SPHERE_DESIGN_RULE is a dataset directory which contains files defining a number of Hardin and Sloane "spherical designs", which can be used for numerical quadrature.
A set of N points on the surface of a 3D sphere is called a spherical T-design if the integral of any polynomial p(x,y,z) of degree at most T over the surface of the sphere is equal to the average value of the polynomial evaluated at the set of points.
Note that the degree of a polynomial in several variables is the highest degree of any of its terms, and that the degree of a term like X^{A}Y^{B}Z^{C} is A+B+C.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
GEOMETRY, a FORTRAN90 library which computes various geometric quantities, including grids on spheres.
SCVT, a FORTRAN90 library which can find a set of well separated points on a sphere using Centroidal Voronoi Tessellations.
SPHERE_DESIGN_RULE, a FORTRAN90 library which returns point sets on the surface of the unit sphere, known as "designs", which can be useful for estimating integrals on the surface, among other uses.
SPHERE_GRID, a dataset directory which contains grids of points, lines, triangles or quadrilaterals on a sphere;
SPHERE_GRID, a FORTRAN90 library which provides a number of ways of generating grids of points, or of points and lines, or of points and lines and faces, over the unit sphere.
SPHERE_LEBEDEV_RULE, a dataset directory which contains sets of Lebedev points on a sphere, which can be used for quadrature rules of a known precision;
SPHERE_VORONOI, a MATLAB program which computes the Voronoi diagram of points on a sphere.
SPHERE_VORONOI_DISPLAY_OPENGL, a C++ program which displays a sphere and randomly selected generator points, and then gradually colors in points in the sphere that are closest to each generator.
SPHERE_XYZ_DISPLAY, a MATLAB program which reads XYZ information defining points in 3D, and displays a unit sphere and the points in the MATLAB graphics window.
SPHERE_XYZ_DISPLAY_OPENGL, a C++ program which reads XYZ information defining points in 3D, and displays a unit sphere and the points, using OpenGL.
STRI_QUAD, a FORTRAN90 library which estimates the integral of a function defined on the sphere.
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