SO3BumpKernel edit page

The Bump kernel is a radial symmetric kernel function depending on a parameter \(r\in (0,pi)\). The function value is 0, if the angle is greater then the halfwidth \(r\). Otherwise it is has a contstant value, such that the mean of the kernel function on \(\mathcal{SO}(3)\) is 1. Hence we use the open set \(U_r = \{ R \in \mathcal{SO}(3) \,|~ \omega®<r \}\) and define the bump kernel \(\psi_r : \matcal{SO}(3) \to \mathbb R\) by

\[ \psi_r® = \frac1{|U_r|} \mathbf{1}_{R \in U_r} \].

Syntax

psi = SO3BumpKernel(40*degree)

Options

halfwidth angle at which the kernel function has reduced to half its peak value
bandwidth harmonic degree

See also

SO3Kernel

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/SO3BumpKernel.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.