A method of SO3FunHarmonic.

the Radon transform of a function on SO(3): its pole figures, inverse pole figures, or their values (MATLAB’s radon, calcPDF and calcIPDF)

Syntax

pf = SO3F.radon(h)

The pole figure of the crystal direction h.

ipf = 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.

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

Superposed pole figures.

Description

The pole figure of h is the mean of the function over the orientations g with g h = r, a function of r on the sphere in the specimen frame; the inverse pole figure of r the same mean as a function of h in the crystal frame. A Laue group, or an antipodal direction, makes them antipodal. Several crystal directions give the superposition of their pole figures, weighted equally unless superposition is given. MATLAB’s bandwidth, which cuts the transform, is not taken: truncate the function first.

Input

SO3F SO3FunHarmonic
h Miller or vector3d, the crystal directions, or a list of them
r vector3d, the specimen directions

Keywords

keyword default description
superposition None the weights of several crystal directions

Output

pf S2FunHarmonic in the specimen frame
ipf S2FunHarmonic in the crystal frame
v array, the values at the pairs of h and r

See also

calcPoleFigure, plotPF, plotIPF, PoleFigure

MATLAB’s SO3FunHarmonic.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/SO3FunHarmonic.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.