base class for scalar functions of a direction on the unit sphere

Description

Use S2FunHarmonic for spherical harmonic coefficients, S2FunHandle for a callable, S2FunTri for values on a triangulation, or S2FunBingham for an axial density. Evaluate a concrete function with f(v), where v is vector3d or Miller directions. A frame can impose crystal symmetry; antipodal functions satisfy f(v)=f(-v).

Directional densities from calcDensity and S2FunBingham have spherical mean one, equivalent to integral 4*pi with surface-area measure. General S2Fun objects may also represent signed or complex functions and are not automatically normalised densities.

This base class supplies the common interface; construct one of its representations.

Members

contour	contour(sF), contour(v), contour(v, data): contour lines
contourf	contourf(sF), contourf(v), contourf(v, data): filled contours
discrepancy	the discrepancy between two densities and/or weighted point sets on the sphere (S2Fun, vector3d) or on SO(3) (SO3Fun, rotation, orientation), in either order
discreteSample	a random sample of n orientations drawn from an orientation density, of directions from a density on the sphere, of numbers from a density on an interval, or n random members of a list
interpolate	a function on the sphere through the values at the nodes, a regularised least squares fit
max	the maximum of a function on SO(3) or the sphere, the value and the position, numLocal local maxima from a grid refined down to the accuracy
min	the minimum of a function on SO(3) or the sphere, the value and the position, numLocal local minima
optimalSample	the sample of n nodes that reproduces a density best up to the bandwidth, on the sphere or the rotation group
pcolor	pcolor(sF), pcolor(v), pcolor(v, data): a coloured surface
plot3d	plot3d(v), plot3d(v, data), plot3d(sF), plot3d(vF), plot3d(oR), plot3d(ori), plot3d(odf)
plot	plot(x, …) draws x as its kind is drawn
plotSection	plotSection(odf), plotSection(odf, ‘sigma’), plotSection(ori, oS, sections=9)
quiver3	arrows in space: tangent vectors in orientation space, a field on the sphere or SO(3), or arrows at positions
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
rotate	rotate(x, rot) is x.rotate(rot), or rot * x for an object without that method
S2Fun	base class for scalar functions of a direction on the unit sphere
smiley	the smiley, a test function on the sphere whose face shows where a plot puts the axes
sum	sum(x) of an MTEX object by its own sum, of an array or with an axis as NumPy sums, of any other iterable as Python sums, so that from mtex import * keeps Python’s sum
surf	a function on the sphere as a surface in space, the sphere pushed out to \|f\| and coloured by f
times	times(A, B) is A.times(B): the product of corresponding coefficients, MATLAB’s A .* B
unimodal	a unimodal function on the sphere, a radial kernel about one direction, as a harmonic expansion
volume	the share of orientations within a radius of a centre: the integral of f over the ball, int_{angle(g, c) < r} f(g) dg, relative to the integral over all orientations

MATLAB’s S2Fun_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/S2Fun_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 S2Fun

Description

See also

Members