the zero range method of the pole figure inversion: where a pole figure vanishes, the ODF vanishes on every fibre through it

Syntax

zrm = zeroRangeMethod(pf)

The defaults.

zrm = zeroRangeMethod(pf, halfwidth=10*degree, delta=0.01)

A wider kernel, a higher background.

isZero = zrm.checkZeroRange(ori)

The orientations ruled out.

isZero = zrm.checkZeroRange(v, i)

The zero positions of the i-th pole figure.

Description

A direction of a pole figure is in its zero range where enough measurements surround it and most of them lie below the background. Both are kernel sums over the measured directions: their density, which must exceed the threshold, and a sum weighting an intensity above the background bg by alpha - 1 and one below it by -1, which must be below -0.1 times the density.

An orientation is ruled out when one of its symmetric poles falls into the zero range of some pole figure. calcODF(pf, zeroRange=True) drops those orientations from the grid of the ansatz functions; calcODF(pf, zeroRange=zrm) uses the method set up here.

Input

`pf`	PoleFigure
`psi`	S2Kernel, the smoothing kernel, given positionally

Keywords

keyword	default	description
`halfwidth`		the halfwidth of the de la Vallee Poussin smoothing kernel, by default twice the resolution of the pole figures
`kernel`		S2Kernel, the smoothing kernel instead
`threshold`		the density below which the data says nothing, by default a tenth of the kernel’s maximum
`delta`		the background as a fraction of the largest intensity, when bg is not given
`bg`		the background intensity, one number or one per pole figure
`alpha`		the weight of an intensity above the background against one below it
`bandwidth`		the bandwidth of the smoothed densities, by default the kernel’s

Output

zrm zeroRangeMethod

Members

checkZeroRange	which orientations the zero range method rules out, those some pole figure is zero at in one of their symmetric poles
plot	plot(x, …) draws x as its kind is drawn
zeroRangeMethod	the zero range method of the pole figure inversion: where a pole figure vanishes, the ODF vanishes on every fibre through it

MATLAB’s zeroRangeMethod_index

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/zeroRangeMethod_index_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.

The class zeroRangeMethod