  azi2,
real &  s12,
real &  m12 
) const
inline

See the documentation for GeodesicExact::ArcDirect.

Definition at line 433 of file GeodesicExact.hpp.

◆ ArcDirect() [6/7]

void GeographicLib::GeodesicExact::ArcDirect ( real  lat1,
real  lon1,
real  azi1,
real  a12,
real &  lat2,
real &  lon2,
real &  azi2,
real &  s12,
real &  M12,
real &  M21 
) const
inline

See the documentation for GeodesicExact::ArcDirect.

Definition at line 446 of file GeodesicExact.hpp.

◆ ArcDirect() [7/7]

void GeographicLib::GeodesicExact::ArcDirect ( real  lat1,
real  lon1,
real  azi1,
real  a12,
real &  lat2,
real &  lon2,
real &  azi2,
real &  s12,
real &  m12,
real &  M12,
real &  M21 
) const
inline

See the documentation for GeodesicExact::ArcDirect.

Definition at line 459 of file GeodesicExact.hpp.

◆ GenDirect()

Math::real GeographicLib::GeodesicExact::GenDirect ( real  lat1,
real  lon1,
real  azi1,
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 direct geodesic calculation. GeodesicExact::Direct and GeodesicExact::ArcDirect are defined in terms of this function.

Parameters
[in]lat1latitude of point 1 (degrees).
[in]lon1longitude of point 1 (degrees).
[in]azi1azimuth at point 1 (degrees).
[in]arcmodeboolean flag determining the meaning of the second parameter.
[in]s12_a12if 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]outmaska bitor'ed combination of GeodesicExact::mask values specifying which of the following parameters should be set.
[out]lat2latitude of point 2 (degrees).
[out]lon2longitude of point 2 (degrees).
[out]azi2(forward) azimuth at point 2 (degrees).
[out]s12distance between point 1 and point 2 (meters).
[out]m12reduced length of geodesic (meters).
[out]M12geodesic scale of point 2 relative to point 1 (dimensionless).
[out]M21geodesic scale of point 1 relative to point 2 (dimensionless).
[out]S12area under the geodesic (meters2).
Returns
a12 arc length of between point 1 and point 2 (degrees).

The GeodesicExact::mask values possible for outmask are

The function value a12 is always computed and returned and this equals s12_a12 is arcmode is true. If outmask includes GeodesicExact::DISTANCE and arcmode is false, then s12 = s12_a12. It is not necessary to include GeodesicExact::DISTANCE_IN in outmask; this is automatically included is arcmode is false.

With the GeodesicExact::LONG_UNROLL bit set, the quantity lon2lon1 indicates how many times and in what sense the geodesic encircles the ellipsoid.

Definition at line 124 of file GeodesicExact.cpp.

References DISTANCE_IN, and GeodesicLineExact.

Referenced by main().

◆ Inverse() [1/7]

Math::real GeographicLib::GeodesicExact::Inverse ( real  lat1,
real  lon1,
real  lat2,
real  lon2,
real &  s12,
real &  azi1,
real &  azi2,
real &  m12,
real &  M12,
real &  M21,
real &  S12 
) const
inline

Perform the inverse geodesic calculation.

Parameters
[in]lat1latitude of point 1 (degrees).
[in]lon1longitude of point 1 (degrees).
[in]lat2latitude of point 2 (degrees).
[in]lon2longitude of point 2 (degrees).
[out]s12distance between point 1 and point 2 (meters).
[out]azi1azimuth at point 1 (degrees).
[out]azi2(forward) azimuth at point 2 (degrees).
[out]m12reduced length of geodesic (meters).
[out]M12geodesic scale of point 2 relative to point 1 (dimensionless).
[out]M21geodesic scale of point 1 relative to point 2 (dimensionless).
[out]S12area under the geodesic (meters2).
Returns
a12 arc length of between point 1 and point 2 (degrees).

lat1 and lat2 should be in the range [−90°, 90°]. The values of azi1 and azi2 returned are in the range [−180°, 180°].

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

The following functions are overloaded versions of GeodesicExact::Inverse 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 564 of file GeodesicExact.hpp.

◆ Inverse() [2/7]

Math::real GeographicLib::GeodesicExact::Inverse ( real  lat1,
real  lon1,
real  lat2,
real  lon2,
real &  s12 
) const
inline

See the documentation for GeodesicExact::Inverse.

Definition at line 576 of file GeodesicExact.hpp.

◆ Inverse() [3/7]

Math::real GeographicLib::GeodesicExact::Inverse ( real  lat1,
real  lon1,
real  lat2,
real  lon2,
real &  azi1,
real &  azi2 
) const
inline

See the documentation for GeodesicExact::Inverse.

Definition at line 587 of file GeodesicExact.hpp.

◆ Inverse() [4/7]

Math::real GeographicLib::GeodesicExact::Inverse ( real  lat1,
real  lon1,
real  lat2,
real  lon2,
real &  s12,
real &  azi1,
real &  azi2 
) const
inline

See the documentation for GeodesicExact::Inverse.

Definition at line 598 of file GeodesicExact.hpp.

◆ Inverse() [5/7]

Math::real GeographicLib::GeodesicExact::Inverse ( real  lat1,
real  lon1,
real  lat2,
real  lon2,
real &  s12,
real &  azi1,
real &  azi2,
real &  m12 
) const
inline

See the documentation for GeodesicExact::Inverse.

Definition at line 610 of file GeodesicExact.hpp.

◆ Inverse() [6/7]

Math::real GeographicLib::GeodesicExact::Inverse ( real  lat1,
real  lon1,
real  lat2,
real  lon2,
real &  s12,
real &  azi1,
real &  azi2,
real &  M12,
real &  M21 
) const
inline

See the documentation for GeodesicExact::Inverse.

Definition at line 622 of file GeodesicExact.hpp.

◆ Inverse() [7/7]

Math::real GeographicLib::GeodesicExact::Inverse ( real  lat1,
real  lon1,
real  lat2,
real  lon2,
real &  s12,
real &  azi1,
real &  azi2,
real &  m12,
real &  M12,
real &  M21 
) const
inline

See the documentation for GeodesicExact::Inverse.

Definition at line 634 of file GeodesicExact.hpp.

◆ GenInverse()

Math::real GeographicLib::GeodesicExact::GenInverse ( real  lat1,
real  lon1,
real  lat2,
real  lon2,
unsigned  outmask,
real &  s12,
real &  azi1,
real &  azi2,
real &  m12,
real &  M12,
real &  M21,
real &  S12 
) const

The general inverse geodesic calculation. GeodesicExact::Inverse is defined in terms of this function.

Parameters
[in]lat1latitude of point 1 (degrees).
[in]lon1longitude of point 1 (degrees).
[in]lat2latitude of point 2 (degrees).
[in]lon2longitude of point 2 (degrees).
[in]outmaska bitor'ed combination of GeodesicExact::mask values specifying which of the following parameters should be set.
[out]s12distance between point 1 and point 2 (meters).
[out]azi1azimuth at point 1 (degrees).
[out]azi2(forward) azimuth at point 2 (degrees).
[out]m12reduced length of geodesic (meters).
[out]M12geodesic scale of point 2 relative to point 1 (dimensionless).
[out]M21geodesic scale of point 1 relative to point 2 (dimensionless).
[out]S12area under the geodesic (meters2).
Returns
a12 arc length of between point 1 and point 2 (degrees).

The GeodesicExact::mask values possible for outmask are

The arc length is always computed and returned as the function value.

Definition at line 520 of file GeodesicExact.cpp.

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

◆ Line()

GeodesicLineExact GeographicLib::GeodesicExact::Line ( real  lat1,
real  lon1,
real  azi1,
unsigned  caps = ALL 
) const

Set up to compute several points on a single geodesic.

Parameters
[in]lat1latitude of point 1 (degrees).
[in]lon1longitude of point 1 (degrees).
[in]azi1azimuth at point 1 (degrees).
[in]capsbitor'ed combination of GeodesicExact::mask values specifying the capabilities the GeodesicLineExact object should possess, i.e., which quantities can be returned in calls to GeodesicLineExact::Position.
Returns
a GeodesicLineExact object.

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

The GeodesicExact::mask values are

The default value of caps is GeodesicExact::ALL which turns on all the capabilities.

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 119 of file GeodesicExact.cpp.

References GeodesicLineExact.

Referenced by main().

◆ InverseLine()

GeodesicLineExact GeographicLib::GeodesicExact::InverseLine ( real  lat1,
real  lon1,
real  lat2,
real  lon2,
unsigned  caps = ALL 
) const

Define a GeodesicLineExact in terms of the inverse geodesic problem.

Parameters
[in]lat1latitude of point 1 (degrees).
[in]lon1longitude of point 1 (degrees).
[in]lat2latitude of point 2 (degrees).
[in]lon2longitude of point 2 (degrees).
[in]capsbitor'ed combination of GeodesicExact::mask values specifying the capabilities the GeodesicLineExact object should possess, i.e., which quantities can be returned in calls to GeodesicLineExact::Position.
Returns
a GeodesicLineExact object.

This function sets point 3 of the GeodesicLineExact to correspond to point 2 of the inverse geodesic problem.

lat1 and lat2 should be in the range [−90°, 90°].

Definition at line 539 of file GeodesicExact.cpp.

References GeographicLib::Math::atan2d(), GeographicLib::Math::cbrt(), GeographicLib::EllipticFunction::D(), GeographicLib::EllipticFunction::deltaD(), GeographicLib::EllipticFunction::deltaE(), GeographicLib::EllipticFunction::deltaH(), DISTANCE, DISTANCE_IN, GeographicLib::EllipticFunction::E(), GeodesicLineExact, GEODESICSCALE, GEOGRAPHICLIB_VOLATILE, GeographicLib::EllipticFunction::H(), GeographicLib::Math::hypot(), GeographicLib::EllipticFunction::k2(), GeographicLib::Math::norm(), GeographicLib::Math::pi(), GeographicLib::Math::polyval(), REDUCEDLENGTH, GeographicLib::EllipticFunction::Reset(), and GeographicLib::Math::sq().

Referenced by main().

◆ DirectLine()

GeodesicLineExact GeographicLib::GeodesicExact::DirectLine ( real  lat1,
real  lon1,
real  azi1,
real  s12,
unsigned  caps = ALL 
) const

Define a GeodesicLineExact in terms of the direct geodesic problem specified in terms of distance.

Parameters
[in]lat1latitude of point 1 (degrees).
[in]lon1longitude of point 1 (degrees).
[in]azi1azimuth at point 1 (degrees).
[in]s12distance between point 1 and point 2 (meters); it can be negative.
[in]capsbitor'ed combination of GeodesicExact::mask values specifying the capabilities the GeodesicLineExact object should possess, i.e., which quantities can be returned in calls to GeodesicLineExact::Position.
Returns
a GeodesicLineExact object.

This function sets point 3 of the GeodesicLineExact to correspond to point 2 of the direct geodesic problem.

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

Definition at line 153 of file GeodesicExact.cpp.

References GenDirectLine().

◆ ArcDirectLine()

GeodesicLineExact GeographicLib::GeodesicExact::ArcDirectLine ( real  lat1,
real  lon1,
real  azi1,
real  a12,
unsigned  caps = ALL 
) const

Define a GeodesicLineExact in terms of the direct geodesic problem specified in terms of arc length.

Parameters
[in]lat1latitude of point 1 (degrees).
[in]lon1longitude of point 1 (degrees).
[in]azi1azimuth at point 1 (degrees).
[in]a12arc length between point 1 and point 2 (degrees); it can be negative.
[in]capsbitor'ed combination of GeodesicExact::mask values specifying the capabilities the GeodesicLineExact object should possess, i.e., which quantities can be returned in calls to GeodesicLineExact::Position.
Returns
a GeodesicLineExact object.

This function sets point 3 of the GeodesicLineExact to correspond to point 2 of the direct geodesic problem.

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

Definition at line 159 of file GeodesicExact.cpp.

References GeographicLib::Math::AngDiff(), GeographicLib::Math::AngRound(), AREA, GeographicLib::Math::degree(), DISTANCE, GenDirectLine(), GEODESICSCALE, GEOGRAPHICLIB_PANIC, GeographicLib::Math::hypot(), GeographicLib::Math::LatFix(), GeographicLib::Math::norm(), GeographicLib::Math::pi(), REDUCEDLENGTH, GeographicLib::Math::sincosd(), GeographicLib::Math::sq(), and std::swap().

◆ GenDirectLine()

GeodesicLineExact GeographicLib::GeodesicExact::GenDirectLine ( real  lat1,
real  lon1,
real  azi1,
bool  arcmode,
real  s12_a12,
unsigned  caps = ALL 
) const

Define a GeodesicLineExact in terms of the direct geodesic problem specified in terms of either distance or arc length.

Parameters
[in]lat1latitude of point 1 (degrees).
[in]lon1longitude of point 1 (degrees).
[in]azi1azimuth at point 1 (degrees).
[in]arcmodeboolean flag determining the meaning of the s12_a12.
[in]s12_a12if 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]capsbitor'ed combination of GeodesicExact::mask values specifying the capabilities the GeodesicLineExact object should possess, i.e., which quantities can be returned in calls to GeodesicLineExact::Position.
Returns
a GeodesicLineExact object.

This function sets point 3 of the GeodesicLineExact to correspond to point 2 of the direct geodesic problem.

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

Definition at line 139 of file GeodesicExact.cpp.

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

Referenced by ArcDirectLine(), DirectLine(), and main().

◆ MajorRadius()

Math::real GeographicLib::GeodesicExact::MajorRadius ( ) const
inline
Returns
a the equatorial radius of the ellipsoid (meters). This is the value used in the constructor.

Definition at line 834 of file GeodesicExact.hpp.

◆ Flattening()

Math::real GeographicLib::GeodesicExact::Flattening ( ) const
inline
Returns
f the flattening of the ellipsoid. This is the value used in the constructor.

Definition at line 840 of file GeodesicExact.hpp.

◆ EllipsoidArea()

Math::real GeographicLib::GeodesicExact::EllipsoidArea ( ) const
inline
Returns
total area of ellipsoid in meters2. The area of a polygon encircling a pole can be found by adding GeodesicExact::EllipsoidArea()/2 to the sum of S12 for each side of the polygon.

Definition at line 848 of file GeodesicExact.hpp.

References GeographicLib::Math::pi().

◆ WGS84()

const GeodesicExact & GeographicLib::GeodesicExact::WGS84 ( )
static

A global instantiation of GeodesicExact with the parameters for the WGS84 ellipsoid.

Definition at line 93 of file GeodesicExact.cpp.

References GeographicLib::Constants::WGS84_a(), and GeographicLib::Constants::WGS84_f().

Friends And Related Function Documentation

◆ GeodesicLineExact

friend class GeodesicLineExact
friend

Definition at line 83 of file GeodesicExact.hpp.

Referenced by GenDirect(), GenDirectLine(), InverseLine(), and Line().


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