SH, SHBand

Syntax

Parameters

pX, pY, pZ	Pointers to the source vectors representing a unit sphere points in Cartesians coordinates.
N	Number of Cartesians points, that is the length of the source vector.
pDstYlm	Pointer to the destination vector to store SH values computed at given points for all orders up to order L, of size N(L+1)(L+1).
pDstBandYlm	Pointer to the destination vector to store SH values computed at given points only for order L, of size N(2L+1).
L	Order, can not be greater than maximum order specified in the function ipprSHInit.
pSHState	Pointer to the external buffer for the SHT state structure that must be initialized with maximum order not less than L.

Description

The functions ipprSH and ipprSHBand are declared in the ippr.h file. These functions calculates the spherical harmonics functions {Y_l^m (x, y, z):0 ≤ l ≤ L, |m| ≤ L} for each input point (pX[i], pY[i], pZ[i]), 0 ≤ i < N, which belong to a unit sphere, that is pX[i]² + pY[i]² + pZ[i]² =1.

ipprSH. For each input point this function computes SH function values for all bands up to L. The total number of values for each point is (L+1)(L+1). They are stored in the destination vector pDstYlm as follows:

pDstYlm [i(L+1)(L+1) + 2l + m] = Y_l^m(pX[i], pY[i], pZ[i]), -L ≤ l ≤ L, |m| ≤ l, 0 ≤ i < N.

That is, they are stored by points, for each point by bands, and for each band by indexes in the following way:

Y_l^m values for the first point, all bands from 0 to L

Y₀⁰ - 0-band;

Y₁^-1, Y₁⁰, Y₁¹ - 1-band;

Y₂^-2, Y₂^-1, Y₂⁰ , Y₂¹, Y₂² - 2-band

...

Y_L^-L, Y_L^-L+1 ,... Y_L^-1, Y_L⁰, Y_L¹,... Y_L^L-1, Y_L^L - L-band.

Then analogous set of Y_l^m values for the second point, all bands from 0 to L, then for the third point and so on up to the N-th point.

ipprSHBand. This function computes SH functions values for each point only for given band L. The total number of values for each point is (2L+1). They are stored in the destination vector pDstBandYlm as follows:

pDstBandYlm [i(2L+1) + L + m] = y_L^m(pX[i], pY[i], pZ[i]), -L ≤ m ≤ L, 0 ≤ i < N.

That is, they are stored by points for the given band L, and for each point by indexes in the following way:

y_L^-L, y_L^-L+1 ,... y_L^-1, y_L⁰, y_L¹,... y_L^L-1, y_L^L.

Return Values

ippStsNoErr	Indicates no error. Any other value indicates an error.
ippStsNullPtrErr	Indicates an error if one of the specified pointers is NULL.
ippStsSizeErr	Indicates an error if N is equal to 0.
ippStsRangeErr	Indicates an error if L is greater that maximum order specified in the function ipprSHInit.