A method of SO3Grid.

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 SO3Grid.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. The nearest and the k nearest go through a quaternion k-d tree, the radius search through the structured search of the equispaced grid, its rings and windows.

Input

S3G SO3Grid
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

equispacedSO3Grid, SO3Grid.radius, orientation.find

MATLAB’s SO3Grid.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/SO3Grid.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.