A geodesic line. More...
#include <GeographicLib/GeodesicLine.hpp>
Public Types | |
enum | mask { NONE, LATITUDE, LONGITUDE, AZIMUTH, DISTANCE, DISTANCE_IN, REDUCEDLENGTH, GEODESICSCALE, AREA, ALL } |
Public Member Functions | |
Constructors | |
GeodesicLine (const Geodesic &g, real lat1, real lon1, real azi1, unsigned caps=ALL) throw () | |
GeodesicLine () throw () | |
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 throw () |
Math::real | Position (real s12, real &lat2, real &lon2) const throw () |
Math::real | Position (real s12, real &lat2, real &lon2, real &azi2) const throw () |
Math::real | Position (real s12, real &lat2, real &lon2, real &azi2, real &m12) const throw () |
Math::real | Position (real s12, real &lat2, real &lon2, real &azi2, real &M12, real &M21) const throw () |
Math::real | Position (real s12, real &lat2, real &lon2, real &azi2, real &m12, real &M12, real &M21) const throw () |
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 throw () |
void | ArcPosition (real a12, real &lat2, real &lon2) const throw () |
void | ArcPosition (real a12, real &lat2, real &lon2, real &azi2) const throw () |
void | ArcPosition (real a12, real &lat2, real &lon2, real &azi2, real &s12) const throw () |
void | ArcPosition (real a12, real &lat2, real &lon2, real &azi2, real &s12, real &m12) const throw () |
void | ArcPosition (real a12, real &lat2, real &lon2, real &azi2, real &s12, real &M12, real &M21) const throw () |
void | ArcPosition (real a12, real &lat2, real &lon2, real &azi2, real &s12, real &m12, real &M12, real &M21) const throw () |
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 throw () |
Inspector functions | |
bool | Init () const throw () |
Math::real | Latitude () const throw () |
Math::real | Longitude () const throw () |
Math::real | Azimuth () const throw () |
Math::real | EquatorialAzimuth () const throw () |
Math::real | EquatorialArc () const throw () |
Math::real | MajorRadius () const throw () |
Math::real | InverseFlattening () const throw () |
unsigned | Capabilities () const throw () |
bool | Capabilities (unsigned testcaps) const throw () |
Deprecated Functions | |
Math::real | Position (real s12, real &lat2, real &lon2, real &azi2, real &m12, bool arcmode) const throw () |
void | Scale (real a12, real &M12, real &M21) const throw () |
Friends | |
class | Geodesic |
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. GeodesicLine.Position returns the location of point 2 a distance s12 along the geodesic. Alternatively GeodesicLine.ArcPosition gives the position of point 2 an arc length a12 along the geodesic. An example of use of this class is:
#include <iostream> #include <iomanip> #include <cmath> #include "GeographicLib/Geodesic.hpp" #include "GeographicLib/GeodesicLine.hpp" int main() { // Print waypoints between JFK and SIN at // approximately 100km intervals. double lat1 = 40.640, lon1 = -73.779, // JFK lat2 = 1.359, lon2 = 177.486; // SIN const GeographicLib::Geodesic& g = GeographicLib::Geodesic::WGS84; double azi1, azi2, a12 = g.Inverse(lat1, lon1, lat2, lon2, azi1, azi2); double ds = 100e3; // Nominal distance between points = 100 km int num = std::ceil(a12/ (90 * ds / 10e6)); // 90 deg = 10e6 m double da = a12/num; // Arc length between points const GeographicLib::GeodesicLine l(g, lat1, lon1, azi1); std::cout << std::fixed << std::setprecision(3); for (int i = 0; i <= num; ++i) { double lat, lon; l.ArcPosition(i * da, lat, lon); std::cout << lat << " " << lon << "\n"; } }
The default copy constructor and assignment operators work with this class, so that, for example, the previous example could start
GeographicLib::GeodesicLine l; l = g.Line(lat1, lon1, azi1);
Similarly, a vector can be used to hold GeodesicLine objects.
The calculations are accurate to better than 15 nm. See Sec. 9 of arXiv:1102.1215 for details.
The algorithms are described in
For more information on geodesics see Geodesics on the Ellipsoid.
Definition at line 78 of file GeodesicLine.hpp.
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. This is merely a duplication of Geodesic::mask.
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. |
ALL |
All capabilities. Calculate everything. |
Definition at line 116 of file GeodesicLine.hpp.
GeographicLib::GeodesicLine::GeodesicLine | ( | const Geodesic & | g, | |
real | lat1, | |||
real | lon1, | |||
real | azi1, | |||
unsigned | caps = ALL | |||
) | throw () |
Constructor for a geodesic line staring at latitude lat1, longitude lon1, and aziumuth azi1 (all in degrees).
[in] | g | A Geodesic object used to compute the necessary information about the GeodesicLine. |
[in] | lat1 | latitude of point 1 (degrees). |
[in] | lon1 | longitude of point 1 (degrees). |
[in] | azi1 | azimuth at point 1 (degrees). |
[in] | caps | bitor'ed combination of GeodesicLine::mask values specifying the capabilities the GeodesicLine object should possess, i.e., which quantities can be returned in calls to GeodesicLib::Position. |
The GeodesicLine::mask values are
The default value of caps is GeodesicLine::ALL which turns on all the capabilities.
If the point is at a pole, the azimuth is defined by keeping the lon1 fixed and writing lat1 = 90 - eps or -90 + eps and taking the limit eps -> 0 from above.
Definition at line 40 of file GeodesicLine.cpp.
GeographicLib::GeodesicLine::GeodesicLine | ( | ) | throw () [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 224 of file GeodesicLine.hpp.
Math::real GeographicLib::GeodesicLine::Position | ( | real | s12, | |
real & | lat2, | |||
real & | lon2, | |||
real & | azi2, | |||
real & | m12, | |||
real & | M12, | |||
real & | M21, | |||
real & | S12 | |||
) | const throw () [inline] |
Compute the position of point 2 which is a distance s12 (meters) from point 1.
[in] | s12 | distance between point 1 and point 2 (meters); it can be signed. |
[out] | lat2 | latitude of point 2 (degrees). |
[out] | lon2 | longitude of point 2 (degrees); requires that the GeodesicLine object was constructed with caps |= GeodesicLine::LONGITUDE. |
[out] | azi2 | (forward) azimuth at point 2 (degrees). |
[out] | m12 | reduced length of geodesic (meters); requires that the GeodesicLine object was constructed with caps |= GeodesicLine::REDUCEDLENGTH. |
[out] | M12 | geodesic scale of point 2 relative to point 1 (dimensionless); requires that the GeodesicLine object was constructed with caps |= GeodesicLine::GEODESICSCALE. |
[out] | M21 | geodesic scale of point 1 relative to point 2 (dimensionless); requires that the GeodesicLine object was constructed with caps |= GeodesicLine::GEODESICSCALE. |
[out] | S12 | area under the geodesic (meters2); requires that the GeodesicLine object was constructed with caps |= GeodesicLine::AREA. |
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 267 of file GeodesicLine.hpp.
References AREA, AZIMUTH, GenPosition(), GEODESICSCALE, LATITUDE, LONGITUDE, and REDUCEDLENGTH.
Referenced by Position().
Math::real GeographicLib::GeodesicLine::Position | ( | real | s12, | |
real & | lat2, | |||
real & | lon2 | |||
) | const throw () [inline] |
See the documentation for GeodesicLine::Position.
Definition at line 281 of file GeodesicLine.hpp.
References GenPosition(), LATITUDE, and LONGITUDE.
Math::real GeographicLib::GeodesicLine::Position | ( | real | s12, | |
real & | lat2, | |||
real & | lon2, | |||
real & | azi2 | |||
) | const throw () [inline] |
See the documentation for GeodesicLine::Position.
Definition at line 291 of file GeodesicLine.hpp.
References AZIMUTH, GenPosition(), LATITUDE, and LONGITUDE.
Math::real GeographicLib::GeodesicLine::Position | ( | real | s12, | |
real & | lat2, | |||
real & | lon2, | |||
real & | azi2, | |||
real & | m12 | |||
) | const throw () [inline] |
See the documentation for GeodesicLine::Position.
Definition at line 302 of file GeodesicLine.hpp.
References AZIMUTH, GenPosition(), LATITUDE, LONGITUDE, and REDUCEDLENGTH.
Math::real GeographicLib::GeodesicLine::Position | ( | real | s12, | |
real & | lat2, | |||
real & | lon2, | |||
real & | azi2, | |||
real & | M12, | |||
real & | M21 | |||
) | const throw () [inline] |
See the documentation for GeodesicLine::Position.
Definition at line 314 of file GeodesicLine.hpp.
References AZIMUTH, GenPosition(), GEODESICSCALE, LATITUDE, and LONGITUDE.
Math::real GeographicLib::GeodesicLine::Position | ( | real | s12, | |
real & | lat2, | |||
real & | lon2, | |||
real & | azi2, | |||
real & | m12, | |||
real & | M12, | |||
real & | M21 | |||
) | const throw () [inline] |
See the documentation for GeodesicLine::Position.
Definition at line 327 of file GeodesicLine.hpp.
References AZIMUTH, GenPosition(), GEODESICSCALE, LATITUDE, LONGITUDE, and REDUCEDLENGTH.
void GeographicLib::GeodesicLine::ArcPosition | ( | real | a12, | |
real & | lat2, | |||
real & | lon2, | |||
real & | azi2, | |||
real & | s12, | |||
real & | m12, | |||
real & | M12, | |||
real & | M21, | |||
real & | S12 | |||
) | const throw () [inline] |
Compute the position of point 2 which is an arc length a12 (degrees) from point 1.
[in] | a12 | arc length between point 1 and point 2 (degrees); it can be signed. |
[out] | lat2 | latitude of point 2 (degrees). |
[out] | lon2 | longitude of point 2 (degrees); requires that the GeodesicLine object was constructed with caps |= GeodesicLine::LONGITUDE. |
[out] | azi2 | (forward) azimuth at point 2 (degrees). |
[out] | s12 | distance between point 1 and point 2 (meters); requires that the GeodesicLine object was constructed with caps |= GeodesicLine::DISTANCE. |
[out] | m12 | reduced length of geodesic (meters); requires that the GeodesicLine object was constructed with caps |= GeodesicLine::REDUCEDLENGTH. |
[out] | M12 | geodesic scale of point 2 relative to point 1 (dimensionless); requires that the GeodesicLine object was constructed with caps |= GeodesicLine::GEODESICSCALE. |
[out] | M21 | geodesic scale of point 1 relative to point 2 (dimensionless); requires that the GeodesicLine object was constructed with caps |= GeodesicLine::GEODESICSCALE. |
[out] | S12 | area under the geodesic (meters2); requires that the GeodesicLine object was constructed with caps |= GeodesicLine::AREA. |
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 378 of file GeodesicLine.hpp.
References AREA, AZIMUTH, DISTANCE, GenPosition(), GEODESICSCALE, LATITUDE, LONGITUDE, and REDUCEDLENGTH.
Referenced by Position(), and Scale().
void GeographicLib::GeodesicLine::ArcPosition | ( | real | a12, | |
real & | lat2, | |||
real & | lon2 | |||
) | const throw () [inline] |
See the documentation for GeodesicLine::ArcPosition.
Definition at line 390 of file GeodesicLine.hpp.
References GenPosition(), LATITUDE, and LONGITUDE.
void GeographicLib::GeodesicLine::ArcPosition | ( | real | a12, | |
real & | lat2, | |||
real & | lon2, | |||
real & | azi2 | |||
) | const throw () [inline] |
See the documentation for GeodesicLine::ArcPosition.
Definition at line 401 of file GeodesicLine.hpp.
References AZIMUTH, GenPosition(), LATITUDE, and LONGITUDE.
void GeographicLib::GeodesicLine::ArcPosition | ( | real | a12, | |
real & | lat2, | |||
real & | lon2, | |||
real & | azi2, | |||
real & | s12 | |||
) | const throw () [inline] |
See the documentation for GeodesicLine::ArcPosition.
Definition at line 413 of file GeodesicLine.hpp.
References AZIMUTH, DISTANCE, GenPosition(), LATITUDE, and LONGITUDE.
void GeographicLib::GeodesicLine::ArcPosition | ( | real | a12, | |
real & | lat2, | |||
real & | lon2, | |||
real & | azi2, | |||
real & | s12, | |||
real & | m12 | |||
) | const throw () [inline] |
See the documentation for GeodesicLine::ArcPosition.
Definition at line 424 of file GeodesicLine.hpp.
References AZIMUTH, DISTANCE, GenPosition(), LATITUDE, LONGITUDE, and REDUCEDLENGTH.
void GeographicLib::GeodesicLine::ArcPosition | ( | real | a12, | |
real & | lat2, | |||
real & | lon2, | |||
real & | azi2, | |||
real & | s12, | |||
real & | M12, | |||
real & | M21 | |||
) | const throw () [inline] |
See the documentation for GeodesicLine::ArcPosition.
Definition at line 436 of file GeodesicLine.hpp.
References AZIMUTH, DISTANCE, GenPosition(), GEODESICSCALE, LATITUDE, and LONGITUDE.
void GeographicLib::GeodesicLine::ArcPosition | ( | real | a12, | |
real & | lat2, | |||
real & | lon2, | |||
real & | azi2, | |||
real & | s12, | |||
real & | m12, | |||
real & | M12, | |||
real & | M21 | |||
) | const throw () [inline] |
See the documentation for GeodesicLine::ArcPosition.
Definition at line 449 of file GeodesicLine.hpp.
References AZIMUTH, DISTANCE, GenPosition(), GEODESICSCALE, LATITUDE, LONGITUDE, and REDUCEDLENGTH.
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 throw () |
The general position function. GeodesicLine::Position and GeodesicLine::ArcPosition are defined in terms of this function.
[in] | arcmode | boolean flag determining the meaning of the second parameter; if arcmode is false, then the GeodesicLine object must have been constructed with caps |= GeodesicLine::DISTANCE_IN. |
[in] | s12_a12 | if arcmode is false, this is the distance between point 1 and point 2 (meters); otherwise it is the arc length between point 1 and point 2 (degrees); it can be signed. |
[in] | outmask | a bitor'ed combination of GeodesicLine::mask values specifying which of the following parameters should be set. |
[out] | lat2 | latitude of point 2 (degrees). |
[out] | lon2 | longitude of point 2 (degrees); requires that the GeodesicLine object was constructed with caps |= GeodesicLine::LONGITUDE. |
[out] | azi2 | (forward) azimuth at point 2 (degrees). |
[out] | s12 | distance between point 1 and point 2 (meters); requires that the GeodesicLine object was constructed with caps |= GeodesicLine::DISTANCE. |
[out] | m12 | reduced length of geodesic (meters); requires that the GeodesicLine object was constructed with caps |= GeodesicLine::REDUCEDLENGTH. |
[out] | M12 | geodesic scale of point 2 relative to point 1 (dimensionless); requires that the GeodesicLine object was constructed with caps |= GeodesicLine::GEODESICSCALE. |
[out] | M21 | geodesic scale of point 1 relative to point 2 (dimensionless); requires that the GeodesicLine object was constructed with caps |= GeodesicLine::GEODESICSCALE. |
[out] | S12 | area under the geodesic (meters2); requires that the GeodesicLine object was constructed with caps |= GeodesicLine::AREA. |
The 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.
Definition at line 128 of file GeodesicLine.cpp.
Referenced by ArcPosition(), and Position().
bool GeographicLib::GeodesicLine::Init | ( | ) | const throw () [inline] |
Definition at line 528 of file GeodesicLine.hpp.
Referenced by Azimuth(), EquatorialArc(), EquatorialAzimuth(), GeographicLib::CassiniSoldner::Init(), InverseFlattening(), Latitude(), Longitude(), and MajorRadius().
Math::real GeographicLib::GeodesicLine::Latitude | ( | ) | const throw () [inline] |
Definition at line 533 of file GeodesicLine.hpp.
References Init().
Referenced by GeographicLib::CassiniSoldner::LatitudeOrigin().
Math::real GeographicLib::GeodesicLine::Longitude | ( | ) | const throw () [inline] |
Definition at line 538 of file GeodesicLine.hpp.
References Init().
Referenced by GeographicLib::CassiniSoldner::LongitudeOrigin().
Math::real GeographicLib::GeodesicLine::Azimuth | ( | ) | const throw () [inline] |
Definition at line 543 of file GeodesicLine.hpp.
References Init().
Math::real GeographicLib::GeodesicLine::EquatorialAzimuth | ( | ) | const throw () [inline] |
Definition at line 549 of file GeodesicLine.hpp.
References Init().
Math::real GeographicLib::GeodesicLine::EquatorialArc | ( | ) | const throw () [inline] |
Definition at line 557 of file GeodesicLine.hpp.
References Init().
Math::real GeographicLib::GeodesicLine::MajorRadius | ( | ) | const throw () [inline] |
Definition at line 565 of file GeodesicLine.hpp.
References Init().
Math::real GeographicLib::GeodesicLine::InverseFlattening | ( | ) | const throw () [inline] |
Definition at line 572 of file GeodesicLine.hpp.
References Init().
unsigned GeographicLib::GeodesicLine::Capabilities | ( | ) | const throw () [inline] |
Definition at line 578 of file GeodesicLine.hpp.
bool GeographicLib::GeodesicLine::Capabilities | ( | unsigned | testcaps | ) | const throw () [inline] |
[in] | testcaps | a set of bitor'ed GeodesicLine::mask values. |
Definition at line 584 of file GeodesicLine.hpp.
Math::real GeographicLib::GeodesicLine::Position | ( | real | s12, | |
real & | lat2, | |||
real & | lon2, | |||
real & | azi2, | |||
real & | m12, | |||
bool | arcmode | |||
) | const throw () [inline] |
DEPRECATED. Return the latitude, lat2, longitude, lon2, and forward azimuth, azi2 (degrees) of the point 2 which is a distance, s12 (in meters), from point 1. Also return the reduced length m12 (meters). s12 can be signed. If arcmode (default false) is set to true, s12 is interpreted as the arc length a12 (in degrees) on the auxiliary sphere. Returned value is the arc length a12 (degrees) if arcmode is false, otherwise it is the distance s12 (meters).
Definition at line 604 of file GeodesicLine.hpp.
References ArcPosition(), and Position().
void GeographicLib::GeodesicLine::Scale | ( | real | a12, | |
real & | M12, | |||
real & | M21 | |||
) | const throw () [inline] |
DEPRECATED. Return the scale of the geodesic line extending an arc length a12 (degrees) from point 1 to point 2. M12 (a number) measures the convergence of initially parallel geodesics. It is defined by the following construction: starting at point 1 proceed at azimuth azi1 + 90o a small distance dt; turn -90o and proceed a distance s12 (not the arc length a12); the distance to point 2 is given by M12 dt. M21 is defined analogously.
Definition at line 624 of file GeodesicLine.hpp.
References ArcPosition().
friend class Geodesic [friend] |
Definition at line 81 of file GeodesicLine.hpp.