Description

Evaluates the orientation dependent function \(f\) on a given set of points using a representation based coefficient transform, that transforms a series of Wigner-D functions into a trivariate Fourier series and using NFFT at the end.

Syntax

f = eval(SO3F,rot)

Input

`SO3F`	`SO3FunHarmonic`
`rot`	`rotation (evaluation nodes)`

Output

`f`	`double [numrot × size(SO3F)]`

Options

`bandwidth`	`cut bandwidth of the harmonic series in evaluation process`
`cutoffParameter`	`NFFT window cutoff m (default: 4)`
`oversampling`	`NFFT oversampling factor sigma (default: 2)`

Flags

`nfsoft`	`use Nonequispace Fast Fourier Transform of the NFFT3 Toolbox (expensive precomputations)`
`noNFFT`	`do direct evaluation of the harmonic series for every orientation (Works for very high bandwidth if the nfft runs out of memory, but gets expensive for many orientations. Hence number of orientations should be less than 100)`

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.eval.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.

SO3FunHarmonic.eval