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

Members

axes the four principal quaternion axes as orientations, MATLAB’s odf.A
bandwidth the bandwidth of the harmonic expansion, the preference maxSO3Bandwidth
eval the values of the distribution at orientations, the mean over the symmetric copies of its axes
frameA the frame the orientations map from, the crystal frame
frameB the frame the orientations map to, the specimen or a second crystal frame
interpolate the function on SO(3) through the values at the orientations, interpolate(nodes, values)
mean the mean value of the function over SO(3), its weight
radon the Radon transform of a Bingham distribution: its pole figure, in closed form, its inverse pole figure, or their values
rotate the distribution turned by a rotation, from the left (the specimen side) or, with side=’right’, from the right (the crystal side)
SO3FunBingham 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
times  
uminus  

MATLAB’s SO3FunBingham_index

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_index_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.