quadratureS2Grid.quadratureS2Grid edit page

Compute nodes and weights for quadrature on Sphere.

Description

The following quadrature rules are implemented:

  • 'optimal' is an optimal precomputed quadrature grid with low number of quadrature points
  • 'ClenshawCurtis' combines the Gauss quadrature in polar angle (theta) with Clenshaw Curtis quadrature in azimuth angle (rho)
  • 'GaussLegendre' combines the Gauss quadrature in in polar angle (theta) with Gauss Legendre quadrature in azimuth angle (rho)

Syntax

S2G = quadratureS2Grid(N)
S2G = quadratureS2Grid(N, 'GaussLegendre')

Input

N bandwidth

Output

S2G quadratureS2Grid

Options

chebychev optimal grid of chebychev style (default)
gauss optimal grid of gaussian style
ClenshawCurtis use Clenshaw Curtis quadrature nodes and weights (default)
GaussLegendre use Gauss Legendre quadrature nodes and weights

See also

regularS2Grid S2FunHarmonic.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/quadratureS2Grid.quadratureS2Grid.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.