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
| SO3F | SO3FunHarmonic |
| oS | @ODFSection |
Output
| f | values at this grid points |
Options
| 'resolution' | shape constant along Euler angles. (default = 2.5°) |
See also
SO3FunHarmonic.eval SO3FunHarmonic.evalNFSOFT SO3FunHarmonic.evalEquispacedFFT
Citing this page.
This page is part of the documentation of
MTEX, a free and open
source MATLAB toolbox for analyzing and modeling crystallographic textures.
It was written by The MTEX Developers and is published at
https://mtex-toolbox.github.io/SO3FunHarmonic.evalODFSections.html.
If you use MTEX, or reuse text or figures from this page, in your research,
please cite
F. Bachmann, R. Hielscher, H. Schaeben: Texture Analysis with MTEX - Free and Open Source Software Toolbox, Solid State Phenomena 160 (2010), 63-68. 10.4028/www.scientific.net/SSP.160.63
BibTeX
@article{bachmann2010mtex,
author = {F. Bachmann and R. Hielscher and H. Schaeben},
title = {Texture Analysis with MTEX - Free and Open Source Software Toolbox},
journal = {Solid State Phenomena},
volume = {160},
pages = {63-68},
year = {2010},
doi = {10.4028/www.scientific.net/SSP.160.63},
url = {https://doi.org/10.4028/www.scientific.net/SSP.160.63}
}Other papers describing specific MTEX methods are listed under Publications — please cite the one that best fits your application. The MTEX source code is licensed under the GNU General Public License v2.0; the text and figures of this documentation are licensed under CC BY 4.0, which permits reuse — including by automated systems — provided The MTEX Developers and this page are credited.