Volume_Quadrature_R​BF_Ball

This function computes quadrature weights on scattered data for evaluating the definite integral over the volume of the ball.

%==========================================================================
%
% This function provides example calls to the function
% Volume_Quadrature_RBF_Ball.m and Volume_Quadrature_RBF_Cube.
%
% The inputs to this function are:
% Domain_Type: Can be either 'Ball' for the ball of volume 1 centered at
% the origin, or 'Cube' for the unit cube (volume 1) centered at the
% origin
%
% Test_Function: This can be 1, 2, 3, or 4
%
% If Test_Function==1, the integrand is a degree 30 trivariate
% polynomial.
%
% If Test_Function==2, the integrand is a shifted and scaled Gaussian
%
% If Test_Function==3, the integrand is the sign(z)
%
% If Test_Function==4, the integrand is atan(5000(x^2+y^2+z^2))
%
% In all cases this function plots the error in the approximation of the
% definite integral of the integrand over the domain type and the
% computation time to construct the weights for different node set types
% and numbers of nodes.
%
% The quadrature weights generated will be saved to a new directory on your
% drive.
%
% The node sets for the ball used here are generated by a modification to
% the algorithm described in:
%
% P. Persson and G. Strang. A simple mesh generator in matlab. SIAM Review, 46(2):329-345,
% June 2004.
%
% The function Volume_Quadrature_RBF_Ball.m is the default implemenation of
% the method described in the preprint:
%
% J. A. Reeger. "Approximation of Definite Integrals Over the Volume of the Ball."
%
%==========================================================================