the von Mises Fisher kernel of a fibre, what fibreODF convolves with; kappa the concentration, larger is sharper

Syntax

fibreVonMisesFisherKernel(90)
fibreVonMisesFisherKernel(halfwidth=10*degree)

Description

The kernel used to smooth an ideal orientation fibre in fibreODF. Larger kappa concentrates the density closer to the fibre. It has mean one; its spherical Radon kernel can be evaluated in closed form.

Evaluate psi at t=cos(omega/2), the cosine of half the rotation angle. Use psi.halfwidth() for the angular width in radians and psi.bandwidth for the maximum degree of its harmonic representation.

Keywords

keyword default description
kappa   positive concentration parameter; larger values give a sharper peak
halfwidth   angular halfwidth in radians, taking precedence over kappa

Output

psi fibreVonMisesFisherKernel

See also

SO3Kernel, calcDensity, calcKernel

Members

halfwidth the halfwidth in closed form, acos(1 - log(2) / kappa)
radon the Radon transform: the kernel on the sphere of the same coefficients, in closed form

Used on

ODFShapes

MATLAB’s fibreVonMisesFisherKernel_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/fibreVonMisesFisherKernel_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.