Evaluate an SO3FunHarmonic on an equispaced grid in Euler angles \[(\alpha_a,\beta_b,\gamma_c) = (\frac{2\pi a}{H_1},\frac{\pi b}{H_2-1},\frac{2\pi c}{H_3})\] where \(a=0,...,H_1-1\), \(b=0,...,H_2-1\) and \(c=0,...,H_3-1\).
Therefore we transform the Harmonic series to an usual Fourier series equivalent as in the function eval. But we use an equispaced FFT instead of the NFFT.
Syntax
f = evalEquispacedFFT(SO3F,rot)Input
| SO3F | SO3FunHarmonic |
| rot | quadratureSO3Grid - 'ClenshawCurtis' |
Output
| f | values at this grid points |
| nodes | orientation |
Example
% construct quadrature grid and evaluate there. Output will be a unique
% part of this grid
SO3F = SO3FunHarmonic.example;
rot = quadratureSO3Grid(62,SO3F.CS)
v = evalEquispacedFFT(SO3F,rot);rot = quadratureSO3Grid (Quartz → y↑→x)
scheme: ClenshawCurtis
bandwidth: 62
grid: 333396 orientations
full grid size: 42 x 125 x 126% for big grid sizes the construction of the quadrature grid is memory
% expansive. Hence construct struct, but the output is full sized
rot = struct('scheme','ClenshawCurtis','bandwidth',350,'CS',SO3F.CS,'SS',specimenSymmetry)
v = evalEquispacedFFT(SO3F,rot);rot =
struct with fields:
scheme: 'ClenshawCurtis'
bandwidth: 350
CS: [1×1 crystalSymmetry]
SS: [1×1 specimenSymmetry]See also
SO3FunHarmonic.eval SO3FunHarmonic.evalNFSOFT SO3FunHarmonic.evalSectionsEquispacedFFT