A method of symmetry.

the fundamental sector of the group on the sphere, the region of the directions one symmetric copy of each falls into

Syntax

sR = pg.fundamentalSector()

The conventional sector.

sR = pg.fundamentalSector(antipodal=True)

With the inversion added.

sR = pg.fundamentalSector(center=vector3d(1, 2, 3))

The Dirichlet domain about a centre.

sR = pg.fundamentalSector(angle=55*degree)

The rotation axes allowed at one rotation angle.

Description

The sector is the conventional one, the sector an inverse pole figure shows, wherever it is a fundamental domain of the group, which it is for every crystal symmetry; for a group turned against its axes it is a Dirichlet domain. With a centre it is the Dirichlet domain of that centre, the directions nearer to it than to any of its symmetric copies.

With an angle it is the sector of rotation axes the fundamental region of orientations allows at that rotation angle: small circles about the symmetry axes, of radius set by the angle and the fold of the axis; MATLAB intersects them with the conventional sector, here they stand alone.

A frame’s fundamentalSector places the sector by the frame’s plotting convention; a group has no convention and places it on x, y, z.

Input

pg symmetry

Keywords

keyword default description
center None vector3d, the centre of a Dirichlet domain
antipodal False add the inversion to the group, the sector of axes
angle None the rotation angle of misorientations, in radians, whose allowed axes are sought

Output

sR sphericalRegion

See also

sphericalRegion, symmetry.fundamentalRegion, conventionalSector, dirichletSector, CrystalSymmetries

MATLAB’s symmetry.fundamentalSector

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/symmetry.fundamentalSector_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.