GeographicLib  1.48
GeographicLib::Geodesic Class Reference

Geodesic calculations More...

#include <GeographicLib/Geodesic.hpp>

## Public Types

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

## Public Member Functions

Constructor
Geodesic (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 GeodesicLine.
GeodesicLine Line (real lat1, real lon1, real azi1, unsigned caps=ALL) const

GeodesicLine InverseLine (real lat1, real lon1, real lat2, real lon2, unsigned caps=ALL) const

GeodesicLine DirectLine (real lat1, real lon1, real azi1, real s12, unsigned caps=ALL) const

GeodesicLine ArcDirectLine (real lat1, real lon1, real azi1, real a12, unsigned caps=ALL) const

GeodesicLine 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 GeodesicWGS84 ()

## Friends

class GeodesicLine

## Detailed Description

Geodesic calculations

The shortest path between two points on a ellipsoid at (lat1, lon1) and (lat2, lon2) is called the geodesic. Its length is s12 and the geodesic from point 1 to point 2 has azimuths azi1 and azi2 at the two end points. (The azimuth is the heading measured clockwise from north. azi2 is the "forward" azimuth, i.e., the heading that takes you beyond point 2 not back to point 1.) In the figure below, latitude if labeled φ, longitude λ (with λ12 = λ2 − λ1), and azimuth α.

Given lat1, lon1, azi1, and s12, we can determine lat2, lon2, and azi2. This is the direct geodesic problem and its solution is given by the function Geodesic::Direct. (If s12 is sufficiently large that the geodesic wraps more than halfway around the earth, there will be another geodesic between the points with a smaller s12.)

Given lat1, lon1, lat2, and lon2, we can determine azi1, azi2, and s12. This is the inverse geodesic problem, whose solution is given by Geodesic::Inverse. Usually, the solution to the inverse problem is unique. In cases where there are multiple solutions (all with the same s12, of course), all the solutions can be easily generated once a particular solution is provided.

The standard way of specifying the direct problem is the specify the distance s12 to the second point. However it is sometimes useful instead to specify the arc length a12 (in degrees) on the auxiliary sphere. This is a mathematical construct used in solving the geodesic problems. The solution of the direct problem in this form is provided by Geodesic::ArcDirect. An arc length in excess of 180° indicates that the geodesic is not a shortest path. In addition, the arc length between an equatorial crossing and the next extremum of latitude for a geodesic is 90°.

This class can also calculate several other quantities related to geodesics. These are:

• reduced length. If we fix the first point and increase azi1 by dazi1 (radians), the second point is displaced m12 dazi1 in the direction azi2 + 90°. The quantity m12 is called the "reduced length" and is symmetric under interchange of the two points. On a curved surface the reduced length obeys a symmetry relation, m12 + m21 = 0. On a flat surface, we have m12 = s12. The ratio s12/m12 gives the azimuthal scale for an azimuthal equidistant projection.
• geodesic scale. Consider a reference geodesic and a second geodesic parallel to this one at point 1 and separated by a small distance dt. The separation of the two geodesics at point 2 is M12 dt where M12 is called the "geodesic scale". M21 is defined similarly (with the geodesics being parallel at point 2). On a flat surface, we have M12 = M21 = 1. The quantity 1/M12 gives the scale of the Cassini-Soldner projection.
• area. The area between the geodesic from point 1 to point 2 and the equation is represented by S12; it is the area, measured counter-clockwise, of the geodesic quadrilateral with corners (lat1,lon1), (0,lon1), (0,lon2), and (lat2,lon2). It can be used to compute the area of any simple geodesic polygon.

Overloaded versions of Geodesic::Direct, Geodesic::ArcDirect, and Geodesic::Inverse allow these quantities to be returned. In addition there are general functions Geodesic::GenDirect, and Geodesic::GenInverse which allow an arbitrary set of results to be computed. The quantities m12, M12, M21 which all specify the behavior of nearby geodesics obey addition rules. If points 1, 2, and 3 all lie on a single geodesic, then the following rules hold:

• s13 = s12 + s23
• a13 = a12 + a23
• S13 = S12 + S23
• m13 = m12 M23 + m23 M21
• M13 = M12 M23 − (1 − M12 M21) m23 / m12
• M31 = M32 M21 − (1 − M23 M32) m12 / m23

Additional functionality is provided by the GeodesicLine class, which allows a sequence of points along a geodesic to be computed.

The shortest distance returned by the solution of the inverse problem is (obviously) uniquely defined. However, in a few special cases there are multiple azimuths which yield the same shortest distance. Here is a catalog of those cases:

• lat1 = −lat2 (with neither point at a pole). If azi1 = azi2, the geodesic is unique. Otherwise there are two geodesics and the second one is obtained by setting [azi1, azi2] → [azi2, azi1], [M12, M21] → [M21, M12], S12 → −S12. (This occurs when the longitude difference is near ±180° for oblate ellipsoids.)
• lon2 = lon1 ± 180° (with neither point at a pole). If azi1 = 0° or ±180°, the geodesic is unique. Otherwise there are two geodesics and the second one is obtained by setting [azi1, azi2] → [−azi1, −azi2], S12 → −S12. (This occurs when lat2 is near −lat1 for prolate ellipsoids.)
• Points 1 and 2 at opposite poles. There are infinitely many geodesics which can be generated by setting [azi1, azi2] → [azi1, azi2] + [d, −d], for arbitrary d. (For spheres, this prescription applies when points 1 and 2 are antipodal.)
• s12 = 0 (coincident points). There are infinitely many geodesics which can be generated by setting [azi1, azi2] → [azi1, azi2] + [d, d], for arbitrary d.

The calculations are accurate to better than 15 nm (15 nanometers) for the WGS84 ellipsoid. 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. Here is a table of the approximate maximum error (expressed as a distance) for an ellipsoid with the same equatorial radius as the WGS84 ellipsoid and different values of the flattening.

    |f|      error
0.01     25 nm
0.02     30 nm
0.05     10 um
0.1     1.5 mm
0.2     300 mm


For very eccentric ellipsoids, use GeodesicExact 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::Geodesic class
#include <iostream>
#include <exception>
using namespace std;
using namespace GeographicLib;
int main() {
try {
// Alternatively: const Geodesic& geod = Geodesic::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 Geodesic and GeodesicLine.

Definition at line 171 of file Geodesic.hpp.

## ◆ mask

Bit masks for what calculations to do. These masks do double duty. They signify to the GeodesicLine::GeodesicLine constructor and to Geodesic::Line what capabilities should be included in the GeodesicLine object. They also specify which results to return in the general routines Geodesic::GenDirect and Geodesic::GenInverse routines. GeodesicLine::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 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 262 of file Geodesic.hpp.

## ◆ Geodesic()

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

Constructor for a ellipsoid with

Parameters
 [in] a equatorial radius (meters). [in] f flattening of ellipsoid. Setting f = 0 gives a sphere. Negative f gives a prolate ellipsoid.
Exceptions
 GeographicErr if a or (1 − f) a is not positive.

Definition at line 42 of file Geodesic.cpp.

References GeographicLib::Math::isfinite().

## ◆ Direct() [1/6]

 Math::real GeographicLib::Geodesic::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

Solve the direct geodesic problem where the length of the geodesic is specified in terms of distance.

Parameters
 [in] lat1 latitude of point 1 (degrees). [in] lon1 longitude of point 1 (degrees). [in] azi1 azimuth at point 1 (degrees). [in] s12 distance between point 1 and point 2 (meters); it can be negative. [out] lat2 latitude of point 2 (degrees). [out] lon2 longitude of point 2 (degrees). [out] azi2 (forward) azimuth at point 2 (degrees). [out] m12 reduced length of geodesic (meters). [out] M12 geodesic scale of point 2 relative to point 1 (dimensionless). [out] M21 geodesic scale of point 1 relative to point 2 (dimensionless). [out] S12 area 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 Geodesic::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 378 of file Geodesic.hpp.

## ◆ Direct() [2/6]

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

See the documentation for Geodesic::Direct.

Definition at line 392 of file Geodesic.hpp.

## ◆ Direct() [3/6]

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

See the documentation for Geodesic::Direct.

Definition at line 404 of file Geodesic.hpp.

## ◆ Direct() [4/6]

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

See the documentation for Geodesic::Direct.

Definition at line 416 of file Geodesic.hpp.

## ◆ Direct() [5/6]

 Math::real GeographicLib::Geodesic::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 Geodesic::Direct.

Definition at line 428 of file Geodesic.hpp.

## ◆ Direct() [6/6]

 Math::real GeographicLib::Geodesic::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 Geodesic::Direct.

Definition at line 441 of file Geodesic.hpp.

## ◆ ArcDirect() [1/7]

 void GeographicLib::Geodesic::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

Solve the direct geodesic problem where the length of the geodesic is specified in terms of arc length.

Parameters
 [in] lat1 latitude of point 1 (degrees). [in] lon1 longitude of point 1 (degrees). [in] azi1 azimuth at point 1 (degrees). [in] a12 arc length between point 1 and point 2 (degrees); it can be negative. [out] lat2 latitude of point 2 (degrees). [out] lon2 longitude of point 2 (degrees). [out] azi2 (forward) azimuth at point 2 (degrees). [out] s12 distance between point 1 and point 2 (meters). [out] m12 reduced length of geodesic (meters). [out] M12 geodesic scale of point 2 relative to point 1 (dimensionless). [out] M21 geodesic scale of point 1 relative to point 2 (dimensionless). [out] S12 area 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 Geodesic::Direct which omit some of the output parameters.

Definition at line 490 of file Geodesic.hpp.

## ◆ ArcDirect() [2/7]

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

See the documentation for Geodesic::ArcDirect.

Definition at line 503 of file Geodesic.hpp.

## ◆ ArcDirect() [3/7]

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

See the documentation for Geodesic::ArcDirect.

Definition at line 514 of file Geodesic.hpp.

## ◆ ArcDirect() [4/7]

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

See the documentation for Geodesic::ArcDirect.

Definition at line 525 of file Geodesic.hpp.

## ◆ ArcDirect() [5/7]

 void GeographicLib::Geodesic::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 Geodesic::ArcDirect.

Definition at line 537 of file Geodesic.hpp.

## ◆ ArcDirect() [6/7]

 void GeographicLib::Geodesic::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 Geodesic::ArcDirect.

Definition at line 550 of file Geodesic.hpp.

## ◆ ArcDirect() [7/7]

 void GeographicLib::Geodesic::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 Geodesic::ArcDirect.

Definition at line 563 of file Geodesic.hpp.

## ◆ GenDirect()

 Math::real GeographicLib::Geodesic::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 problem. Geodesic::Direct and Geodesic::ArcDirect are defined in terms of this function.

Parameters
 [in] lat1 latitude of point 1 (degrees). [in] lon1 longitude of point 1 (degrees). [in] azi1 azimuth at point 1 (degrees). [in] arcmode boolean flag determining the meaning of the s12_a12. [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 Geodesic::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). [out] azi2 (forward) azimuth at point 2 (degrees). [out] s12 distance between point 1 and point 2 (meters). [out] m12 reduced length of geodesic (meters). [out] M12 geodesic scale of point 2 relative to point 1 (dimensionless). [out] M21 geodesic scale of point 1 relative to point 2 (dimensionless). [out] S12 area under the geodesic (meters2).
Returns
a12 arc length of between point 1 and point 2 (degrees).

The Geodesic::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 Geodesic::DISTANCE and arcmode is false, then s12 = s12_a12. It is not necessary to include Geodesic::DISTANCE_IN in outmask; this is automatically included is arcmode is false.

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

Definition at line 123 of file Geodesic.cpp.

References DISTANCE_IN, and GeodesicLine.

## ◆ Inverse() [1/7]

 Math::real GeographicLib::Geodesic::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

Solve the inverse geodesic problem.

Parameters
 [in] lat1 latitude of point 1 (degrees). [in] lon1 longitude of point 1 (degrees). [in] lat2 latitude of point 2 (degrees). [in] lon2 longitude of point 2 (degrees). [out] s12 distance between point 1 and point 2 (meters). [out] azi1 azimuth at point 1 (degrees). [out] azi2 (forward) azimuth at point 2 (degrees). [out] m12 reduced length of geodesic (meters). [out] M12 geodesic scale of point 2 relative to point 1 (dimensionless). [out] M21 geodesic scale of point 1 relative to point 2 (dimensionless). [out] S12 area 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 solution to the inverse problem is found using Newton's method. If this fails to converge (this is very unlikely in geodetic applications but does occur for very eccentric ellipsoids), then the bisection method is used to refine the solution.

The following functions are overloaded versions of Geodesic::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 673 of file Geodesic.hpp.

## ◆ Inverse() [2/7]

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

See the documentation for Geodesic::Inverse.

Definition at line 685 of file Geodesic.hpp.

## ◆ Inverse() [3/7]

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

See the documentation for Geodesic::Inverse.

Definition at line 696 of file Geodesic.hpp.

## ◆ Inverse() [4/7]

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

See the documentation for Geodesic::Inverse.

Definition at line 707 of file Geodesic.hpp.

## ◆ Inverse() [5/7]

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

See the documentation for Geodesic::Inverse.

Definition at line 719 of file Geodesic.hpp.

## ◆ Inverse() [6/7]

 Math::real GeographicLib::Geodesic::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 Geodesic::Inverse.

Definition at line 731 of file Geodesic.hpp.

## ◆ Inverse() [7/7]

 Math::real GeographicLib::Geodesic::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 Geodesic::Inverse.

Definition at line 743 of file Geodesic.hpp.

## ◆ GenInverse()

 Math::real GeographicLib::Geodesic::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. Geodesic::Inverse is defined in terms of this function.

Parameters
 [in] lat1 latitude of point 1 (degrees). [in] lon1 longitude of point 1 (degrees). [in] lat2 latitude of point 2 (degrees). [in] lon2 longitude of point 2 (degrees). [in] outmask a bitor'ed combination of Geodesic::mask values specifying which of the following parameters should be set. [out] s12 distance between point 1 and point 2 (meters). [out] azi1 azimuth at point 1 (degrees). [out] azi2 (forward) azimuth at point 2 (degrees). [out] m12 reduced length of geodesic (meters). [out] M12 geodesic scale of point 2 relative to point 1 (dimensionless). [out] M21 geodesic scale of point 1 relative to point 2 (dimensionless). [out] S12 area under the geodesic (meters2).
Returns
a12 arc length of between point 1 and point 2 (degrees).

The Geodesic::mask values possible for outmask are

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

Definition at line 493 of file Geodesic.cpp.

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

## ◆ Line()

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

Set up to compute several points on a single geodesic.

Parameters
 [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 Geodesic::mask values specifying the capabilities the GeodesicLine object should possess, i.e., which quantities can be returned in calls to GeodesicLine::Position.
Returns
a GeodesicLine object.

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

The Geodesic::mask values are

The default value of caps is Geodesic::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 Geodesic.cpp.

References GeodesicLine.

## ◆ InverseLine()

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

Define a GeodesicLine in terms of the inverse geodesic problem.

Parameters
 [in] lat1 latitude of point 1 (degrees). [in] lon1 longitude of point 1 (degrees). [in] lat2 latitude of point 2 (degrees). [in] lon2 longitude of point 2 (degrees). [in] caps bitor'ed combination of Geodesic::mask values specifying the capabilities the GeodesicLine object should possess, i.e., which quantities can be returned in calls to GeodesicLine::Position.
Returns
a GeodesicLine object.

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

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

Definition at line 510 of file Geodesic.cpp.

## ◆ DirectLine()

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

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

Parameters
 [in] lat1 latitude of point 1 (degrees). [in] lon1 longitude of point 1 (degrees). [in] azi1 azimuth at point 1 (degrees). [in] s12 distance between point 1 and point 2 (meters); it can be negative. [in] caps bitor'ed combination of Geodesic::mask values specifying the capabilities the GeodesicLine object should possess, i.e., which quantities can be returned in calls to GeodesicLine::Position.
Returns
a GeodesicLine object.

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

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

Definition at line 149 of file Geodesic.cpp.

References GenDirectLine().

## ◆ ArcDirectLine()

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

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

Parameters
 [in] lat1 latitude of point 1 (degrees). [in] lon1 longitude of point 1 (degrees). [in] azi1 azimuth at point 1 (degrees). [in] a12 arc length between point 1 and point 2 (degrees); it can be negative. [in] caps bitor'ed combination of Geodesic::mask values specifying the capabilities the GeodesicLine object should possess, i.e., which quantities can be returned in calls to GeodesicLine::Position.
Returns
a GeodesicLine object.

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

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

Definition at line 154 of file Geodesic.cpp.

## ◆ GenDirectLine()

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

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

Parameters
 [in] lat1 latitude of point 1 (degrees). [in] lon1 longitude of point 1 (degrees). [in] azi1 azimuth at point 1 (degrees). [in] arcmode boolean flag determining the meaning of the s12_a12. [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] caps bitor'ed combination of Geodesic::mask values specifying the capabilities the GeodesicLine object should possess, i.e., which quantities can be returned in calls to GeodesicLine::Position.
Returns
a GeodesicLine object.

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

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

Definition at line 136 of file Geodesic.cpp.

Referenced by ArcDirectLine(), and DirectLine().

## ◆ MajorRadius()

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

Definition at line 942 of file Geodesic.hpp.

## ◆ Flattening()

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

Definition at line 948 of file Geodesic.hpp.

## ◆ EllipsoidArea()

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

Definition at line 956 of file Geodesic.hpp.

References GeographicLib::Math::pi().

## ◆ WGS84()

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

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

Definition at line 89 of file Geodesic.cpp.

## ◆ GeodesicLine

 friend class GeodesicLine
friend

Definition at line 174 of file Geodesic.hpp.

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

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