Divided differences of auxiliary latitudes. More...

#include <GeographicLib/DAuxLatitude.hpp>

Inheritance diagram for GeographicLib::DAuxLatitude:

Public Member Functions
	DAuxLatitude (real a, real f)

Math::real	DConvert (int auxin, int auxout, const AuxAngle &zeta1, const AuxAngle &zeta2) const

Math::real	DParametric (const AuxAngle &phi1, const AuxAngle &phi2) const

Math::real	DRectifying (const AuxAngle &phi1, const AuxAngle &phi2) const

Math::real	DIsometric (const AuxAngle &phi1, const AuxAngle &phi2) const

Public Member Functions inherited from GeographicLib::AuxLatitude
	AuxLatitude (real a, real f)

AuxAngle	Convert (int auxin, int auxout, const AuxAngle &zeta, bool exact=false) const

Math::real	Convert (int auxin, int auxout, real zeta, bool exact=false) const

AuxAngle	ToAuxiliary (int auxout, const AuxAngle &phi, real *diff=nullptr) const

AuxAngle	FromAuxiliary (int auxin, const AuxAngle &zeta, int *niter=nullptr) const

Math::real	RectifyingRadius (bool exact=false) const

Math::real	AuthalicRadiusSquared (bool exact=false) const

Math::real	EquatorialRadius () const

Math::real	PolarSemiAxis () const

Math::real	Flattening () const

Static Public Member Functions
static Math::real	DClenshaw (bool sinp, real Delta, real szeta1, real czeta1, real szeta2, real czeta2, const real c[], int K)

static Math::real	Dlam (real x, real y)

static Math::real	Dp0Dpsi (real x, real y)

Static Public Member Functions inherited from GeographicLib::AuxLatitude
static AuxLatitude	axes (real a, real b)

static Math::real	Clenshaw (bool sinp, real szeta, real czeta, const real c[], int K)

static const AuxLatitude &	WGS84 ()

Additional Inherited Members
Public Types inherited from GeographicLib::AuxLatitude
enum	aux { GEOGRAPHIC , PARAMETRIC , GEOCENTRIC , RECTIFYING , CONFORMAL , AUTHALIC , AUXNUMBER , PHI , BETA , THETA , MU , CHI , XI , COMMON , GEODETIC , REDUCED }

Static Public Attributes inherited from GeographicLib::AuxLatitude
static const int	Lmax

Protected Member Functions inherited from GeographicLib::AuxLatitude
AuxAngle	Parametric (const AuxAngle &phi, real *diff=nullptr) const

AuxAngle	Geocentric (const AuxAngle &phi, real *diff=nullptr) const

AuxAngle	Rectifying (const AuxAngle &phi, real *diff=nullptr) const

AuxAngle	Conformal (const AuxAngle &phi, real *diff=nullptr) const

AuxAngle	Authalic (const AuxAngle &phi, real *diff=nullptr) const

Detailed Description

Divided differences of auxiliary latitudes.

This class computed the divided differences of auxiliary latitudes and some other divided differences needed to support rhumb line calculations.

Definition at line 23 of file DAuxLatitude.hpp.

Constructor & Destructor Documentation

◆ DAuxLatitude()

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

inline

Constructor

Parameters

[in]	a	equatorial radius.
[in]	f	flattening of ellipsoid. Setting f = 0 gives a sphere. Negative f gives a prolate ellipsoid.

Exceptions

GeographicErr if a or (1 − f) a is not positive.

Definition at line 37 of file DAuxLatitude.hpp.

Member Function Documentation

◆ DConvert()

Math::real GeographicLib::DAuxLatitude::DConvert	(	int	auxin,
		int	auxout,
		const AuxAngle &	zeta1,
		const AuxAngle &	zeta2
	)		const

The divided difference of one auxiliary latitude with respect to another.

Parameters

[in]	auxin	an AuxLatitude::aux indicating the type of auxiliary latitude zeta.
[in]	auxout	an AuxLatitude::aux indicating the type of auxiliary latitude eta.
[in]	zeta1	the first of the input auxiliary latitudeas.
[in]	zeta2	the second of the input auxiliary latitude.

Returns: the divided difference (eta2 - eta1) / (zeta2 - zeta1).

Note: This routine uses the series method.

In the expression for the divided difference above, the angle quantities should be understood as the conventional measure of angle (either in radians or in degrees).

The Fourier coefficients for a specific auxin and auxout are computed and saved on the first call; the saved coefficients are used on subsequent calls. The series method is accurate for abs(f) ≤ 1/150.

Definition at line 195 of file DAuxLatitude.cpp.

References DClenshaw(), GeographicLib::AuxLatitude::Lmax, GeographicLib::AuxAngle::normalized(), GeographicLib::AuxAngle::radians(), GeographicLib::AuxAngle::x(), and GeographicLib::AuxAngle::y().

Referenced by GeographicLib::Rhumb::GenInverse(), and GeographicLib::RhumbLine::GenPosition().

◆ DParametric()

Math::real GeographicLib::DAuxLatitude::DParametric	(	const AuxAngle &	phi1,
		const AuxAngle &	phi2
	)		const

The divided difference of the parametric latitude with respect to the geographic latitude.

Parameters

[in]	phi1	the first geographic latitude as an AuxAngle.
[in]	phi2	the second geographic latitude as an AuxAngle.

Returns: the divided difference (beta2 - beta1) / (phi2 - phi1), where beta is the parametric latitude.

Note: This routine uses the exact formulas and is valid for arbitrary latitude.

Definition at line 46 of file DAuxLatitude.cpp.

References GeographicLib::AuxAngle::tan().

Referenced by DRectifying().

◆ DRectifying()

Math::real GeographicLib::DAuxLatitude::DRectifying	(	const AuxAngle &	phi1,
		const AuxAngle &	phi2
	)		const

The divided difference of the rectifying latitude with respect to the geographic latitude.

Parameters

[in]	phi1	the first geographic latitude as an AuxAngle.
[in]	phi2	the second geographic latitude as an AuxAngle.

Returns: the divided difference (mu2 - mu1) / (phi2 - phi1), where mu is the rectifying latitude.

Note: This routine uses the exact formulas and is valid for arbitrary latitude.

Definition at line 25 of file DAuxLatitude.cpp.

References DParametric(), GeographicLib::AuxLatitude::Parametric(), GeographicLib::AuxAngle::radians(), GeographicLib::AuxLatitude::Rectifying(), GeographicLib::AuxLatitude::RectifyingRadius(), GeographicLib::Math::sq(), and GeographicLib::AuxAngle::tan().

Referenced by GeographicLib::Rhumb::GenInverse(), and GeographicLib::RhumbLine::GenPosition().

◆ DIsometric()

Math::real GeographicLib::DAuxLatitude::DIsometric	(	const AuxAngle &	phi1,
		const AuxAngle &	phi2
	)		const

The divided difference of the isometric latitude with respect to the geographic latitude.

Parameters

[in]	phi1	the first geographic latitude as an AuxAngle.
[in]	phi2	the second geographic latitude as an AuxAngle.

Returns: the divided difference (psi2 - psi1) / (phi2 - phi1), where psi = asinh( tan(chi) ) is the isometric latitude and chi is the conformal latitude.

Note: This routine uses the exact formulas and is valid for arbitrary latitude.

Definition at line 183 of file DAuxLatitude.cpp.

References GeographicLib::AuxAngle::tan().

Referenced by GeographicLib::Rhumb::GenInverse(), and GeographicLib::RhumbLine::GenPosition().

◆ DClenshaw()

Math::real GeographicLib::DAuxLatitude::DClenshaw	(	bool	sinp,
		real	Delta,
		real	szeta1,
		real	czeta1,
		real	szeta2,
		real	czeta2,
		const real	c[],
		int	K
	)

static

The divided difference of AuxLatitude::Clenshaw.

Parameters

[in]	sinp	if true sum the sine series, else sum the cosine series.
[in]	Delta	either 1 or (zeta2 - zeta1) in radians.
[in]	szeta1	sin(zeta1).
[in]	czeta1	cos(zeta1).
[in]	szeta2	sin(zeta2).
[in]	czeta2	cos(zeta2).
[in]	c	the array of coefficients.
[in]	K	the number of coefficients.

Returns: the divided difference.

The result is

   ( AuxLatitude::Clenshaw(sinp, szeta2, czeta2, c, K) -
     AuxLatitude::Clenshaw(sinp, szeta1, czeta1, c, K) ) / Delta

Warning: Delta must be either 1 or (zeta2 - zeta1); other values will return nonsense.

Definition at line 211 of file DAuxLatitude.cpp.

Referenced by DConvert().

◆ Dlam()

static Math::real GeographicLib::DAuxLatitude::Dlam	(	real	x,
		real	y
	)

inlinestatic

The divided difference of the isometric latitude with respect to the conformal latitude.

Parameters

[in]	x	tan(chi1).
[in]	y	tan(chi2).

Returns: the divided difference (psi2 - psi1) / (chi2 - chi1), where psi = asinh( tan(chi) ).

Note: This parameters for this routine are the tangents of conformal latitude.

This routine computes Dasinh(x, y) / Datan(x, y).

Definition at line 144 of file DAuxLatitude.hpp.

Referenced by GeographicLib::Rhumb::GenInverse(), and GeographicLib::RhumbLine::GenPosition().

◆ Dp0Dpsi()

static Math::real GeographicLib::DAuxLatitude::Dp0Dpsi	(	real	x,
		real	y
	)

inlinestatic

The divided difference of the spherical rhumb area term with respect to the isometric latitude.

Parameters

[in]	x	tan(chi1).
[in]	y	tan(chi2).

Returns: the divided difference (p0(chi2) - p0(chi1)) / (psi2 - psi1), where p0(chi) = log( sec(chi) ) and psi = asinh( tan(chi) ).

Note: This parameters for this routine are the tangents of conformal latitude.

Definition at line 165 of file DAuxLatitude.hpp.

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

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ DAuxLatitude()

Member Function Documentation

◆ DConvert()

◆ DParametric()

◆ DRectifying()

◆ DIsometric()

◆ DClenshaw()

◆ Dlam()

◆ Dp0Dpsi()