a vector field on the sphere by the spherical harmonic expansions of its three Cartesian components
Syntax
vF = S2VectorFieldHarmonic(lambda v: v.cross(vector3d.Z), bandwidth=16)
A callable of the directions.
vF = S2VectorFieldHarmonic(v, w, weights=wq)
Vectors at directions, by quadrature.
vF = S2VectorFieldHarmonic([sFx, sFy, sFz])
The component functions.
vF = S2VectorFieldHarmonic(fhat, cs)
The coefficients, (L+1)^2 x 3.
vF = S2VectorFieldHarmonic(sF.grad())
The expansion of another field.
vF = S2VectorFieldHarmonic.quadrature(lambda v: v.cross(vector3d.Z))
MATLAB’s form.
Description
A callable is evaluated on a quadrature grid of the bandwidth and expanded; vectors w at directions v are expanded with the quadrature weights given, equal ones by default, which suits directions spread evenly; two component functions leave z zero. The field is projected onto the fields equivariant under the group of the frame, which a crystal frame asks for, unless symmetrise=False. vF.x, vF.y, vF.z are the components, vF.bandwidth the largest degree.
Input
fun |
callable taking a vector3d and returning vector3d, or an S2VectorField |
v |
vector3d, the directions of given vectors |
w |
vector3d, the vectors at them |
sFx, sFy, sFz |
S2FunHarmonic, the components |
fhat |
complex array of (L+1)^2 x 3 coefficients |
cs |
crystalFrame or specimenFrame of the directions |
Keywords
| keyword | default | description |
|---|---|---|
bandwidth |
the largest degree of the expansion, by default the preference ‘defaultS2Bandwidth’; truncates a field given | |
weights |
the quadrature weights of the directions v | |
symmetrise |
project onto the fields equivariant under the group of the frame |
Output
vF |
S2VectorFieldHarmonic |
See also
S2VectorField, S2FunHarmonic, S2AxisFieldHarmonic, S2FunVectorField
Members
| angle | the angle between two fields at every direction, or between the field and a constant vector, a function on the sphere |
| antipode | the field of the antipode, v(-xi) |
| bandwidth | the harmonic degree up to which the components are expanded |
| component | one component as a function without the group |
| cross | F x x = -[x]_x F, on the rows of the coefficients F [x]_x |
| dot | the inner product with a constant vector, exact, a function without the group |
| dot | the inner product with a constant vector, exact, a function without the group |
| eval | the vectors of the field at the directions x, vF(x) |
| fhat | the coefficients of the components in MTEX’s basis, one column per component |
| interpolate | the least squares fit to vectors at directions |
| isclose | whether two fields agree in their coefficients up to the relative tolerance rtol |
| mean | the mean vector of the field over the sphere, read off the coefficients of degree zero |
| minus | |
| mtimes | |
| norm | the length at every direction, a function on the sphere, as MATLAB’s norm |
| norm | the length at every direction, a function on the sphere, as MATLAB’s norm |
| normal | the field of the outer normals, v at v, exact at bandwidth one |
| normalize | the field scaled to unit length at every direction |
| plot | plot(x, …) draws x as its kind is drawn |
| plotSection | plotSection(odf), plotSection(odf, ‘sigma’), plotSection(ori, oS, sections=9) |
| plus | |
| quadrature | S2VectorFieldHarmonic.quadrature(f, bandwidth=L), from a callable or from nodes and values with their weights, MATLAB’s name for the constructor |
| quiver3 | arrows in space: tangent vectors in orientation space, a field on the sphere or SO(3), or arrows at positions |
| quiver | arrows: tangent vectors at directions, a vector or axis field on the sphere, arrows at orientations in the sections of the current figure, or directions on a map or a volume |
| quiverSection | arrows on a section plot: of a function on the sphere along one of its circles, or at orientations in the sections of orientation space |
| rdivide | |
| rotate | v’(xi) = r v(r^-1 xi): the components rotate and mix |
| S2VectorField | a vector field on the sphere by the spherical harmonic expansions of its three Cartesian components |
| S2VectorFieldHarmonic | a vector field on the sphere by the spherical harmonic expansions of its three Cartesian components |
| symmetrise | the projection onto the equivariant fields of the frame, v(s xi) = s v(xi) for the elements of the group including the improper ones |
| times | |
| truncate | the field cut off, or padded with zeros, at the bandwidth L |
| uminus | |
| x | the Cartesian components as functions |
| y | the y component as a function on the sphere |
| z | the z component as a function on the sphere |
Used on
MATLAB’s S2VectorFieldHarmonic_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/S2VectorFieldHarmonic_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.