the Dirichlet domain of a point group about a centre, a fundamental domain for every group, whatever axes it is written in

Syntax

sR = dirichletSector(cs)

About the centre of the conventional sector.

sR = dirichletSector(cs, center=vector3d(1, 2, 3))

About another centre.

sR = dirichletSector(cs, antipodal=True)

Of the Laue group, for axes.

sR = dirichletSector(pg, frame=cs)

Of a group, the region given in a frame.

Description

The region is bounded by the great circles bisecting the centre and each of its images under the group: the directions nearer the centre than any of its other images. Where the centre is not given, it is the centre of the conventional sector, or, when the inversion cancels it, the one of the proper subgroup. fundamentalSector takes the Dirichlet domain only for a group the conventional sector does not fit, such as the rotations two frames share.

Input

pg a point group, or a reference frame, whose group is taken and which the region is given in

Keywords

keyword default description
center None vector3d, the centre of the domain; by default the centre of the conventional sector
frame None the referenceFrame the region is given in
antipodal False the domain of the Laue group, for axes

Output

sR sphericalRegion

See also

fundamentalSector, sphericalRegion, tilesSphere, 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/dirichletSector_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.