Efficient spherical quadrature rules with positive weights

This function provides efficient (numerical) quadrature rules on the sphere in a 3D space. The weights in each quadrature are all positive.

The function "SphQuadrat.m" returns efficient quadrature rules on the sphere in a 3-dimensional space. The quadrature rules consist of the coordinates of the samling points and the (positive) weights of each point. Cartesian and spherical coordinate systems are available; please note that the notation of elevation angles θ in the spsherical coordinate systems differs from that in MATLAB. That is, the function returns vertical angles θ maesured from the z-axis.

Available exactitude degrees of the quadratures are MAT files containing the points and the weights of the quadratures are named as "xxx-yyyyy.mat", where "xxx" denotes the degree of exactitude and "yyyyy" denotes the number of points.

By default, the weights are normalized as while the function also provides -normalization and the-number-of-points-normalization

Reference: Manuel Gräf, Efficient Algorithms for the Computation of Optimal Quadrature Points on Riemannian Manifolds, Ph.D. thesis, Technische Universität Chemnitz, (2013)