A method of orientation.

the disjoint list of orientations, symmetric equivalents within a tolerance taken as one

Syntax

u = unique(ori)

One of each, sorted.

u = unique(ori, tol=1*degree)

Within 1 degree as one.

u = unique(ori, stable=True)

In the order of first appearance.

u = unique(ori, symmetry=False)

The rotations as stored.

u, iOri, iu = unique(ori, return_index=True, return_inverse=True)

The index maps.

Description

Two orientations are one when their misorientation angle, symmetry reduced, is below tol. Every orientation not yet taken takes the later ones within the tolerance, so the first of each is kept. They are sorted by the coefficients of their equivalents in the fundamental region, or with stable kept in the order of first appearance.

Input

ori orientation

Keywords

keyword default description
tol 0.001 the angular tolerance, in radians
symmetry True take symmetric equivalents as one; False compares the rotations as stored, MATLAB’s ‘noSymmetry’
stable False keep the order of first appearance instead of sorting
return_index False also return iOri
return_inverse False also return iu

Output

u orientation, a one-dimensional list
iOri indices with u = ori.flatten()[iOri]
iu indices with ori.flatten() = u[iu]

See also

quaternion.unique, orientation.isclose, orientation.symmetrise

MATLAB’s orientation.unique

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/orientation.unique_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.