A method of SO3FunComposition.

the share of orientations within a radius of a centre: the integral of f over the ball, int_{angle(g, c) < r} f(g) dg, relative to the integral over all orientations; MATLAB’s volume

Syntax

v = volume(odf, ori, 20*degree)

Around an orientation.

v = volume(odf, ori, 20*degree, resolution=1*degree)

A finer local grid.

v = volume(odf, f, 10*degree)

Around a fibre.

v = volume(sF, xvector, 20*degree)

A spherical function around a direction.

v = volume(ori, center, 10*degree)

The share of a list of orientations.

Description

The volume is the mean of f on a local grid in the ball times the ball’s share of the fundamental region, counting its symmetric copies, at most one. A uniform density gives the share of the ball itself, so a value above it marks a preferred orientation.

On the sphere the ball is a spherical cap; an antipodal function over a cap of 90 degree gives its mean value.

The centre may also be:

  • a fibre: the volume of the tube about it, as fibreVolume.
  • a list of centres: one value each, an empty array for none.

Given a list of orientations instead of a function, the result is the share of them within the radius.

Input

f SO3Fun, S2Fun or orientation
center orientation, fibre, or vector3d on the sphere
radius the radius of the ball, an angle

Keywords

keyword default description
resolution None the spacing of the local grid, by default the smaller of 1.25 degree and a thirtieth of the radius (on the sphere 0.1 degree and a two hundredth)

Output

v the share of the volume, a number, or an array of one per centre

See also

fibreVolume, entropy, SO3FunHarmonic.mean

MATLAB’s SO3FunComposition.volume

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/SO3FunComposition.volume_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.