the de la Vallee Poussin kernel on the sphere, (1 + kappa) ((1 + t) / 2)^kappa: nonnegative and a finite series, the kernel recommended for texture analysis

Syntax

S2DeLaValleePoussinKernel(20)
S2DeLaValleePoussinKernel(halfwidth=10*degree)

Description

A nonnegative, mean-one kernel for densities of directions and fibre ODFs. Larger kappa gives a narrower peak. Integer kappa gives a finite polynomial; for a noninteger kappa the stored harmonic expansion is truncated.

Evaluate psi at t=cos(theta), the cosine of the angular distance on the sphere. 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 S2DeLaValleePoussinKernel

Members

halfwidth

the halfwidth in closed form, acos(2 * 2^(-1 / kappa) - 1)

Used on

EBSDAdvancedMaps, SO3FunConvolution, S2Kernels, VectorsDensityEstimation

MATLAB’s S2DeLaValleePoussinKernel_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/S2DeLaValleePoussinKernel_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.

The class S2DeLaValleePoussinKernel