the axis distribution of an SO(3) function, an S2 function of the rotation axes symmetric under the rotations the two frames share; with v its values at the axes v; for two frames the axis distribution of the uniform distribution, exactly; MATLAB’s calcAxisDistribution

Syntax

adf = calcAxisDistribution(mdf)

The axis distribution.

value = calcAxisDistribution(mdf, v)

Its values at the axes v.

adf = calcAxisDistribution(mdf, minAngle=20*degree, maxAngle=40*degree)

Only rotations by 20 to 40 degree.

value = calcAxisDistribution(mdf, v, resolution=1*degree)

A finer angle quadrature.

adf = calcAxisDistribution(cs1, cs2)

Of the uniform distribution.

Description

By default the rotation angle is integrated over the full range the fundamental region allows for the axis in question, by a rectangle rule of the step resolution (2.5 degree). The keywords minAngle and maxAngle restrict that range to a window, which is what the axis angle sections show; an axis for which the window lies outside the fundamental region contributes zero. The quadrature keeps its step, so a narrow window is integrated with few points. The distribution is antipodal for a function with grain exchange.

Input

`f`	SO3Fun, or a crystal frame cs1 for the uniform distribution
`v`	vector3d, the axes to evaluate at, or the second frame cs2

Keywords

keyword	default	description
`bandwidth`	`64`	the bandwidth of the harmonic expansion of adf

Output

`adf`	S2FunHarmonic, or S2FunHandle for the uniform distribution
`value`	the values at the axes v

Used on

AxisDistributionFunction, MisorientationDistributionFunction

MATLAB’s SO3Fun.calcAxisDistribution

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/SO3Fun.calcAxisDistribution_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.

SO3Fun.calcAxisDistribution