A geodesic line. More...

#include <GeodesicLine.hpp>

Public Types
enum	mask { NONE, LATITUDE, LONGITUDE, AZIMUTH, DISTANCE, DISTANCE_IN, REDUCEDLENGTH, GEODESICSCALE, AREA, ALL }
	Bit masks for what calculations to do. More...
Public Member Functions
Constructors
	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).
	GeodesicLine () throw ()
	A default constructor.
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 ()
	Compute the position of point 2 which is a distance s12 (meters) from point 1.
Math::real	Position (real s12, real &lat2, real &lon2) const throw ()
	See the documentation for GeodesicLine::Position.
Math::real	Position (real s12, real &lat2, real &lon2, real &azi2) const throw ()
	See the documentation for GeodesicLine::Position.
Math::real	Position (real s12, real &lat2, real &lon2, real &azi2, real &m12) const throw ()
	See the documentation for GeodesicLine::Position.
Math::real	Position (real s12, real &lat2, real &lon2, real &azi2, real &M12, real &M21) const throw ()
	See the documentation for GeodesicLine::Position.
Math::real	Position (real s12, real &lat2, real &lon2, real &azi2, real &m12, real &M12, real &M21) const throw ()
	See the documentation for GeodesicLine::Position.
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 ()
	Compute the position of point 2 which is an arc length a12 (degrees) from point 1.
void	ArcPosition (real a12, real &lat2, real &lon2) const throw ()
	See the documentation for GeodesicLine::ArcPosition.
void	ArcPosition (real a12, real &lat2, real &lon2, real &azi2) const throw ()
	See the documentation for GeodesicLine::ArcPosition.
void	ArcPosition (real a12, real &lat2, real &lon2, real &azi2, real &s12) const throw ()
	See the documentation for GeodesicLine::ArcPosition.
void	ArcPosition (real a12, real &lat2, real &lon2, real &azi2, real &s12, real &m12) const throw ()
	See the documentation for GeodesicLine::ArcPosition.
void	ArcPosition (real a12, real &lat2, real &lon2, real &azi2, real &s12, real &M12, real &M21) const throw ()
	See the documentation for GeodesicLine::ArcPosition.
void	ArcPosition (real a12, real &lat2, real &lon2, real &azi2, real &s12, real &m12, real &M12, real &M21) const throw ()
	See the documentation for GeodesicLine::ArcPosition.
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 ()
	The general position function.
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 ()
Private Types
enum	captype { CAP_NONE = Geodesic::CAP_NONE, CAP_C1 = Geodesic::CAP_C1, CAP_C1p = Geodesic::CAP_C1p, CAP_C2 = Geodesic::CAP_C2, CAP_C3 = Geodesic::CAP_C3, CAP_C4 = Geodesic::CAP_C4, CAP_ALL = Geodesic::CAP_ALL, OUT_ALL = Geodesic::OUT_ALL }
typedef Math::real	real
Private Attributes
real	_lat1
real	_lon1
real	_azi1
real	_a
real	_f
real	_b
real	_c2
real	_f1
real	_salp0
real	_calp0
real	_k2
real	_salp1
real	_calp1
real	_ssig1
real	_csig1
real	_stau1
real	_ctau1
real	_somg1
real	_comg1
real	_A1m1
real	_A2m1
real	_A3c
real	_B11
real	_B21
real	_B31
real	_A4
real	_B41
real	_C1a [nC1_+1]
real	_C1pa [nC1p_+1]
real	_C2a [nC2_+1]
real	_C3a [nC3_]
real	_C4a [nC4_]
unsigned	_caps
Static Private Attributes
static const int	nC1_ = Geodesic::nC1_
static const int	nC1p_ = Geodesic::nC1p_
static const int	nC2_ = Geodesic::nC2_
static const int	nC3_ = Geodesic::nC3_
static const int	nC4_ = Geodesic::nC4_
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. 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

C. F. F. Karney, Geodesics on an ellipsoid of revolution, Feb. 2011; preprint arXiv:1102.1215v1.
C. F. F. Karney, Algorithms for geodesics, Sept. 2011; preprint arxiv:1109.4448.

For more information on geodesics see geodesic.

Example of use:

Geod is a command-line utility providing access to the functionality of Geodesic and GeodesicLine.

Member Typedef Documentation

typedef Math::real GeographicLib::GeodesicLine::real [private]

Member Enumeration Documentation

enum GeographicLib::GeodesicLine::captype [private]

Enumerator:

CAP_NONE
CAP_C1
CAP_C1p
CAP_C2
CAP_C3
CAP_C4
CAP_ALL
OUT_ALL

enum GeographicLib::GeodesicLine::mask

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.
ALL	All capabilities. Calculate everything.

Constructor & Destructor Documentation

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).

Parameters:

[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

caps |= GeodesicLine::LATITUDE for the latitude lat2; this is added automatically
caps |= GeodesicLine::LONGITUDE for the latitude lon2
caps |= GeodesicLine::AZIMUTH for the latitude azi2; this is added automatically
caps |= GeodesicLine::DISTANCE for the distance s12
caps |= GeodesicLine::REDUCEDLENGTH for the reduced length m12
caps |= GeodesicLine::GEODESICSCALE for the geodesic scales M12 and M21
caps |= GeodesicLine::AREA for the area S12
caps |= GeodesicLine::DISTANCE_IN permits the length of the geodesic to be given in terms of s12; without this capability the length can only be specified in terms of arc length.

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.

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.

Member Function Documentation

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.

Parameters:

[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.

void GeographicLib::GeodesicLine::ArcPosition	(	real	a12,
		real &	lat2,
		real &	lon2
	)		const throw () `[inline]`

See the documentation for GeodesicLine::ArcPosition.

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

See the documentation for GeodesicLine::ArcPosition.

void GeographicLib::GeodesicLine::ArcPosition	(	real	a12,
		real &	lat2,
		real &	lon2,
		real &	azi2,
		real &	s12
	)		const throw () `[inline]`

See the documentation for GeodesicLine::ArcPosition.

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.

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.

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.

Math::real GeographicLib::GeodesicLine::Azimuth ( ) const throw () [inline]

Returns:: azi1 the azimuth (degrees) of the geodesic line at point 1.

unsigned GeographicLib::GeodesicLine::Capabilities ( ) const throw () [inline]

Returns:: caps the computational capabilities that this object was constructed with. LATITUDE and AZIMUTH are always included.

bool GeographicLib::GeodesicLine::Capabilities ( unsigned testcaps ) const throw () [inline]

Parameters:

[in] testcaps a set of bitor'ed GeodesicLine::mask values.

Returns:: true if the GeodesicLine object has all these capabilities.

Math::real GeographicLib::GeodesicLine::EquatorialArc ( ) const throw () [inline]

Returns:: a1 the arc length (degrees) between the northward equatorial crossing and point 1.

Math::real GeographicLib::GeodesicLine::EquatorialAzimuth ( ) const throw () [inline]

Returns:: azi0 the azimuth (degrees) of the geodesic line as it crosses the equator in a northward direction.

Math::real GeographicLib::GeodesicLine::Flattening ( ) const throw () [inline]

Returns:: f the flattening of the ellipsoid. This is the value inherited from the Geodesic object used in the constructor.

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.

Parameters:

[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.

Returns:: a12 arc length of between point 1 and point 2 (degrees).

The GeodesicLine::mask values possible for outmask are

outmask |= GeodesicLine::LATITUDE for the latitude lat2.
outmask |= GeodesicLine::LONGITUDE for the latitude lon2.
outmask |= GeodesicLine::AZIMUTH for the latitude azi2.
outmask |= GeodesicLine::DISTANCE for the distance s12.
outmask |= GeodesicLine::REDUCEDLENGTH for the reduced length m12.
outmask |= GeodesicLine::GEODESICSCALE for the geodesic scales M12 and M21.
outmask |= GeodesicLine::AREA for the area S12.

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.

bool GeographicLib::GeodesicLine::Init ( ) const throw () [inline]

Returns:: true if the object has been initialized.

Math::real GeographicLib::GeodesicLine::Latitude ( ) const throw () [inline]

Returns:: lat1 the latitude of point 1 (degrees).

Math::real GeographicLib::GeodesicLine::Longitude ( ) const throw () [inline]

Returns:: lon1 the longitude of point 1 (degrees).

Math::real GeographicLib::GeodesicLine::MajorRadius ( ) const throw () [inline]

Returns:: a the equatorial radius of the ellipsoid (meters). This is the value inherited from the Geodesic object used in the constructor.

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.

Parameters:

[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.

Returns:: a12 arc length of between point 1 and 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.

Math::real GeographicLib::GeodesicLine::Position	(	real	s12,
		real &	lat2,
		real &	lon2
	)		const throw () `[inline]`

See the documentation for GeodesicLine::Position.

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

See the documentation for GeodesicLine::Position.

Math::real GeographicLib::GeodesicLine::Position	(	real	s12,
		real &	lat2,
		real &	lon2,
		real &	azi2,
		real &	m12
	)		const throw () `[inline]`

See the documentation for GeodesicLine::Position.

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.

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.

Friends And Related Function Documentation

friend class Geodesic [friend]

Member Data Documentation

real GeographicLib::GeodesicLine::_a [private]

real GeographicLib::GeodesicLine::_A1m1 [private]

real GeographicLib::GeodesicLine::_A2m1 [private]

real GeographicLib::GeodesicLine::_A3c [private]

real GeographicLib::GeodesicLine::_A4 [private]

real GeographicLib::GeodesicLine::_azi1 [private]

real GeographicLib::GeodesicLine::_b [private]

real GeographicLib::GeodesicLine::_B11 [private]

real GeographicLib::GeodesicLine::_B21 [private]

real GeographicLib::GeodesicLine::_B31 [private]

real GeographicLib::GeodesicLine::_B41 [private]

real GeographicLib::GeodesicLine::_C1a[nC1_+1] [private]

real GeographicLib::GeodesicLine::_C1pa[nC1p_+1] [private]

real GeographicLib::GeodesicLine::_c2 [private]

real GeographicLib::GeodesicLine::_C2a[nC2_+1] [private]

real GeographicLib::GeodesicLine::_C3a[nC3_] [private]

real GeographicLib::GeodesicLine::_C4a[nC4_] [private]

real GeographicLib::GeodesicLine::_calp0 [private]

real GeographicLib::GeodesicLine::_calp1 [private]

unsigned GeographicLib::GeodesicLine::_caps [private]

real GeographicLib::GeodesicLine::_comg1 [private]

real GeographicLib::GeodesicLine::_csig1 [private]

real GeographicLib::GeodesicLine::_ctau1 [private]

real GeographicLib::GeodesicLine::_f [private]

real GeographicLib::GeodesicLine::_f1 [private]

real GeographicLib::GeodesicLine::_k2 [private]

real GeographicLib::GeodesicLine::_lat1 [private]

real GeographicLib::GeodesicLine::_lon1 [private]

real GeographicLib::GeodesicLine::_salp0 [private]

real GeographicLib::GeodesicLine::_salp1 [private]

real GeographicLib::GeodesicLine::_somg1 [private]

real GeographicLib::GeodesicLine::_ssig1 [private]

real GeographicLib::GeodesicLine::_stau1 [private]

const int GeographicLib::GeodesicLine::nC1_ = Geodesic::nC1_ [static, private]

const int GeographicLib::GeodesicLine::nC1p_ = Geodesic::nC1p_ [static, private]

const int GeographicLib::GeodesicLine::nC2_ = Geodesic::nC2_ [static, private]

const int GeographicLib::GeodesicLine::nC3_ = Geodesic::nC3_ [static, private]

const int GeographicLib::GeodesicLine::nC4_ = Geodesic::nC4_ [static, private]

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

/home/cube/development/c/updraft/Updraft/src/libraries/GeographicLib/GeodesicLine.hpp
/home/cube/development/c/updraft/Updraft/src/libraries/GeographicLib/GeodesicLine.cpp

Public Types

Public Member Functions

Private Types

Private Attributes

Static Private Attributes

Friends

Detailed Description

Member Typedef Documentation

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation