a radially symmetric spherical kernel represented by Legendre coefficients.

Syntax

psi = S2Kernel(A)
values = psi(np.cos(theta))

Description

The series is sum(A[n]*P_n(t)), with t=cos(theta) and P_n the Legendre polynomial. A[0] is the mean over the sphere under uniform probability. Arbitrary coefficients are neither rescaled to mean one nor constrained to give nonnegative values.

Use a kernel family for a specified smoothing profile, or S2KernelHandle for a callable formula. Spherical kernels describe directional density estimates and smoothing around orientation fibres.

Input

`A`	one-dimensional real coefficient array, degrees zero through L

Output

psi S2Kernel

Properties

`A`	Legendre coefficients through the stored bandwidth
`bandwidth`	largest stored Legendre degree

Members

calcFourier	the Legendre coefficients A_0 .
conv	the convolution with another kernel on the sphere or SO(3): the coefficients multiplied and divided by 2n+1, a kernel on the sphere
grad	the derivative of a kernel on the sphere with respect to the polar angle, or to its cosine
minus
mrdivide
mtimes
norm	the L2 norm of the kernel, sqrt(sum_n A_n^2 / (2n+1))
plotSpektra	the Chebyshev coefficients of a kernel, or the harmonic power of a function, per degree
plus
radon	the Funk transform: A_n P_n(0)
rdivide
S2Kernel	a radially symmetric spherical kernel represented by Legendre coefficients
times
uminus

MATLAB’s S2Kernel_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/S2Kernel_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 S2Kernel