a function on SO(3) as a sum of radial kernels at centre orientations, plus a constant: a radial basis function ODF

Syntax

SO3F = SO3FunRBF(ori, psi, weights)

Kernels psi at the orientations ori.

SO3F = SO3FunRBF(ori, psi, weights, c0)

Plus the constant c0.

SO3F = SO3FunRBF(ori)

10 degree kernels, the weights giving a mean of one.

Description

The function is c0 + sum_i w_i psi(angle(g, ori_i)), every centre taken with all its symmetrically equivalent orientations, in the crystal and specimen frames of the centres. unimodalODF and calcDensity build one, SO3FunRBF.interpolate fits one through values.

Scaling, adding a constant, adding another kernel sum of the same kernel, rotation, inversion and convolution with a kernel keep the function a kernel sum. Its harmonic form, through which it is evaluated, is computed once and kept until a centre, the kernel, the weights or the constant are set.

MATLAB’s SO3FunRBF(F), approximating another SO3Fun, is not ported.

Input

`center`	orientation, the centres of the kernels
`psi`	SO3Kernel; by default the de la Vallee Poussin kernel of halfwidth 10 degree
`weights`	one weight per centre; by default equal, giving a mean of one
`c0`	the constant added

Output

SO3F SO3FunRBF

Properties

`center`	kernel centres as orientations
`psi`	radial kernel shared by the centres
`weights`	coefficients multiplying the individual kernel contributions
`c0`	constant contribution to the function
`CS, SS`	crystal and specimen reference frames
`antipodal`	whether grain exchange symmetry is used

Signature

SO3FunRBF(center, psi=None, weights=None, c0=0.0)

Used on

SO3FunConvolution, SO3FunOperations, SO3Kernels

MATLAB’s SO3FunRBF.SO3FunRBF

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/SO3FunRBF.SO3FunRBF_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.

SO3FunRBF.SO3FunRBF