GeographicLib
1.21
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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 | Flattening () const throw () |
unsigned | Capabilities () const throw () |
bool | Capabilities (unsigned testcaps) 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.
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 are described in
For more information on geodesics see Geodesics on the ellipsoid.
Example of use:
// Example of using the GeographicLib::GeodesicLine class // $Id: df5c5ffe6534d46e343544430de8c13fc8119bfb $ #include <iostream> #include <exception> #include <cmath> #include <iomanip> #include <GeographicLib/Geodesic.hpp> #include <GeographicLib/GeodesicLine.hpp> #include <GeographicLib/Constants.hpp> using namespace std; using namespace GeographicLib; int main() { try { // Print waypoints between JFK and SIN Geodesic geod(Constants::WGS84_a(), Constants::WGS84_f()); // Alternatively: const Geodesic& geod = Geodesic::WGS84; double lat1 = 40.640, lon1 = -73.779, // JFK lat2 = 1.359, lon2 = 103.989; // SIN double s12, azi1, azi2, a12 = geod.Inverse(lat1, lon1, lat2, lon2, s12, azi1, azi2); const GeographicLib::GeodesicLine line(geod, lat1, lon1, azi1); // Alternatively // const GeographicLib::GeodesicLine line = geod.Line(lat1, lon1, azi1); double ds = 500e3; // Nominal distance between points = 500 km int num = int(ceil(s12 / ds)); // The number of intervals cout << fixed << setprecision(3); { // Use intervals of equal length double ds = s12 / 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 = a12 / 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; } return 0; }
Geod is a command-line utility providing access to the functionality of Geodesic and GeodesicLine.
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.
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 96 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 azimuth 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. |
lat1 should be in the range [-90, 90]; lon1 and azi1 should be in the range [-180, 360].
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 41 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 207 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 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 252 of file GeodesicLine.hpp.
Referenced by GeographicLib::Gnomonic::Reverse().
Math::real GeographicLib::GeodesicLine::Position | ( | real | s12, |
real & | lat2, | ||
real & | lon2 | ||
) | const throw () [inline] |
See the documentation for GeodesicLine::Position.
Definition at line 266 of file GeodesicLine.hpp.
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 276 of file GeodesicLine.hpp.
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 287 of file GeodesicLine.hpp.
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 299 of file GeodesicLine.hpp.
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 312 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 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. |
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 365 of file GeodesicLine.hpp.
void GeographicLib::GeodesicLine::ArcPosition | ( | real | a12, |
real & | lat2, | ||
real & | lon2 | ||
) | const throw () [inline] |
See the documentation for GeodesicLine::ArcPosition.
Definition at line 377 of file GeodesicLine.hpp.
void GeographicLib::GeodesicLine::ArcPosition | ( | real | a12, |
real & | lat2, | ||
real & | lon2, | ||
real & | azi2 | ||
) | const throw () [inline] |
See the documentation for GeodesicLine::ArcPosition.
Definition at line 388 of file GeodesicLine.hpp.
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 400 of file GeodesicLine.hpp.
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 411 of file GeodesicLine.hpp.
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 423 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 throw () [inline] |
See the documentation for GeodesicLine::ArcPosition.
Definition at line 436 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 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 129 of file GeodesicLine.cpp.
Referenced by GeographicLib::CassiniSoldner::Forward().
bool GeographicLib::GeodesicLine::Init | ( | ) | const throw () [inline] |
Definition at line 515 of file GeodesicLine.hpp.
Math::real GeographicLib::GeodesicLine::Latitude | ( | ) | const throw () [inline] |
Definition at line 520 of file GeodesicLine.hpp.
Math::real GeographicLib::GeodesicLine::Longitude | ( | ) | const throw () [inline] |
Definition at line 526 of file GeodesicLine.hpp.
Math::real GeographicLib::GeodesicLine::Azimuth | ( | ) | const throw () [inline] |
Definition at line 532 of file GeodesicLine.hpp.
Math::real GeographicLib::GeodesicLine::EquatorialAzimuth | ( | ) | const throw () [inline] |
Definition at line 539 of file GeodesicLine.hpp.
Math::real GeographicLib::GeodesicLine::EquatorialArc | ( | ) | const throw () [inline] |
Definition at line 548 of file GeodesicLine.hpp.
Math::real GeographicLib::GeodesicLine::MajorRadius | ( | ) | const throw () [inline] |
Definition at line 557 of file GeodesicLine.hpp.
Math::real GeographicLib::GeodesicLine::Flattening | ( | ) | const throw () [inline] |
Definition at line 564 of file GeodesicLine.hpp.
unsigned GeographicLib::GeodesicLine::Capabilities | ( | ) | const throw () [inline] |
Definition at line 580 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 586 of file GeodesicLine.hpp.
friend class Geodesic [friend] |
Definition at line 62 of file GeodesicLine.hpp.