an axis field on the sphere by a harmonic series: an axis without sign at every direction, as the principal directions of a stress or the polarisations of a wave

Syntax

aF = S2AxisFieldHarmonic(lambda v: ..., cs, bandwidth=16)

Approximates a function of the directions.

aF = S2AxisFieldHarmonic(v, axes, bandwidth=16)

Fits axes given at the directions v.

aF = S2AxisFieldHarmonic(vF)

Approximates a vector or axis field.

aF = S2AxisFieldHarmonic(fhat, cs)

From the coefficients of the six components.

Description

Since an axis has no sign, the field expands not the axis a but the six entries of the symmetric matrix a a^T in spherical harmonics. Evaluation recovers the axis as the leading eigenvector of that matrix.

A function or a field is approximated by quadrature on a grid of the bandwidth. Axes at scattered directions enter the quadrature sum with the weights given, equal by default; S2AxisFieldHarmonic.interpolate fits them by least squares instead. The field is symmetrised under the group of its frame unless symmetrise=False.

The coefficient form takes a (L+1)^2 x 6 matrix, one column per component xx, xy, xz, yy, yz, zz, in MTEX’s basis: the coefficients aF.fhat returns. S2AxisField is the abstract class of axis fields, S2AxisFieldHandle the field of a function evaluated where it is asked.

Input

`fhat`	a function of vector3d returning axes, S2VectorField or S2AxisField, vector3d of directions, or the coefficient matrix
`args`	the axes at the directions, and the crystalFrame or specimenFrame of the field

Keywords

keyword	default	description
`bandwidth`	`None`	the largest harmonic degree; by default the preference ‘defaultS2Bandwidth’, for a field the field’s
`weights`	`None`	the quadrature weights of axes at scattered directions
`symmetrise`	`True`	symmetrise the field under the group of its frame

Output

`aF`	S2AxisFieldHarmonic

Used on

S2FunAxisField

MATLAB’s S2AxisField.S2AxisField

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/S2AxisField.S2AxisField_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.

S2AxisField.S2AxisField