S2FunMLS.S2FunMLS edit page

A class representing a function on the 2-sphere S^2.

The function is not stored by coefficients, but by nodes and values. It is evaluated by a moving least squares approximation: at every evaluation point a small weighted least squares problem over a local polynomial ansatz space is solved, using only the nodes in a compactly supported neighborhood of that point.

Syntax

S2F = S2FunMLS(nodes, values);
S2F = S2FunMLS(nodes, values, 'degree', 3, 'oF', 4);
S2F = S2FunMLS(nodes, values, 'delta', 5*degree, 'weight', @(t)(...));
S2F = S2FunMLS(nodes, values, 'centered', true, 'monomials', true, ...
  'subsample', 'tangent', true);
S2F = S2FunMLS(nodes, values, 'detectOutliers', ...
  'use_vor_weights', 'use_smooth_delta');

Input

nodes vector3d (data points)
values array of function values assigned to the nodes

Output

S2F S2FunMLS

Options

degree polynomial degree used for approximation
oF oversampling factor; nn is S2F.dim times this factor
oF_max maximal oversampling factor for range search
delta support radius of the weight function; delta = 0 uses KNN
monomials use a monomial basis, otherwise spherical harmonics
centered evaluate the basis in local coordinates around the north pole
tangent use monomials on the tangent plane (requires centered = true) (NOTE: centered and tangent automatically enable the monomial basis)
weight @function_handle (weight function)
predefined choices are 'auto' (default, a degree-dependent Wendland C6 variant), 'C1hat', 'const', 'cos', 'hat', 'indicator', 'plateau', 'squared hat', 'wendland', 'wendlandC6', 'wendlandSquared', and 'wendlandC6Squared'
use_smooth_delta use a smooth local support radius with about S2F.nn neighbors at each center
candidateFactor KNN candidates fetched per center as a multiple of nn (default 2, only used with use_smooth_delta)
use_vor_weights multiply the local weights by Voronoi areas
distance metric for neighbor search (default: 'euclidean')
run 'help rangesearch' for the available options
s symmetry of the nodes
regularize use goal-oriented regularization of the local systems
mincond center-amplification threshold where regularization starts
maxcond center-amplification threshold where full correction is used
targetcond inverse-amplification bound at full correction; one is the minimum-norm constant-preserving limit (The property names are retained for compatibility. They no longer refer to the ordinary condition number of the Gram matrix.)
outlierDetectionRange number of neighbors used for outlier detection

Flags

detectOutliers detect local outliers and reduce their MLS weights
subsample select a subset that minimizes the Lebesgue constant

See also

SO3FunMLS S2FunHarmonic S2FunTri S2FunMLS.eval S2FunMLS.approximate

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/S2FunMLS.S2FunMLS.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.