a reference frame, the coordinate system data is expressed in: an identity, a basis, the point group the data is invariant under and the default plotting convention
Syntax
f = referenceFrame(name='lab', axesNames=('A', 'B', 'C'))
A frame of the canonical basis.
f = referenceFrame(basis)
A frame of the given basis vectors.
Description
The base class of crystalFrame, the frame glued to the lattice of a phase, and specimenFrame, the frame of a sample; use those. A frame carries an identity, a name such as ‘measurement’, ‘rolling’ or a mineral; the basis vectors in canonical Euclidean coordinates, whose lengths count; the point group; and the plotting convention its data is drawn in. Frames are handles compared by identity, registered and sealed by the session; transformationMatrix gives the change of coordinates between two frames.
Input
basis |
vector3d or 3 x 3 array, the basis vectors in canonical coordinates, by default the canonical basis |
Keywords
| keyword | default | description |
|---|---|---|
name |
the identity of the frame | |
axesNames |
the names of the three axes | |
how2plot |
the default plottingConvention of the frame | |
sym |
the point group, by default the trivial one | |
color |
the colour of the frame’s data in a phase map |
Output
f |
referenceFrame |
See also
crystalFrame, specimenFrame, plottingConvention, referenceFrame.transformationMatrix
Members
| axesNames | the names of the three axes, (‘X’, ‘Y’, ‘Z’), (‘a’, ‘b’, ‘c’) or (‘RD’, ‘TD’, ‘ND’) |
| basis | the basis vectors of the frame in the canonical Euclidean coordinates, one per row |
| byName | the specimen frame registered under a name |
| char | the name of the frame, or its class name |
| clone | make an editable, unregistered copy of a reference frame |
| conventionalSector | the conventional sector of the group, the one MTEX draws, oriented by the up and east directions of the frame’s plotting convention |
| conventionChar | the plotting convention in the frame’s own axes names, e.g |
| disjoint | the sibling frame carrying the intersection of the two groups |
| elements | the rotational axes of the group, both signs, and their multiplicities |
| factor | the factorisation of the two groups: self = rot1 * d and other = d * rot2 with d the common elements |
| fullSym | the largest group registered over this basis |
| fundamentalRegion | the fundamental region in orientation space of this group, or of the pair with another frame |
| fundamentalSector | the fundamental sector of the group of the frame on the sphere, the region an inverse pole figure shows |
| how2plot | the default plotting convention the frame is drawn with, a plottingConvention or None |
| id | numeric identifier of the point group carried by the frame |
| intern | the session instance of a frame: the registered one when it agrees by key, otherwise this one, registered and sealed from now on |
| isAligned | whether two frames have the same basis, up to a relative tolerance on the basis vectors |
| isclose | whether two frames may be treated as one: the same class of group and aligned bases, and for crystal frames the same mineral (MATLAB’s eqTol) |
| isCompatible | whether a transition between the frames exists, and the transition |
| isIndexed | whether the frame is an indexed phase, False for the notIndexedFrame |
| isLaue | whether the point group is a Laue group, i.e |
| isProper | whether the point group has proper rotations only |
| lattice | the crystal system of the point group, a latticeType |
| Laue | the sibling frame carrying the Laue group, the group with the inversion added |
| LaueName | the international symbol of the Laue class of the group |
| mineral | the mineral of the frame, its name |
| multiplicityPerpZ | the highest order of a rotation of the group about an axis perpendicular to z |
| multiplicityZ | the highest order of a rotation of the group about the z axis |
| nfold | the highest order of a symmetry axis of the group |
| numProper | the number of proper rotations in the point group |
| numSym | the number of elements of the point group |
| plot | the elements of the point group of a frame drawn on the upper hemisphere, as the international tables draw them |
| pointGroup | the Hermann-Mauguin symbol of the point group |
| properGroup | replace each point-group operation by its proper rotational part |
| properSubGroup | return a sibling frame containing only the group’s proper rotations |
| referenceFrame | a reference frame, the coordinate system data is expressed in: an identity, a basis, the point group the data is invariant under and the default plotting convention |
| reset | clear the session’s frame register, named frames and default frame |
| rot | the elements of the point group, an orthogonalTransform |
| rotations | return only the proper rotations in this frame’s point group |
| Schoenflies | the Schoenflies symbol of the point group |
| sibling | this frame with another group in it, from the register |
| sim | whether two frames describe the same symmetry, without requiring aligned bases |
| stripSym | return an interned sibling frame with the same basis and no nontrivial symmetry |
| sym | the point group the frame carries, a symmetry |
| transformationMatrix | the transition matrix taking coordinates in this frame to coordinates in the other, on normalised bases: with the unit axes as rows, inv(B) A is the rotation between the two settings of one lattice |
| union | return a frame whose group is generated by this group and another group or operation |
MATLAB’s referenceFrame_index
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/referenceFrame_index_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.