the bump kernel on SO(3): constant on the rotations of angle below delta, zero beyond, of mean one

Syntax

SO3BumpKernel(40*degree)
SO3BumpKernel(halfwidth=10*degree, bandwidth=64)

Description

A uniform kernel inside a rotational ball, with zero values on and outside its boundary. Its constant value is chosen so that the mean over SO(3) is one. The direct evaluation retains the sharp boundary; a harmonic truncation can ring there.

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
`delta`		angular radius of the open support in radians
`halfwidth`		angular halfwidth in radians, taking precedence over delta
`bandwidth`		maximum harmonic degree; the maxS1Bandwidth preference when omitted

Output

psi SO3BumpKernel

Members

grad	the derivative of the bump kernel, zero wherever it exists
halfwidth	the halfwidth, the radius delta of the bump
radon	the Radon transform: the kernel on the sphere of the same coefficients, in closed form

Used on

ODFShapes, SO3Kernels

MATLAB’s SO3BumpKernel_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/SO3BumpKernel_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 SO3BumpKernel