hypersphere_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the surface of the unit hypersphere in M dimensions.
The surface of the unit hypersphere in M dimensions is defined by
sum ( 1 <= i <= m ) x(i)^2 = 1
The integrands are all of the form
f(x) = product ( 1 <= m <= m ) x(i) ^ e(i)
where the exponents e 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.
hypersphere_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.
hypersphere, a MATLAB code which carries out various operations for an M-dimensional hypersphere, including converting between Cartesian and spherical coordinates, stereographic projection, sampling the surface of the sphere, and computing the surface area and volume.
hypersphere_monte_carlo, a MATLAB code which uses the Monte Carlo method to estimate the integral of a function over the surface of the unit hypersphere in M dimensions.
matlab_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the surface or interior of some geometric object, including a line, quadrilateral, box, circle, disk, sphere, ball and others.