GeographicLib::JacobiConformal Class Reference

Jacobi's conformal projection of a triaxial ellipsoid. More...

#include <JacobiConformal.hpp>

Public Member Functions
	JacobiConformal (real a, real b, real c)
	JacobiConformal (real a, real b, real c, real ab, real bc)
Math::real	x () const
Math::real	x (real somg, real comg) const
Math::real	x (real omg) const
Math::real	y () const
Math::real	y (real sbet, real cbet) const
Math::real	y (real bet) const

Detailed Description

Jacobi's conformal projection of a triaxial ellipsoid.

NOTE: This is just sample code. It is not part of GeographicLib itself.

This is a conformal projection of the ellipsoid to a plane in which the grid lines are straight; see Jacobi, Vorlesungen über Dynamik, §28. The constructor takes the semi-axes of the ellipsoid (which must be in order). Member functions map the ellipsoidal coordinates ω and β separately to x and y. Jacobi's coordinates have been multiplied by (a²−c²)^1/2 / (2b) so that the customary results are returned in the cases of a sphere or an ellipsoid of revolution.

The ellipsoid is oriented so that the large principal ellipse, \(Z=0\), is the equator, \(\beta=0\), while the small principal ellipse, \(Y=0\), is the prime meridian, \(\omega=0\). The four umbilic points, \(\left|\omega\right| = \left|\beta\right| = \frac12\pi\), lie on middle principal ellipse in the plane \(X=0\).

For more information on this projection, see Jacobi's conformal projection.

Definition at line 44 of file JacobiConformal.hpp.

Constructor & Destructor Documentation

JacobiConformal() [1/2]

GeographicLib::JacobiConformal::JacobiConformal ( real  a, real  b, real  c  )

inline

Constructor for a trixial ellipsoid with semi-axes.

Parameters

[in]	a	the largest semi-axis.
[in]	b	the middle semi-axis.
[in]	c	the smallest semi-axis.

The semi-axes must satisfy a ≥ b ≥ c > 0 and a > c. This form of the constructor cannot be used to specify a sphere (use the next constructor).

Definition at line 64 of file JacobiConformal.hpp.

JacobiConformal() [2/2]

GeographicLib::JacobiConformal::JacobiConformal ( real  a, real  b, real  c, real  ab, real  bc  )

inline

Alternate constructor for a triaxial ellipsoid.

Parameters

[in]	a	the largest semi-axis.
[in]	b	the middle semi-axis.
[in]	c	the smallest semi-axis.
[in]	ab	the relative magnitude of a − b.
[in]	bc	the relative magnitude of b − c.

This form can be used to specify a sphere. The semi-axes must satisfy a ≥ b ≥ c > 0. The ratio ab : bc must equal (a−b) : (b−c) with ab ≥ 0, bc ≥ 0, and ab + bc > 0.

Definition at line 95 of file JacobiConformal.hpp.

Member Function Documentation

x() [1/3]

Math::real GeographicLib::JacobiConformal::x ( ) const

inline

Returns

the quadrant length in the x direction.

Definition at line 117 of file JacobiConformal.hpp.

References GeographicLib::EllipticFunction::Pi(), and GeographicLib::Math::sq().

Referenced by x().

x() [2/3]

Math::real GeographicLib::JacobiConformal::x ( real  somg, real  comg  ) const

inline

The x projection.

Parameters

[in]	somg	sin(ω).
[in]	comg	cos(ω).

Returns

x.

Definition at line 125 of file JacobiConformal.hpp.

References GeographicLib::EllipticFunction::Delta(), GeographicLib::EllipticFunction::Pi(), and GeographicLib::Math::sq().

x() [3/3]

Math::real GeographicLib::JacobiConformal::x ( real  omg ) const

inline

The x projection.

Parameters

[in]

omg

ω (in degrees).

Returns

x (in degrees).

ω must be in [−180°, 180°].

Definition at line 138 of file JacobiConformal.hpp.

References GeographicLib::Math::degree(), GeographicLib::Math::sincosd(), and x().

y() [1/3]

Math::real GeographicLib::JacobiConformal::y ( ) const

inline

Returns

the quadrant length in the y direction.

Definition at line 146 of file JacobiConformal.hpp.

References GeographicLib::EllipticFunction::Pi(), and GeographicLib::Math::sq().

Referenced by y().

y() [2/3]

Math::real GeographicLib::JacobiConformal::y ( real  sbet, real  cbet  ) const

inline

The y projection.

Parameters

[in]	sbet	sin(β).
[in]	cbet	cos(β).

Returns

y.

Definition at line 154 of file JacobiConformal.hpp.

References GeographicLib::EllipticFunction::Delta(), GeographicLib::EllipticFunction::Pi(), and GeographicLib::Math::sq().

y() [3/3]

Math::real GeographicLib::JacobiConformal::y ( real  bet ) const

inline

The y projection.

Parameters

[in]

bet

β (in degrees).

Returns

y (in degrees).

β must be in (−180°, 180°].

Definition at line 167 of file JacobiConformal.hpp.

References GeographicLib::Math::degree(), GeographicLib::Math::sincosd(), and y().

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

• JacobiConformal.hpp