a sum of functions of different representations: evaluation adds the values, the harmonic form adds the harmonic forms

Input

terms functions on SO(3) to add, with compatible crystal and specimen frames

Members

bandwidth	the largest bandwidth of the components
CS	the crystal frame the components share
discreteSample	a random sample of n orientations drawn from an orientation density, of directions from a density on the sphere, of numbers from a density on an interval, or n random members of a list
eval	the sum of the values of the components at the orientations x
grad	the gradient with respect to the tangent space basis, at the orientations x or as a field, left or right sided
mean	the sum of the means of the components
radon	the Radon transform of a function on SO(3): its pole figures, inverse pole figures or the values of either, through the harmonic form of the bandwidth
rotate	the composition of the components rotated by r from the left or the right
SO3FunComposition	a sum of functions of different representations: evaluation adds the values, the harmonic form adds the harmonic forms
SS	the specimen frame the components share
times
uminus
volume	the share of orientations within a radius of a centre: the integral of f over the ball, int_{angle(g, c) < r} f(g) dg, relative to the integral over all orientations

MATLAB’s SO3FunComposition_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/SO3FunComposition_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 SO3FunComposition

Input

Members