GeographicLib  1.45
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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 (a2c2)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 41 of file JacobiConformal.hpp.

Constructor & Destructor Documentation

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

Constructor for a trixial ellipsoid with semi-axes

Parameters
[in]athe largest semi-axis.
[in]bthe middle semi-axis.
[in]cthe smallest semi-axis.

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

Definition at line 59 of file JacobiConformal.hpp.

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

Alternate constructor for a triaxial ellipsoid.

Parameters
[in]athe largest semi-axis.
[in]bthe middle semi-axis.
[in]cthe smallest semi-axis.
[in]abthe relative magnitude of ab.
[in]bcthe relative magnitude of bc.

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

Definition at line 88 of file JacobiConformal.hpp.

Member Function Documentation

Math::real GeographicLib::JacobiConformal::x ( ) const
inline
Returns
the quadrant length in the x direction

Definition at line 108 of file JacobiConformal.hpp.

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

Referenced by x().

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

The x projection

Parameters
[in]somgsin(ω)
[in]comgcos(ω)
Returns
x

Definition at line 116 of file JacobiConformal.hpp.

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

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

The x projection

Parameters
[in]omgω (in degrees)
Returns
x (in degrees)

ω must be in (−180°, 180°].

Definition at line 129 of file JacobiConformal.hpp.

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

Math::real GeographicLib::JacobiConformal::y ( ) const
inline
Returns
the quadrant length in the y direction

Definition at line 137 of file JacobiConformal.hpp.

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

Referenced by y().

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

The y projection

Parameters
[in]sbetsin(β)
[in]cbetcos(β)
Returns
y

Definition at line 145 of file JacobiConformal.hpp.

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

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

The y projection

Parameters
[in]betβ (in degrees)
Returns
y (in degrees)

β must be in (−180°, 180°].

Definition at line 158 of file JacobiConformal.hpp.

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


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