al::SphericalHarmonic< L_MAX > Class Template Reference

Spherical harmonic evaluator using cached coefficients. More...

#include <C:/Users/Andres/source/repos/casm_viewer/external/tinc/external/allolib/include/al/math/al_Spherical.hpp>

Public Member Functions
template<class T >
Complex< T >	operator() (int l, int m, const Complex< T > &ctheta, const Complex< T > &cphi) const
	Evaluate spherical harmonic. More...

Static Public Member Functions
template<class T >
static Complex< T >	expim (int m, const Complex< T > &ctheta)
static double	coef (int l, int m)
	Get normalization coefficient.
static const double &	coefTab (int l, int m)
	Get normalization coefficient (tabulated)
static double	coefCalc (int l, int m)
	Get normalization coefficient (calculated)

Detailed Description

template<int L_MAX = 16>
class al::SphericalHarmonic< L_MAX >

Spherical harmonic evaluator using cached coefficients.

Spherical harmonics are solutions to Laplace's differential equation on the surface of a 2-sphere. The solutions are complex functions parameterized by two integers, l and m, and two angles defining an orientation in space. The l number determines the number of nodal lines (circles with zero magnitude) and m determines the number of latitudinal nodal lines (geodesics intersecting the z axis). When |m| = l, the harmonics are "beach ball"-like (sectoral) and when m = 0, the harmonics are "target"-like (zonal). Other values of m produce a checkerboard pattern (tesseral). Th Condon-Shortley phase factor of (-1)^m is included.

Definition at line 167 of file al_Spherical.hpp.

Member Function Documentation

operator()()

template<int L_MAX = 16>

template<class T >

Complex<T> al::SphericalHarmonic< L_MAX >::operator() ( int  l, int  m, const Complex< T > &  ctheta, const Complex< T > &  cphi  ) const

inline

Evaluate spherical harmonic.

Parameters

[in]	l	number of nodal lines
[in]	m	number of latitudinal nodal lines, |m| <= l
[in]	ctheta	unit magnitude complex number describing longitudinal angle in [0, 2pi]
[in]	cphi	unit magnitude complex number describing latitudinal angle in [0, pi]

Definition at line 180 of file al_Spherical.hpp.

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

• al_Spherical.hpp