quadratureSO3Grid.quadratureSO3Grid edit page

Compute nodes and weights for quadrature on SO(3).

Description

The following quadrature rules are implemented:

  • 'ClenshawCurtis' combines the Gauss quadrature in 1st and 3rd Euler angle (alpha, gamma) with Clenshaw Curtis quadrature in 2nd Euler angle (beta)
  • 'GaussLegendre' combines the Gauss quadrature in 1st and 3rd Euler angle (alpha, gamma) with Gauss Legendre quadrature in 2nd Euler angle (beta)

Syntax

SO3G = quadratureSO3rid(N, 'ClenshawCurtis')
[SO3G, W] = quadratureSO3rid(N,CS,SS,'ClenshawCurtis') % quadrature grid of type Clenshaw Curtis

Input

N bandwidth
CS,SS @symmetries

Output

SO3G orientation grid
W quadrature weights

Options

ClenshawCurtis use Clenshaw Curtis quadrature nodes and weights (default)
GaussLegendre use Gauss Legendre quadrature nodes and weights

See also

regularSO3Grid SO3FunHarmonic.quadrature

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/quadratureSO3Grid.quadratureSO3Grid.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.