evalODFSections

Plotting @SO3FunHarmonics on Sections needs evaluation. We can evaluate (also for high bandwidths) fast on equispaced grids by fft.

Therefore we transform the SO(3) Fourier series to an usual Fourier series equivalent as in the function eval. But we use an 2-variate equispaced FFT instead of the NFFT in second step.

In case of phi1Sections, phi2Sections, alphaSections and gammaSections one Euler angle is fixed by the section. The other 2 Euler angles reads as equispaced grids. The grid of the gammaSections for instance reads as \[(\alpha_a,\beta_b,\gamma_c) = (\frac{2\pi a}{H_1},\frac{\pi b}{H_2-1},\gamma_c)\] where \(a=0,...,H_1-1\), \(b=0,...,H_2-1\) and \(c=0,...,S_{num}\).

In case of the sigma sections the grid reads as \[(\alpha_a,\beta_b,\gamma_c) = (\frac{2\pi a}{H_1},\frac{\pi b}{H_2-1},\sigma_c+\pi/6-\frac{2\pi a}{H_1})\] where \(a=0,...,H_1-1\), \(b=0,...,H_2-1\) and \(c=0,...,S_{num}\). Here we transform to an ordinary Fourier series and evaluate with FFT along 2nd Euler angle. Moreover we use an rank-1 lattice based FFT along 1st and 3rd Euler angle, which means we apply the FFT diagonal over the Index set.

Syntax

f = evalODFSections(SO3F,oS,'resolution',2.5*degree)

Input

Output

Options

See also

SO3FunHarmonic.eval SO3FunHarmonic.evalNFSOFT SO3FunHarmonic.evalEquispacedFFT