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

Options

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

Output

SO3G orientation grid
W quadrature 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.