a region of orientation space bounded by planes in the quaternions, mostly the fundamental region of a pair of frames

Syntax

oR = fundamentalRegion(cs)

The fundamental region of a crystal frame.

oR = fundamentalRegion(cs, cs, antipodal=True)

Of misorientations, with grain exchange.

oR = orientationRegion(N, cs, specimenFrame())

The region bounded by the quaternions N.

Description

The region holds the quaternions q with dot(q, N) <= 0 for every bounding quaternion N; q and -q are the same rotation.

The fundamental region of two frames, which fundamentalRegion builds, is the set of rotations closer to the identity than to any of their symmetric equivalents; projectIntoFundamentalRegion maps orientations into it. Where the two frames share rotations, about a common axis for instance, the planes alone do not separate the equivalents, and the region also restricts the rotation axes to a sector.

Input

N quaternion, or an array (n, 4), the normals of the bounding planes
frameA the first frame, the crystal frame
frameB the second frame, the specimen or a second crystal frame

Keywords

keyword default description
antipodal False identify a misorientation with its inverse, the grain exchange symmetry
common None the rotations, as an array (n, 4), the two frames share
sector None sphericalRegion, the sector of rotation axes where the frames share rotations
axisCenter None the centre of that sector, an array of three

Output

oR orientationRegion, with oR.CS and oR.SS its two frames, MATLAB’s CS1 and CS2

See also

fundamentalRegion, orientation.projectIntoFundamentalRegion, orientationRegion.checkInside, orientationRegion.plot, fundamentalSector

MATLAB’s orientationRegion.orientationRegion

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/orientationRegion.orientationRegion_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.