A method of S2Fun.

the smiley, a test function on the sphere whose face shows where a plot puts the axes

Syntax

sF = S2Fun.smiley()

Its harmonic expansion by quadrature.

sF = S2Fun.smiley(bandwidth=256)

Of a given bandwidth.

values = S2Fun.smiley(v)

Its values at the directions v.

sF = S2Fun.smiley(exact=True)

The function itself, as a handle.

sF = S2Fun.smiley(even=True)

On both hemispheres, an antipodal function.

Description

The face is a sum of quadratic splines of the cosine about nine centres, the head, two eyes, the mouth and the nose; it reads upright in the convention ‘y↑→x’. The even smiley adds its reflection through the origin, so it takes the same value at v and -v. Further keywords go to S2FunHarmonic.quadrature.

Input

`v`	vector3d, directions to evaluate at

Keywords

keyword	default	description
`exact`	`False`	return the function as an S2FunHandle instead of its expansion
`even`	`False`	the antipodal smiley, the face also on the lower hemisphere

Output

`sF`	S2FunHarmonic, or S2FunHandle with exact=True
`values`	array of the shape of v

Used on

ClusterDemo, ContourPlots, SO3FunConvolution, S2FunHarmonicRepresentation, S2FunOperations, S2FunPlotting, S2FunSampling, S2FunSym, S2FunVectorValued

MATLAB’s S2Fun.smiley

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/S2Fun.smiley_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.

S2Fun.smiley