the Bingham distribution estimated from orientations; MATLAB’s calcBinghamODF

Syntax

odf = calcBinghamODF(ori)

By the large concentration approximation.

odf = calcBinghamODF(ori, weights=w)

Weighted orientations.

odf = calcBinghamODF(ori, exact=True)

The concentrations matching the moments exactly.

Description

The eigen decomposition of the quaternion tensor of the sample, projected to the fundamental region about its mean, gives the axes, and the concentrations follow from the eigenvalues, by the large concentration approximation kappa_i = -1/(2 lambda_i) shifted to a smallest value of zero, or exactly by Newton on the moments.

Input

ori orientation

Keywords

keyword	default	description
`weights`	`None`	a weight per orientation
`exact`	`False`	solve for the concentrations whose moments are the eigenvalues, instead of the large concentration approximation

Output

odf SO3FunBingham

Used on

BinghamODFs

MATLAB’s orientation.calcBinghamODF

source

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/orientation.calcBinghamODF_py.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.

orientation.calcBinghamODF