sphere_triangle_quad, a Fortran77 code which estimates the integral of a scalar function F(X,Y,Z) over a spherical triangle on the unit sphere.
Three methods of estimation are very crude and cannot be improved:
One method of estimation uses random sampling, the Monte Carlo method, whose accuracy can be improved by increasing the number of sample points.
Another method is based on the centroid rule, but allows the user to decompose the original spherical triangle into collection of smaller triangles. The accuracy of the estimate should improve as the size of these triangles decreases.
The computer code and data files described and made available on this web page are distributed under the MIT license
sphere_triangle_quad is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version.
random_data, a Fortran77 library which generates sample points for various probability distributions, spatial dimensions, and geometries;
SPHERE_EXACTNESS, a Fortran77 program which tests the monomial exactness of a quadrature rule over the surface of the unit sphere in 3D.
SPHERE_GRID, a Fortran77 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 surface of the unit sphere in 3D.
SPHERE_INTEGRALS, a Fortran77 library which defines test functions for integration over the surface of the unit sphere in 3D.
SPHERE_LEBEDEV_RULE, a Fortran77 library which computes Lebedev quadrature rules over the surface of the unit sphere in 3D.
SPHERE_MONTE_CARLO, a Fortran77 library which applies a Monte Carlo method to estimate the integral of a function over the surface of the sphere in 3D;
SPHERE_QUAD, a Fortran77 library which approximates an integral over the surface of the unit sphere by applying a triangulation to the surface;
SPHERE_TRIANGLE_MONTE_CARLO, a Fortran77 library which estimates the integral of a function over a spherical triangle using the Monte Carlo method.
STROUD, a Fortran77 library which approximates the integral of a function on the surface or in the interior of a variety of geometric shapes.