the variants of a parent to child orientation relationship, and the child or parent orientations they give

Syntax

p2cVariants = variants(p2c)

The child variants.

p2pVariants = variants(p2c, parent=True)

The parent variants.

oriChild = variants(p2c, oriParent)

Every child variant of every parent.

oriChild = variants(p2c, oriParent, variantId)

One per parent, chosen by its id.

oriParent = variants(p2c, oriChild)

Every parent of every child.

oriParent = variants(p2c, oriChild, variantId)

One per child, chosen by its id.

odfChild = variants(p2c, odfParent)

The child texture.

Description

The child variants are the distinct p2c * r over the rotations r of the parent group modulo the child group; the parent variants, with parent=True, are the distinct r * p2c over the child group modulo the parent group.

They are numbered as MTEX numbers them, for Kurdjumov-Sachs as Morito does; this order is what a variant id means. The ids count from 1 up to the number of variants; an id outside is refused.

The second argument decides what is returned:

parent orientations: their child orientations, the representative of each parent in the fundamental region times the inverse child variants, along a new last axis, or one per parent with ids.
child orientations: their parent orientations instead, in the parent frame.
a parent texture (an SO3Fun): the child texture.

Input

`p2c`	orientation, the parent to child misorientation, from the parent frame to the child frame
`second`	orientation, the parent orientations, or the child orientations; SO3Fun, a parent texture; or ‘parent’, ‘child’
`ids`	the variant ids, one per orientation, broadcast against them; for a texture an SO3Fun of the parent orientations weighting the parents

Keywords

keyword	default	description
`parent`	`False`	the parent variants instead of the child variants

Output

`p2cVariants`	orientation, the variants, a list
`oriChild`	orientation, oriParent.shape + (numVariants,), or oriParent.shape with ids
`oriParent`	orientation, oriChild.shape + (numVariants,), or oriChild.shape with ids
`odfChild`	SO3Fun, the child texture

Used on

MisorientationTheory, LowLevelParentGrainReconstruction, MaParentGrainReconstruction, MaParentGrainReconstructionAdvanced, MartensiteVariants, ParentChildVariants, PhaseTransitions, TransformationTexture

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/variants_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.

variants