A method of SO3FunHarmonic.

the convolution with another SO(3) function, a kernel, a function on the sphere or a vector of multipliers per degree, as conv(f, g); with inverse=True of the inverse of f

Syntax

SO3F = conv(SO3F1, SO3F2)

Two functions on SO(3).

SO3F = conv(SO3F1, psi)

With an SO3Kernel, a smoothing.

sF2 = conv(SO3F1, sF1)

With a function on the sphere, a function on the sphere.

SO3F = SO3F1.conv(psi, inverse=True)

Of the inverse function f(g^-1).

Description

Two functions on SO(3) chain: the specimen frame of SO3F2 must be the crystal frame of SO3F1, and the result maps from the crystal frame of SO3F2 to the specimen frame of SO3F1. A function on the sphere lives in the specimen frame of SO3F1 and gives one in its crystal frame. A kernel or the multipliers scale the coefficients degree by degree. See SO3FunConvolution for the definitions.

Input

SO3F1 SO3FunHarmonic
g SO3Fun, SO3Kernel, S2Fun, S2Kernel, or an array of multipliers per degree

Keywords

keyword default description
inverse False convolve the inverse function f(g^-1), its frames exchanged

Output

SO3F SO3FunHarmonic
sF2 S2FunHarmonic, for a function or kernel on the sphere

See also

SO3Kernel.conv, S2FunHarmonic.conv, SO3FunConvolution

MATLAB’s SO3FunHarmonic.conv

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/SO3FunHarmonic.conv_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.