rotation.calcDensity edit page

computes an ODF from individual orientations

The function calcDensity applies one of the following algorithms to compute an ODF from a list of orientations.

direct kernel density estimation
kernel density estimation via Fourier series
Bingham estimation

Description

If the number of orientations is very large (more than about 10 * bandwidth^3) the Fourier method rounds the orientations onto a regular quadrature grid and computes the Fourier coefficients by a plain FFT instead of the NFFT, see SO3FunHarmonic.adjoint. The rounding error is at most half the grid spacing and hence negligible compared to the kernel halfwidth. Use the flag 'exact' to avoid any gridding.

Syntax

% use kernel density estimation with a 10 degree kernel
odf = calcDensity(ori,'halfwidth',10*degree)

% use grain area as weights for the orientations
odf = calcDensity(grains.meanOrientation,'weights',grains.area)

% use a specific kernel
psi = SO3AbelPoissonKernel('halfwidth',10*degree)
odf = calcDensity(ori,'kernel',psi)

% compute the ODF as a Fourier series of order 16
odf = calcDensity(ori,'order',16)

Input

ori orientation

Output

odf SO3Fun

Options

`weights`	`list of weights for the orientations`
`halfwidth`	`halfwidth of the kernel function (default is 10 degree)`
`resolution`	`resolution of the grid where the ODF is approximated`
`kernel`	`SO3Kernel function (default -- SO3 de la Valee Poussin kernel)`
`order`	`order up to which Fourier coefficients are calculated`

Flags

`silent`	`no output`
`exact`	`no approximation to a corser grid`
`Fourier`	`force Fourier method`
`Bingham`	`model bingham odf`
`noFourier`	`no Fourier method`

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/rotation.calcDensity.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.

rotation.calcDensity