the volume of a fibre: the share of an orientation density within a radius of the fibre of the orientations that map the crystal direction h onto the specimen direction r

Syntax

v = fibreVolume(odf, h, r, radius)
The volume within radius of the fibre h   r. 
v = fibreVolume(odf, fibre(h, r), radius)

The fibre given as a fibre.

v = fibreVolume(odf, h, r, radius, resolution=2*degree)

A coarser quadrature.

Description

The function is averaged over the tube about the fibre, the orientations g with g h within the radius of r: the directions u on the cap of the radius about r, and for each the turns about u equispaced. The mean times the tube’s share of orientation space, over the symmetrically equivalent copies of h, is the volume, at most one; for the uniform density it is (1 - cos radius) / 2 times the number of the copies.

Input

f SO3Fun, an orientation density
h Miller, the crystal direction, or a fibre, whose h and r are taken
r vector3d, the specimen direction; with a fibre the radius
radius the angle of the tube about the fibre in radians

Keywords

keyword default description
resolution None the spacing of the quadrature of the tube; by default the smaller of one degree and a thirtieth of the radius

Output

v float, the volume between 0 and 1

See also

SO3Fun.volume, SO3Fun.entropy, fibre, ODFCharacteristics

MATLAB’s SO3Fun.fibreVolume

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.fibreVolume_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.