GeographicLib  1.47
Public Types | Friends | List of all members
GeographicLib::GeodesicLine Class Reference

A geodesic line. More...

#include <GeographicLib/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
 

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

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 70 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 120 of file GeodesicLine.hpp.

Constructor & Destructor Documentation

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]gA Geodesic object used to compute the necessary information about the GeodesicLine.
[in]lat1latitude of point 1 (degrees).
[in]lon1longitude of point 1 (degrees).
[in]azi1azimuth at point 1 (degrees).
[in]capsbitor'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

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.

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

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 234 of file GeodesicLine.hpp.

Referenced by GeodesicLine().

Member Function Documentation

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]s12distance from point 1 to point 2 (meters); it can be negative.
[out]lat2latitude of point 2 (degrees).
[out]lon2longitude of point 2 (degrees); requires that the GeodesicLine object was constructed with caps |= GeodesicLine::LONGITUDE.
[out]azi2(forward) azimuth at point 2 (degrees).
[out]m12reduced length of geodesic (meters); requires that the GeodesicLine object was constructed with caps |= GeodesicLine::REDUCEDLENGTH.
[out]M12geodesic scale of point 2 relative to point 1 (dimensionless); requires that the GeodesicLine object was constructed with caps |= GeodesicLine::GEODESICSCALE.
[out]M21geodesic scale of point 1 relative to point 2 (dimensionless); requires that the GeodesicLine object was constructed with caps |= GeodesicLine::GEODESICSCALE.
[out]S12area 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 280 of file GeodesicLine.hpp.

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

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

See the documentation for GeodesicLine::Position.

Definition at line 294 of file GeodesicLine.hpp.

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

See the documentation for GeodesicLine::Position.

Definition at line 304 of file GeodesicLine.hpp.

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 315 of file GeodesicLine.hpp.

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 327 of file GeodesicLine.hpp.

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 340 of file GeodesicLine.hpp.

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]a12arc length from point 1 to point 2 (degrees); it can be negative.
[out]lat2latitude of point 2 (degrees).
[out]lon2longitude of point 2 (degrees); requires that the GeodesicLine object was constructed with caps |= GeodesicLine::LONGITUDE.
[out]azi2(forward) azimuth at point 2 (degrees).
[out]s12distance from point 1 to point 2 (meters); requires that the GeodesicLine object was constructed with caps |= GeodesicLine::DISTANCE.
[out]m12reduced length of geodesic (meters); requires that the GeodesicLine object was constructed with caps |= GeodesicLine::REDUCEDLENGTH.
[out]M12geodesic scale of point 2 relative to point 1 (dimensionless); requires that the GeodesicLine object was constructed with caps |= GeodesicLine::GEODESICSCALE.
[out]M21geodesic scale of point 1 relative to point 2 (dimensionless); requires that the GeodesicLine object was constructed with caps |= GeodesicLine::GEODESICSCALE.
[out]S12area 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 393 of file GeodesicLine.hpp.

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

See the documentation for GeodesicLine::ArcPosition.

Definition at line 405 of file GeodesicLine.hpp.

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

See the documentation for GeodesicLine::ArcPosition.

Definition at line 416 of file GeodesicLine.hpp.

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 428 of file GeodesicLine.hpp.

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 439 of file GeodesicLine.hpp.

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 451 of file GeodesicLine.hpp.

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 464 of file GeodesicLine.hpp.

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]arcmodeboolean 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_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]outmaska bitor'ed combination of GeodesicLine::mask values specifying which of the following parameters should be set.
[out]lat2latitude of point 2 (degrees).
[out]lon2longitude of point 2 (degrees); requires that the GeodesicLine object was constructed with caps |= GeodesicLine::LONGITUDE.
[out]azi2(forward) azimuth at point 2 (degrees).
[out]s12distance from point 1 to point 2 (meters); requires that the GeodesicLine object was constructed with caps |= GeodesicLine::DISTANCE.
[out]m12reduced length of geodesic (meters); requires that the GeodesicLine object was constructed with caps |= GeodesicLine::REDUCEDLENGTH.
[out]M12geodesic scale of point 2 relative to point 1 (dimensionless); requires that the GeodesicLine object was constructed with caps |= GeodesicLine::GEODESICSCALE.
[out]M21geodesic scale of point 1 relative to point 2 (dimensionless); requires that the GeodesicLine object was constructed with caps |= GeodesicLine::GEODESICSCALE.
[out]S12area 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

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.

References GeographicLib::Math::AngNormalize(), GeographicLib::Math::atan2d(), GeographicLib::Math::copysign(), GeographicLib::Math::degree(), GeographicLib::Math::hypot(), GeographicLib::Math::NaN(), GeographicLib::Math::sincosd(), and GeographicLib::Math::sq().

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

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

Specify position of point 3 in terms of distance.

Parameters
[in]s13the 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.

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

Specify position of point 3 in terms of arc length.

Parameters
[in]a13the 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().

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

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

Parameters
[in]arcmodeboolean 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_a13if 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.

bool GeographicLib::GeodesicLine::Init ( ) const
inline
Returns
true if the object has been initialized.

Definition at line 588 of file GeodesicLine.hpp.

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

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

Definition at line 593 of file GeodesicLine.hpp.

References GeographicLib::Math::NaN().

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

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

Definition at line 599 of file GeodesicLine.hpp.

References GeographicLib::Math::NaN().

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

Math::real GeographicLib::GeodesicLine::Azimuth ( ) const
inline
Returns
azi1 the azimuth (degrees) of the geodesic line at point 1.

Definition at line 605 of file GeodesicLine.hpp.

References GeographicLib::Math::NaN().

Referenced by main().

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

The sine and cosine of azi1.

Parameters
[out]sazi1the sine of azi1.
[out]cazi1the cosine of azi1.

Definition at line 614 of file GeodesicLine.hpp.

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 623 of file GeodesicLine.hpp.

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

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

The sine and cosine of azi0.

Parameters
[out]sazi0the sine of azi0.
[out]cazi0the cosine of azi0.

Definition at line 632 of file GeodesicLine.hpp.

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 641 of file GeodesicLine.hpp.

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

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 649 of file GeodesicLine.hpp.

References GeographicLib::Math::NaN().

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 656 of file GeodesicLine.hpp.

References GeographicLib::Math::NaN().

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 663 of file GeodesicLine.hpp.

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

Test what capabilities are available.

Parameters
[in]testcapsa set of bitor'ed GeodesicLine::mask values.
Returns
true if the GeodesicLine object has all these capabilities.

Definition at line 671 of file GeodesicLine.hpp.

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

The distance or arc length to point 3.

Parameters
[in]arcmodeboolean flag determining the meaning of returned value.
Returns
s13 if arcmode is false; a13 if arcmode is true.

Definition at line 683 of file GeodesicLine.hpp.

References GeographicLib::Math::NaN().

Referenced by main().

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

Definition at line 689 of file GeodesicLine.hpp.

Math::real GeographicLib::GeodesicLine::Arc ( ) const
inline
Returns
a13, the arc length to point 3 (degrees).

Definition at line 694 of file GeodesicLine.hpp.

Friends And Related Function Documentation

friend class Geodesic
friend

Definition at line 73 of file GeodesicLine.hpp.


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