the restricted distance kernel on the sphere, -2 sin(acos(t) / 2), cut at the degree N: negative, a distance between directions that makes points repel each other

Syntax

psi = S2RestrictedDistanceKernel()

Description

This is the negative chord distance between unit directions. It is used in point-repulsion objectives and is not a probability density. Direct evaluation uses the distance formula; N limits the harmonic representation.

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
N   maximum harmonic degree; the maxS2Bandwidth preference when omitted

Output

psi S2RestrictedDistanceKernel

See also

S2Kernel, calcDensity, calcKernel

Members

bandwidth the degree N the kernel is cut at

MATLAB’s S2RestrictedDistanceKernel

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/S2RestrictedDistanceKernel_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.