dropSymmetry edit page

drop a symmetry that a rotation does not respect, keeping its frame

Rotating a function by a rotation which is not one of its own symmetry elements destroys that symmetry. The group is then dropped and the reference frame kept - the data still lives where it lived, it just no longer claims to be symmetric (ADR 0003, see symmetry/stripSym).

Description

This replaces twenty three copies of the same block that had drifted into three different guards. numSym(sym.Laue) > 2 is the correct one: it says the point group is neither 1 nor -1, hence claims something a rotation can destroy. The length(sym.rot) > 2 spelling some copies used is a different test - it under-warns for every non centrosymmetric group of order two, so an ODF with point group 2 kept a symmetry claim that the rotation had just invalidated.

The membership test covers a single rotation and a list at once: all(any(rot(:).' == sym.rot(:))) reduces to any(rot == sym.rot(:)) when rot is scalar, which is what rotate needs and rotate_outer generalises.

It also gates the products in orientation/private/ensureSym: a rotation applied on the left acts in the specimen frame and can destroy the specimen symmetry, on the right it acts in the crystal frame. That guard used to be a separate one testing dot_outer(sym.rot,rot) > 0.99 - a quaternion dot of 0.99 is a rotation angle of 16.2 degree, so any rotation up to sixteen degrees counted as a symmetry element and the claim survived untouched.

Syntax

SO3F.CS = dropSymmetry(SO3F.CS,rot,'crystal','ODF')
SO3F.SS = dropSymmetry(SO3F.SS,rot,'specimen','ODF')

Input

sym symmetry
rot rotation, one or many
side 'crystal' or 'specimen', for the warning
what what is being rotated, for the warning, e.g. 'ODF'

Output

sym symmetry, the trivial group on the same frame when it was dropped

See also

symmetry.symmetry SO3Fun.rotate SO3VectorField.rotate orientation.mtimes

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/dropSymmetry.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.