HE_Mesh  6.0.1
wblut.math.WB_SphericalHarmonics Class Reference

Static Public Member Functions

static double Plm (final int L, final int M, final double x)
 
static WB_Coord rotateSpherical (final double angle, final double ax, final double ay, final double az, final double theta, final double phi)
 
static WB_Complex Y (final int L, final int M, final double theta, final double phi)
 
static WB_Complex Y (final int L, final int M, final double theta, final double phi, final double angle, final double ax, final double ay, final double az)
 
static double Ylm (final int L, final int M, final double theta, final double phi)
 
static double Ylm (final int L, final int M, final double theta, final double phi, final double angle, final double ax, final double ay, final double az)
 
static double Ylm2 (final int L, final int M, final double theta, final double phi)
 
static double Ylm2 (final int L, final int M, final double theta, final double phi, final double angle, final double ax, final double ay, final double az)
 

Static Private Member Functions

static double[][] initNormalization ()
 
static double getNormalizationLUT (final int L, final int M)
 
static double getNormalization (final int L, final int M)
 

Detailed Description

Spherical harmonic functions and associated Legendre polynomials. Calculated using recurrence relations: https://en.wikipedia.org/wiki/Associated_Legendre_polynomials# Recurrence_formula

Member Function Documentation

static double wblut.math.WB_SphericalHarmonics.getNormalization ( final int  L,
final int  M 
)
staticprivate
static double wblut.math.WB_SphericalHarmonics.getNormalizationLUT ( final int  L,
final int  M 
)
staticprivate
static double [][] wblut.math.WB_SphericalHarmonics.initNormalization ( )
staticprivate
static double wblut.math.WB_SphericalHarmonics.Plm ( final int  L,
final int  M,
final double  x 
)
static

Associated Legendre polynomial at x. Recurrence property:

Parameters
LSpherical harmonic order
MSpherical harmonic index
x
Returns
static WB_Coord wblut.math.WB_SphericalHarmonics.rotateSpherical ( final double  angle,
final double  ax,
final double  ay,
final double  az,
final double  theta,
final double  phi 
)
static
static WB_Complex wblut.math.WB_SphericalHarmonics.Y ( final int  L,
final int  M,
final double  theta,
final double  phi 
)
static

Complex spherical harmonic of order l, index m

Parameters
Lspherical harmonic order.
Mspherical harmonic index. -l<=m<=l
theta
phi
Returns
Y(theta, phi)

References wblut.math.WB_Complex.conjugate(), wblut.math.WB_SphericalHarmonics.getNormalizationLUT(), wblut.math.WB_Complex.mul(), wblut.math.WB_Complex.negate(), and wblut.math.WB_SphericalHarmonics.Plm().

static WB_Complex wblut.math.WB_SphericalHarmonics.Y ( final int  L,
final int  M,
final double  theta,
final double  phi,
final double  angle,
final double  ax,
final double  ay,
final double  az 
)
static
static double wblut.math.WB_SphericalHarmonics.Ylm ( final int  L,
final int  M,
final double  theta,
final double  phi 
)
static
static double wblut.math.WB_SphericalHarmonics.Ylm ( final int  L,
final int  M,
final double  theta,
final double  phi,
final double  angle,
final double  ax,
final double  ay,
final double  az 
)
static
static double wblut.math.WB_SphericalHarmonics.Ylm2 ( final int  L,
final int  M,
final double  theta,
final double  phi 
)
static
static double wblut.math.WB_SphericalHarmonics.Ylm2 ( final int  L,
final int  M,
final double  theta,
final double  phi,
final double  angle,
final double  ax,
final double  ay,
final double  az 
)
static

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