A method of SO3FibonacciGrid.

the nearest grid rotation of every orientation, or the k nearest, or all within a radius, up to the symmetries of the grid’s frames; MATLAB’s SO3FibonacciGrid.find

Syntax

ind, d = S3G.find(ori)

The nearest grid point, d = cos(w/2).

ind, d = S3G.find(ori, 3)

The 3 nearest, d their angles.

I, D = S3G.find(ori, 10*degree)

Every grid point within 10 degree.

Description

The angle w is the misorientation angle reduced by the symmetries of both frames. As MATLAB’s SO3Grid.find, the nearest form gives cos(w/2), the other two the angles. Every search goes through a quaternion k-d tree.

Input

S3G SO3FibonacciGrid
ori orientation, or rotations taken between the grid’s frames

Keywords

keyword default description
epsOrK None an integer k for the k nearest, a float for the radius of the search

Output

ind the index of the nearest grid point, of the shape of ori; with k a (n, k) array
d cos(w/2) of the nearest; with k the (n, k) angles
I, D with a radius the sparse incidence and the sparse angles, (n x grid)

See also

superfibonacciSO3Grid, SO3Grid.find, orientation.find

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/SO3FibonacciGrid.find_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.