A method of SO3FunComposition.

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

Syntax

S2F = SO3F.radon(h)

The pole figure of the crystal direction h.

S2F = SO3F.radon(r=r)

The inverse pole figure of the specimen direction r.

v = SO3F.radon(h, r)

The pole figure of h at the directions r.

S2F = SO3F.radon([h1, h2], superposition=[0.6, 0.4])

A superposed pole figure.

Description

The pole figure of h at r is the mean of the function over all orientations carrying h onto r. A function without coefficients, a composition, a handle, is expanded to an SO3FunHarmonic of the bandwidth first. MATLAB’s pdf, ipdf and calcPDF are this function.

Input

SO3F SO3Fun
h Miller or vector3d, the crystal direction, or a list of them to superpose

Keywords

keyword default description
r None vector3d, the specimen direction of the inverse pole figure, or the directions to evaluate the pole figure at
superposition None the weights of several crystal directions, equal unless given
bandwidth None the bandwidth of the harmonic form a function without coefficients is expanded to

Output

S2F S2FunHarmonic, the pole figure in the specimen frame or the inverse pole figure in the crystal frame
v the values at r

See also

SO3FunHarmonic.radon, plotPF, plotIPF

MATLAB’s SO3FunComposition.radon

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.radon_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.