the folds of a group’s sector, in the order they are applied. Every fold halves the sector and flips the half between the white centre and the black one; the loop stops when every boundary plane is a mirror of the group the folds have generated. The groups -1, -3 and -4 have no such fold and no smooth one to one key; hasSmoothKey says so. -3 and -4 fold their wedge once all the same; the hemisphere of -1 has no plane to single out and stays whole, white at its pole, as MATLAB’s key

Syntax

folds = sectorFolds(crystalFrame('432').sym)

One fold: 432 halves its sector to that of m-3m.

folds = sectorFolds(crystalFrame('m-3m').sym)

No fold: the sector is bounded by mirrors.

folds = sectorFolds(cs.sym, cs.fundamentalSector(), tol=1e-4)

Another sector, a looser test.

Description

A candidate plane folds the sector when the reflection in it maps the boundary planes of the sector onto themselves, within tol, and it is taken when it doubles the group to a reflection group. Which half a fold keeps is a convention: the half the first axis of the frame not lying in the plane points into.

Input

pg symmetry, the point group
sR sphericalRegion, the sector to fold; by default the group’s conventional sector

Keywords

keyword default description
tol 1e-06 the tolerance of the test whether a reflection maps the sector onto itself

Output

folds list of (3,) arrays, the normals of the folding planes in the order they apply

See also

hasSmoothKey, regionCenter, HSVDirectionKey

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/sectorFolds_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.