Sets
Last update: February 06, 2021.
In this homepage we have stored several pointsets suitable for interpolation or cubature on intervals, simplex (triangle), square, disk and polygons.
We point out that concerning cubature rules in Phyton, a comprehensive list can be found at https://awesomeopensource.com/project/nschloe/quadpy.
INTERVAL:
» Interpolation
 General set with low Lebesgue constant: [.m]
 Extended Chebyshev: [.m]
 GaussLegendreLobatto (Fekete points in the interval): [.m]
SIMPLEX (TRIANGLE):
» Interpolation/Least squares sets
 General set with low Lebesgue constant: [.m] (last update: Jan 08, 2017, old version: [.m]).
 General set with low Lebesgue constant and GaussLegendreLobatto distribution on the side: [.m]
 General set with high absolute value of the Vandermonde matrix, i.e. (quasi) Fekete points: [.m]
 Symmetric set with low Lebesgue constant: [.m]
 Weakly Admissible Mesh: [.m]
 Approximate Fekete points (with degree from 1 to 70): [.m]
» Cubature
 Best cubature sets on the triangle (up to degree 50): [.m]
» Comparisons
 For a comparison on several interpolation sets see also: [html].
 For a comparison on several cubature sets see also: [html].
» Other contributions

You may find useful the Mfile for the evaluation of the Vandermonde matrix w.r.t.
 Dubiner Legendre basis [.m] as orthonormal basis;
 ProriolDubiner [.m] as orthogonal basis with its derivatives (in a form suitable for cubature, i.e. it is the transpose of the Vandermonde matrix for interpolation purposes).
SQUARE:
» Interpolation
 General set with low Lebesgue constant: [.m] (last update: Jan 08, 2017, old version: [.m]).
 General set with high absolute value of the Vandermonde matrix, i.e. (quasi) Fekete points: [.m]
 PaduaJacobi points with low Lebesgue constant: [.m]
 PaduaJacobi points with high absolute value of the Vandermonde matrix: [.m]
 Padua points: [.m]
» Cubature
 Almost minimal rules on the square (Legendre weight): [.m]
DISK:
» Interpolation/Least squares sets
» Cubature
 Cubature rules (Legendre weight): [.m]
SPHERE:
» Interpolation
 Maximum Determinant (Fekete, Extremal) points on the sphere S2 (R. Womersley homepage).
 Minimum Energy points on the sphere S2 (R. Womersley homepage).
 Recursive Zonal Equal Area (EQ) Sphere Partitioning (P. Leopardi homepage).
 Spherical designs: Efficient Spherical Designs with Good Geometric Properties (R. Womersley homepage).
 Spherical designs: Quadrature Rules on Manifolds: Putatively Optimal Quadrature Rules on the Sphere S2 (M. Graf homepage).
 Spherical designs: Spherical Designs (R. H. Hardin and N. J. A. Sloane homepage). Each file stores a unique vector v, so that x=v(1:3:end), y=v(2:3:end), z=v(3:3:end) and weights are equal.
 AlbrechtCollatz rules: [.m].
 HeoXu rules: [.m].
 Lebedev rules: [.m] (see also [.html]).
 McLaren rules: [.m].