the Bingham distribution on SO(3): the density exp(q’ A diag(kappa) A’ q) on the quaternions, symmetrised over the crystal and specimen frames, with four concentrations kappa and four orthonormal quaternion axes A; BinghamODF builds it from axes, orientations or a fibre

Syntax

SO3FunBingham(kappa, A, cs, ss)

SO3FunBingham(kappa, A, cs, cs, antipodal=True)

With exchange symmetry.

Input

`kappa`	four Bingham concentration parameters, one per quaternion axis
`A`	orthonormal quaternion axes as columns of a 4-by-4 matrix, or four rotations or orientations
`frames`	crystal and specimen frames; inherited from orientation axes when omitted
`weight`	mean density over SO(3); default 1
`antipodal`	impose grain-exchange symmetry f(g)=f(inv(g)); default False

Signature

SO3FunBingham(kappa, A, *frames, weight=1.0, antipodal=False)

MATLAB’s SO3FunBingham.SO3FunBingham

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/SO3FunBingham.SO3FunBingham_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.