A class representing a function on the 2-sphere S^2.
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) |
| w | @function_handle (weight function) |
| predefined choices include 'C1hat' (default), 'const', 'cos', 'hat', 'indicator', 'squared hat', 'wendland', and 'wendlandC6' | |
| use_smooth_delta | use a smooth local support radius with about S2F.nn neighbors at each center |
| use_vor_weights | multiply the local weights by Voronoi areas |
| distance | metric for neighbor search (default: 'euclidean') |
| 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 | center amplification approached at full correction (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 |