A method of S2FunHarmonic.

the Funk transform, the mean over the great circle perpendicular to every direction; radon(delta) over the small circle at pi/2 + delta; MATLAB’s radon

Syntax

sF = radon(sF)

The mean over the great circles.

sF = radon(sF, 10*degree)

The mean over the small circles at 100 degree.

Description

The transform is a convolution: the coefficients of degree n are multiplied by the Legendre polynomial P_n(cos(pi/2 + delta)), for the great circle (-1)^(n/2) (n-1)!!/n!! of an even n and zero of an odd one, so the odd part of a function is lost; invRadon inverts it on the even functions.

Input

sF S2FunHarmonic

Keywords

keyword default description
delta None the angle by which the circle is moved from the great circle

Output

sF S2FunHarmonic

See also

S2FunHarmonic.invRadon, calcPDF

MATLAB’s S2FunHarmonic.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/S2FunHarmonic.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.