Geodesic calculations More...

#include <Geodesic.hpp>

Collaboration diagram for GeographicLib::Geodesic:

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
Constructor
	Geodesic (real a, real f)
	Constructor for a ellipsoid with.
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 throw ()
	Perform the direct geodesic calculation where the length of the geodesic is specify in terms of distance.
Math::real	Direct (real lat1, real lon1, real azi1, real s12, real &lat2, real &lon2) const throw ()
	See the documentation for Geodesic::Direct.
Math::real	Direct (real lat1, real lon1, real azi1, real s12, real &lat2, real &lon2, real &azi2) const throw ()
	See the documentation for Geodesic::Direct.
Math::real	Direct (real lat1, real lon1, real azi1, real s12, real &lat2, real &lon2, real &azi2, real &m12) const throw ()
	See the documentation for Geodesic::Direct.
Math::real	Direct (real lat1, real lon1, real azi1, real s12, real &lat2, real &lon2, real &azi2, real &M12, real &M21) const throw ()
	See the documentation for Geodesic::Direct.
Math::real	Direct (real lat1, real lon1, real azi1, real s12, real &lat2, real &lon2, real &azi2, real &m12, real &M12, real &M21) const throw ()
	See the documentation for Geodesic::Direct.
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 throw ()
	Perform the direct geodesic calculation where the length of the geodesic is specify in terms of arc length.
void	ArcDirect (real lat1, real lon1, real azi1, real a12, real &lat2, real &lon2) const throw ()
	See the documentation for Geodesic::ArcDirect.
void	ArcDirect (real lat1, real lon1, real azi1, real a12, real &lat2, real &lon2, real &azi2) const throw ()
	See the documentation for Geodesic::ArcDirect.
void	ArcDirect (real lat1, real lon1, real azi1, real a12, real &lat2, real &lon2, real &azi2, real &s12) const throw ()
	See the documentation for Geodesic::ArcDirect.
void	ArcDirect (real lat1, real lon1, real azi1, real a12, real &lat2, real &lon2, real &azi2, real &s12, real &m12) const throw ()
	See the documentation for Geodesic::ArcDirect.
void	ArcDirect (real lat1, real lon1, real azi1, real a12, real &lat2, real &lon2, real &azi2, real &s12, real &M12, real &M21) const throw ()
	See the documentation for Geodesic::ArcDirect.
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 throw ()
	See the documentation for Geodesic::ArcDirect.
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 throw ()
	The general direct geodesic calculation.
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 throw ()
	Perform the inverse geodesic calculation.
Math::real	Inverse (real lat1, real lon1, real lat2, real lon2, real &s12) const throw ()
	See the documentation for Geodesic::Inverse.
Math::real	Inverse (real lat1, real lon1, real lat2, real lon2, real &azi1, real &azi2) const throw ()
	See the documentation for Geodesic::Inverse.
Math::real	Inverse (real lat1, real lon1, real lat2, real lon2, real &s12, real &azi1, real &azi2) const throw ()
	See the documentation for Geodesic::Inverse.
Math::real	Inverse (real lat1, real lon1, real lat2, real lon2, real &s12, real &azi1, real &azi2, real &m12) const throw ()
	See the documentation for Geodesic::Inverse.
Math::real	Inverse (real lat1, real lon1, real lat2, real lon2, real &s12, real &azi1, real &azi2, real &M12, real &M21) const throw ()
	See the documentation for Geodesic::Inverse.
Math::real	Inverse (real lat1, real lon1, real lat2, real lon2, real &s12, real &azi1, real &azi2, real &m12, real &M12, real &M21) const throw ()
	See the documentation for Geodesic::Inverse.
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 throw ()
	The general inverse geodesic calculation.
Interface to GeodesicLine.
GeodesicLine	Line (real lat1, real lon1, real azi1, unsigned caps=ALL) const throw ()
	Set up to compute several points on a singe geodesic.
Inspector functions.
Math::real	MajorRadius () const throw ()
Math::real	Flattening () const throw ()
Math::real	EllipsoidArea () const throw ()
Static Public Attributes
static const Geodesic	WGS84
	A global instantiation of Geodesic with the parameters for the WGS84 ellipsoid.
Private Types
enum	captype { CAP_NONE = 0U, CAP_C1 = 1U<<0, CAP_C1p = 1U<<1, CAP_C2 = 1U<<2, CAP_C3 = 1U<<3, CAP_C4 = 1U<<4, CAP_ALL = 0x1FU, OUT_ALL = 0x7F80U }
typedef Math::real	real
Private Member Functions
void	Lengths (real eps, real sig12, real ssig1, real csig1, real ssig2, real csig2, real cbet1, real cbet2, real &s12s, real &m12a, real &m0, bool scalep, real &M12, real &M21, real C1a[], real C2a[]) const throw ()
real	InverseStart (real sbet1, real cbet1, real sbet2, real cbet2, real lam12, real &salp1, real &calp1, real &salp2, real &calp2, real C1a[], real C2a[]) const throw ()
real	Lambda12 (real sbet1, real cbet1, real sbet2, real cbet2, real salp1, real calp1, real &salp2, real &calp2, real &sig12, real &ssig1, real &csig1, real &ssig2, real &csig2, real &eps, real &domg12, bool diffp, real &dlam12, real C1a[], real C2a[], real C3a[]) const throw ()
void	A3coeff () throw ()
real	A3f (real eps) const throw ()
void	C3coeff () throw ()
void	C3f (real eps, real c[]) const throw ()
void	C4coeff () throw ()
void	C4f (real k2, real c[]) const throw ()
Static Private Member Functions
static real	SinCosSeries (bool sinp, real sinx, real cosx, const real c[], int n) throw ()
static real	AngNormalize (real x) throw ()
static real	AngRound (real x) throw ()
static void	SinCosNorm (real &sinx, real &cosx) throw ()
static real	Astroid (real x, real y) throw ()
static real	A1m1f (real eps) throw ()
static void	C1f (real eps, real c[]) throw ()
static void	C1pf (real eps, real c[]) throw ()
static real	A2m1f (real eps) throw ()
static void	C2f (real eps, real c[]) throw ()
Private Attributes
real	_a
real	_f
real	_f1
real	_e2
real	_ep2
real	_n
real	_b
real	_c2
real	_etol2
real	_A3x [nA3x_]
real	_C3x [nC3x_]
real	_C4x [nC4x_]
Static Private Attributes
static const int	nA1_ = GEOD_ORD
static const int	nC1_ = GEOD_ORD
static const int	nC1p_ = GEOD_ORD
static const int	nA2_ = GEOD_ORD
static const int	nC2_ = GEOD_ORD
static const int	nA3_ = GEOD_ORD
static const int	nA3x_ = nA3_
static const int	nC3_ = GEOD_ORD
static const int	nC3x_ = (nC3_ * (nC3_ - 1)) / 2
static const int	nC4_ = GEOD_ORD
static const int	nC4x_ = (nC4_ * (nC4_ + 1)) / 2
static const unsigned	maxit_ = 50
static const real	tiny_ = sqrt(numeric_limits<real>::min())
static const real	tol0_ = numeric_limits<real>::epsilon()
static const real	tol1_ = 200 * tol0_
static const real	tol2_ = sqrt(numeric_limits<real>::epsilon())
static const real	xthresh_ = 1000 * tol2_
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.)

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 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 provide by Geodesic::ArcDirect. An arc length in excess of 180^o 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^o.

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 the second point is displaced m12 dazi1 in the direction azi2 + 90^o. 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. Consider the quadrilateral bounded by the following lines: the geodesic from point 1 to point 2, the meridian from point 2 to the equator, the equator from lon2 to lon1, the meridian from the equator to point 1. The area of this quadrilateral is represented by S12 with a clockwise traversal of the perimeter counting as a positive area and 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. Let points 1, 2, and 3 all lie on a single geodesic, then

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 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::Geodesic::real [private]

Member Enumeration Documentation

enum GeographicLib::Geodesic::captype [private]

Enumerator:

CAP_NONE
CAP_C1
CAP_C1p
CAP_C2
CAP_C3
CAP_C4
CAP_ALL
OUT_ALL

enum GeographicLib::Geodesic::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.
ALL	All capabilities. Calculate everything.

Constructor & Destructor Documentation

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. If f > 1, set flattening to 1/f.

An exception is thrown if either of the axes of the ellipsoid is non-positive.

Member Function Documentation

Math::real GeographicLib::Geodesic::A1m1f ( real eps ) throw () [static, private]

Math::real GeographicLib::Geodesic::A2m1f ( real eps ) throw () [static, private]

void GeographicLib::Geodesic::A3coeff ( ) throw () [private]

Math::real GeographicLib::Geodesic::A3f ( real eps ) const throw () [private]

static real GeographicLib::Geodesic::AngNormalize ( real x ) throw () [inline, static, private]

static real GeographicLib::Geodesic::AngRound ( real x ) throw () [inline, static, private]

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 throw () `[inline]`

Perform the direct geodesic calculation where the length of the geodesic is specify 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 signed.
[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]; lon1 and azi1 should be in the range [-180, 360]. 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 and writing lat = 90 - eps or -90 + eps and taking the limit eps -> 0 from above. An arc length greater that 180 degrees 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 degrees.)

The following functions are overloaded versions of Geodesic::Direct which omit some of the output parameters.

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

See the documentation for Geodesic::ArcDirect.

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

See the documentation for Geodesic::ArcDirect.

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

See the documentation for Geodesic::ArcDirect.

void GeographicLib::Geodesic::ArcDirect	(	real	lat1,
		real	lon1,
		real	azi1,
		real	a12,
		real &	lat2,
		real &	lon2,
		real &	azi2,
		real &	s12,
		real &	m12
	)		const throw () `[inline]`

See the documentation for Geodesic::ArcDirect.

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 throw () `[inline]`

See the documentation for Geodesic::ArcDirect.

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 throw () `[inline]`

See the documentation for Geodesic::ArcDirect.

Math::real GeographicLib::Geodesic::Astroid	(	real	x,
		real	y
	)		throw () `[static, private]`

void GeographicLib::Geodesic::C1f	(	real	eps,
		real	c[]
	)		throw () `[static, private]`

void GeographicLib::Geodesic::C1pf	(	real	eps,
		real	c[]
	)		throw () `[static, private]`

void GeographicLib::Geodesic::C2f	(	real	eps,
		real	c[]
	)		throw () `[static, private]`

void GeographicLib::Geodesic::C3coeff ( ) throw () [private]

void GeographicLib::Geodesic::C3f	(	real	eps,
		real	c[]
	)		const throw () `[private]`

void GeographicLib::Geodesic::C4coeff ( ) throw () [private]

void GeographicLib::Geodesic::C4f	(	real	k2,
		real	c[]
	)		const throw () `[private]`

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 throw () `[inline]`

Perform the direct geodesic calculation where the length of the geodesic is specify 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 signed.
[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]; lon1 and azi1 should be in the range [-180, 360]. 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 and writing lat = 90 - eps or -90 + eps and taking the limit eps -> 0 from above. An arc length greater that 180 degrees 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 degrees.)

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.

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

See the documentation for Geodesic::Direct.

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

See the documentation for Geodesic::Direct.

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

See the documentation for Geodesic::Direct.

Math::real GeographicLib::Geodesic::Direct	(	real	lat1,
		real	lon1,
		real	azi1,
		real	s12,
		real &	lat2,
		real &	lon2,
		real &	azi2,
		real &	M12,
		real &	M21
	)		const throw () `[inline]`

See the documentation for Geodesic::Direct.

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 throw () `[inline]`

See the documentation for Geodesic::Direct.

Math::real GeographicLib::Geodesic::EllipsoidArea ( ) const throw () [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.

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

Returns:: f the flattening of the ellipsoid. This is the value used in the constructor.

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 throw ()

The general direct geodesic calculation.

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 second parameter.
[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 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

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

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.

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 throw ()

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

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

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

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 throw () `[inline]`

Perform the inverse geodesic calculation.

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]; lon1 and lon2 should be in the range [-180, 360]. 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 and writing lat = 90 - eps or -90 + eps and taking the limit eps -> 0 from above. If the routine fails to converge, then all the requested outputs are set to Math::NaN(). (Test for such results with Math::isnan.) This is not expected to happen with ellipsoidal models of the earth; please report all cases where this occurs.

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.

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

See the documentation for Geodesic::Inverse.

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

See the documentation for Geodesic::Inverse.

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

See the documentation for Geodesic::Inverse.

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

See the documentation for Geodesic::Inverse.

Math::real GeographicLib::Geodesic::Inverse	(	real	lat1,
		real	lon1,
		real	lat2,
		real	lon2,
		real &	s12,
		real &	azi1,
		real &	azi2,
		real &	M12,
		real &	M21
	)		const throw () `[inline]`

See the documentation for Geodesic::Inverse.

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 throw () `[inline]`

See the documentation for Geodesic::Inverse.

Math::real GeographicLib::Geodesic::InverseStart	(	real	sbet1,
		real	cbet1,
		real	sbet2,
		real	cbet2,
		real	lam12,
		real &	salp1,
		real &	calp1,
		real &	salp2,
		real &	calp2,
		real	C1a[],
		real	C2a[]
	)		const throw () `[private]`

Math::real GeographicLib::Geodesic::Lambda12	(	real	sbet1,
		real	cbet1,
		real	sbet2,
		real	cbet2,
		real	salp1,
		real	calp1,
		real &	salp2,
		real &	calp2,
		real &	sig12,
		real &	ssig1,
		real &	csig1,
		real &	ssig2,
		real &	csig2,
		real &	eps,
		real &	domg12,
		bool	diffp,
		real &	dlam12,
		real	C1a[],
		real	C2a[],
		real	C3a[]
	)		const throw () `[private]`

void GeographicLib::Geodesic::Lengths	(	real	eps,
		real	sig12,
		real	ssig1,
		real	csig1,
		real	ssig2,
		real	csig2,
		real	cbet1,
		real	cbet2,
		real &	s12s,
		real &	m12a,
		real &	m0,
		bool	scalep,
		real &	M12,
		real &	M21,
		real	C1a[],
		real	C2a[]
	)		const throw () `[private]`

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

Set up to compute several points on a singe 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 GeodesicLib::Position.

lat1 should be in the range [-90, 90]; lon1 and azi1 should be in the range [-180, 360].

The Geodesic::mask values are

caps |= Geodesic::LATITUDE for the latitude lat2; this is added automatically
caps |= Geodesic::LONGITUDE for the latitude lon2
caps |= Geodesic::AZIMUTH for the latitude azi2; this is added automatically
caps |= Geodesic::DISTANCE for the distance s12
caps |= Geodesic::REDUCEDLENGTH for the reduced length m12
caps |= Geodesic::GEODESICSCALE for the geodesic scales M12 and M21
caps |= Geodesic::AREA for the area S12
caps |= Geodesic::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 Geodesic::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.

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

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

static void GeographicLib::Geodesic::SinCosNorm	(	real &	sinx,
		real &	cosx
	)		throw () `[inline, static, private]`

Math::real GeographicLib::Geodesic::SinCosSeries	(	bool	sinp,
		real	sinx,
		real	cosx,
		const real	c[],
		int	n
	)		throw () `[static, private]`

Friends And Related Function Documentation

friend class GeodesicLine [friend]

Member Data Documentation

real GeographicLib::Geodesic::_a [private]

real GeographicLib::Geodesic::_A3x[nA3x_] [private]

real GeographicLib::Geodesic::_b [private]

real GeographicLib::Geodesic::_c2 [private]

real GeographicLib::Geodesic::_C3x[nC3x_] [private]

real GeographicLib::Geodesic::_C4x[nC4x_] [private]

real GeographicLib::Geodesic::_e2 [private]

real GeographicLib::Geodesic::_ep2 [private]

real GeographicLib::Geodesic::_etol2 [private]

real GeographicLib::Geodesic::_f [private]

real GeographicLib::Geodesic::_f1 [private]

real GeographicLib::Geodesic::_n [private]

const unsigned GeographicLib::Geodesic::maxit_ = 50 [static, private]

const int GeographicLib::Geodesic::nA1_ = GEOD_ORD [static, private]

const int GeographicLib::Geodesic::nA2_ = GEOD_ORD [static, private]

const int GeographicLib::Geodesic::nA3_ = GEOD_ORD [static, private]

const int GeographicLib::Geodesic::nA3x_ = nA3_ [static, private]

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

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

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

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

const int GeographicLib::Geodesic::nC3x_ = (nC3_ * (nC3_ - 1)) / 2 [static, private]

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

const int GeographicLib::Geodesic::nC4x_ = (nC4_ * (nC4_ + 1)) / 2 [static, private]

const Math::real GeographicLib::Geodesic::tiny_ = sqrt(numeric_limits<real>::min()) [static, private]

const Math::real GeographicLib::Geodesic::tol0_ = numeric_limits<real>::epsilon() [static, private]

const Math::real GeographicLib::Geodesic::tol1_ = 200 * tol0_ [static, private]

const Math::real GeographicLib::Geodesic::tol2_ = sqrt(numeric_limits<real>::epsilon()) [static, private]

const Geodesic GeographicLib::Geodesic::WGS84 [static]

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

const Math::real GeographicLib::Geodesic::xthresh_ = 1000 * tol2_ [static, private]

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

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

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Public Member Functions

Static Public Attributes

Private Types

Private Member Functions

Static Private Member Functions

Private Attributes

Static Private Attributes

Friends

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Friends And Related Function Documentation

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