the bump kernel on the sphere: 2 / (1 - cos delta) on the cap of radius delta, zero beyond, a density of mean one

Syntax

S2BumpKernel(10*degree)
S2BumpKernel(halfwidth=10*degree, bandwidth=64)

Description

A uniform kernel inside a spherical cap, with zero values on and outside its boundary. Its constant value is chosen so that the mean over the sphere is one. A finite harmonic representation approximates the discontinuity and can ring.

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
delta   angular radius of the open support in radians
halfwidth   angular halfwidth in radians, taking precedence over delta
bandwidth   maximum harmonic degree; chosen by the coefficient cutoff when omitted

Output

psi S2BumpKernel

See also

S2Kernel, calcDensity, calcKernel

Members

grad the derivative of the bump kernel, zero wherever it exists
halfwidth the halfwidth, the radius delta of the cap

Used on

S2Kernels

MATLAB’s S2BumpKernel_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/S2BumpKernel_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.