a function on SO(3) given by a callable that receives orientations

Syntax

SO3F = SO3FunHandle(lambda o: np.cos(angle(o, r)), cs)

A function of the orientations of cs.

SO3F = SO3FunHandle(fun, cs, ss, bandwidth=32)

Both frames, the bandwidth of its harmonic form.

SO3F = SO3FunHandle(fun, cs, ss, symmetrise=True)

Averaged over the groups on every call.

SO3F = SO3FunHandle(fun, cs, cs, antipodal=True)

With exchange symmetry, f(g) = f(inv(g)).

SO3F = SO3FunHandle(odf)

The handle of another SO3Fun.

Description

Nothing is precomputed: evaluating the function calls fun on orientations in the frames of the function, exactly. Every operation that needs coefficients, a pole figure, a convolution, a rotation, goes through SO3FunHarmonic(SO3F) of the bandwidth. The callable is trusted to be invariant under the groups unless symmetrise asks for the average. Exchange symmetry needs the same frame on both sides.

Input

`fun`	callable taking an orientation and returning its values, or an SO3Fun
`frames`	the crystal frame and the specimen frame, one or both, positionally

Keywords

keyword	default	description
`bandwidth`		the bandwidth of the harmonic form, by default the preference ‘defaultSO3Bandwidth’
`antipodal`		exchange symmetry, f(g) = f(inv(g)), for misorientations
`real`		the function takes only real values; the imaginary part of the values is dropped
`symmetrise`		average the callable over the groups of both frames on every call

Output

SO3F SO3FunHandle

Properties

`fun`	callable used for evaluation, including requested symmetry averaging
`bandwidth`	degree used when a harmonic approximation is needed
`CS, SS`	crystal and specimen frames passed to orientation queries
`isReal`	whether evaluation discards imaginary values
`antipodal`	whether grain exchange symmetry is requested

Members

cat	cat(a, b, …) is type(a).cat(a, b, …): the list of the operands, MATLAB’s [a, b], the carried attributes joined
eval	evaluate the callable at orientations in the function’s reference frames
rotate	the function rotated by r from the left or the right, through the harmonic form
SO3FunHandle	a function on SO(3) given by a callable that receives orientations

Used on

SO3FunHarmonicRepresentation, SO3FunApproximationTheory, SO3FunConcept, SO3FunConvolution, SO3FunDefinition

MATLAB’s SO3FunHandle_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/SO3FunHandle_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.

The class SO3FunHandle