The spherical Bump kernel is a radial symmetric kernel function depending on the halfwidth \(r\in (0,pi)\). The function value is 0, if the angle is greater then the halfwidth \(r\). Otherwise it is the reciprocal \(\frac{2}{1-\cos r}\) of the relative area of the spherical cap, so that the kernel is a density: it has mean value one over the sphere and its first Legendre coefficient is A(1) = 1, as for every other kernel in this folder.
Syntax
psi = S2BumpKernel(10*degree)
psi = S2BumpKernel('halfwidth',10*degree)Options
| halfwidth | angle at which the kernel function has reduced to half its peak value |
| bandwidth | harmonic degree |
See also
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/S2BumpKernel.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.