construct an orientation distribution from Bingham concentrations and quaternion axes

Syntax

odf = BinghamODF(20, cs)

Concentrated about the identity in this crystal frame.

odf = BinghamODF(20, f)

Concentrated about an orientation fibre.

odf = BinghamODF([20, 10, 0, 0], A, cs, ss)

Four orthogonal quaternion axes.

Description

The density is proportional to exp(sum_i kappa[i] * dot(q, A[:, i])**2), averaged over the crystal and specimen symmetry groups. A larger concentration favours the corresponding quaternion axis. Adding the same constant to all four concentrations leaves the density unchanged. Missing concentrations are padded with zeros.

A fibre supplies two quaternion axes with the same concentration when kappa is scalar. A single orientation supplies its frames and selects the identity quaternion basis; its rotation does not set the peak position. To rotate a distribution, rotate the resulting ODF, or provide four explicitly rotated orthogonal quaternion axes.

Additional keywords are passed to SO3FunBingham: weight sets the mean (default 1), and antipodal imposes grain-exchange symmetry.

Input

`kappa`	one to four concentration parameters
`A`	orthogonal 4-by-4 matrix with quaternion axes as columns, four rotations or orientations, a fibre, a crystalFrame, or one orientation supplying its frames; None selects the identity basis
`frames`	crystal and specimen frames when they are not supplied by A; when A is a crystal direction, the first extra argument is the specimen direction of the fibre

Output

odf SO3FunBingham, of mean one unless a different weight is supplied

Signature

BinghamODF(kappa, A=None, *frames, **kwargs)

Used on

OrientationEmbeddings, BinghamODFs, SO3FunDefinition

MATLAB’s BinghamODF

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/BinghamODF_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.

BinghamODF