a function on the sphere given by a callable that receives directions

Syntax

sF = S2FunHandle(lambda v: v.z**2)

A function of the directions.

sF = S2FunHandle(fun, cs)

In a crystal frame.

sF = S2FunHandle(fun, cs, antipodal=True)

Averaged over v and -v and the group.

sF = S2FunHandle(fun, cs, symmetrise=True)

Averaged over the group on every call.

sF = S2FunHandle(fun, cs, bandwidth=64)

The bandwidth of its harmonic form.

Description

Nothing is precomputed: evaluating the function calls fun on the directions, normalised and in the frame of the function, exactly. Every operation that needs coefficients, a convolution, a quadrature, a smooth plot, goes through S2FunHarmonic(sF) of the bandwidth. An antipodal function is averaged over v and -v and the group of the frame, unless symmetrise=False says the callable is symmetric by construction. An S2FunHarmonic given as fun becomes the handle of its evaluation.

Input

`fun`	callable taking a vector3d and returning its values, or an S2Fun
`frame`	crystalFrame or specimenFrame the directions are expressed in

Keywords

keyword	default	description
`bandwidth`		the bandwidth of the harmonic form, by default the quadrature bandwidth
`antipodal`		the function fulfils f(v) = f(-v)
`real`		the function takes only real values; the imaginary part of the values is dropped
`symmetrise`		average the callable over the group of the frame (and over v and -v when antipodal) on every call; by default only when antipodal

Output

`sF`	S2FunHandle

Properties

`fun`	callable used for evaluation, including requested symmetry averaging
`bandwidth`	degree used when a harmonic approximation is needed
`frame`	reference frame passed to directional queries
`isReal`	whether evaluation discards imaginary values
`antipodal`	whether opposite directions are identified

Members

CS	the frame of the function, MATLAB’s sF.CS
eval	evaluate the callable at unit directions in the function’s frame
exp	the pointwise exponential, a handle evaluated when asked
log	the pointwise logarithm, a handle evaluated when asked
mean	the mean over the sphere, through the harmonic form
rotate	the function rotated by r, through the harmonic form
S2FunHandle	a function on the sphere given by a callable that receives directions
textureIndex	the texture index of a function on SO(3) or on the sphere, the squared L2 norm of its harmonic expansion

Used on

SO3FunConvolution

MATLAB’s S2FunHandle_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/S2FunHandle_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 S2FunHandle