the Abel Poisson kernel on SO(3), sum_n (2n+1) kappa^(2n) U_2n(t), kappa in (0, 1)

Syntax

SO3AbelPoissonKernel(0.4)
SO3AbelPoissonKernel(halfwidth=5*degree)

Description

A nonnegative kernel with mean one on orientation space. Increasing kappa towards one narrows the peak and requires more harmonic degrees. It has an infinite series, which MTEX truncates when a harmonic representation is needed.

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`		concentration in (0, 1), with larger values giving a sharper peak
`halfwidth`		angular halfwidth in radians, taking precedence over kappa

Output

psi SO3AbelPoissonKernel

Members

radon

the Radon transform: the kernel on the sphere of the same coefficients, in closed form

Used on

ODFShapes, RBFApproximationTheory, SO3Kernels

MATLAB’s SO3AbelPoissonKernel_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/SO3AbelPoissonKernel_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 SO3AbelPoissonKernel