A method of SO3FunRBF.

the Radon transform of a kernel sum: the pole figure of a crystal direction, the inverse pole figure of a specimen direction, or the pole density of both

Syntax

S2F = SO3F.radon(h)

The pole figure of h.

S2F = SO3F.radon(r=r)

The inverse pole figure of r.

v = SO3F.radon(h, r)

The pole figure of h at r.

S2F = SO3F.radon([h1, h2], superposition=[0.3, 0.7])

The superposed pole figure.

Description

The Radon transform of f at (h, r) is the mean of f over the orientations taking h to r. For a kernel sum it is again a sum of radial kernels on the sphere, the kernel’s Radon transform at the centres applied to h, returned as a harmonic expansion. Several crystal directions are superposed with the weights of superposition. It replaces MATLAB’s calcPDF, pdf and ipdf.

Input

SO3F SO3FunRBF
h Miller or vector3d, the crystal direction, or a list of them to superpose
r vector3d, the specimen direction

Keywords

keyword default description
superposition None the weights of the superposed crystal directions
bandwidth None the harmonic degree of the result, by default the kernel’s

Output

S2F S2FunHarmonic, the pole figure on the specimen sphere or the inverse pole figure on the crystal sphere
v the values at r, given h and r

See also

calcPoleFigure, SO3FunCBF.radon, plotPF, plotIPF

MATLAB’s SO3FunRBF.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/SO3FunRBF.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.