Efficient spherical quadrature rules with positive weights

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 spherical coordinate systems differs from that in MATLAB. That is, the function returns vertical angles θ measured from the z-axis.

Available exactitude degrees of the quadratures are 0,2,4,...,100.

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 sum(weight)=1, while the function also provides 4pi-normalization sum(weight)=4*pi and the-number-of-points-normalization sum(weight)=numel(weight).

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