sphere_integrals, a C++ code which returns the exact value of the integral of any monomial over the surface of the unit sphere in 3D.
The surface of the unit sphere in 3D is defined by
x^2 + y^2 + z^2 = 1
The integrands are all of the form
f(x,y,z) = x^a y^b z^c
where the exponents are nonnegative integers.
If any exponent is an odd integer, the integral will be zero.
Thus, the "interesting" results occur when all exponents are even.
The information on this web page is distributed under the MIT license.
sphere_integrals is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.
cpp_integrals, a C++ code which returns the exact value of the integral of any monomial over a line, square, cube, a polygon, a circle, a disk, a sphere, a ball, a triangle, a tetrahedron, a simplex, and various other geometric regions.
sphere_monte_carlo, a C++ code which uses the Monte Carlo method to estimate the integral of a function over the surface of the unit sphere in 3D.