**sphere_monte_carlo**,
a MATLAB code which
estimates the integral of F(X,Y,Z)
over the surface of the unit sphere in 3D.

The computer code and data files described and made available on this web page are distributed under the MIT license

**sphere_monte_carlo** is available in
a C version and
a C++ version and
a FORTRAN90 version and
a MATLAB version and
a Python version.

annulus_monte_carlo a MATLAB code which uses the monte carlo method to estimate the integral of a function over the interior of a circular annulus in 2d.

ball_monte_carlo, a MATLAB code which applies a monte carlo method to estimate integrals of a function over the interior of the unit ball in 3d;

circle_monte_carlo, a MATLAB code which applies a monte carlo method to estimate the integral of a function on the circumference of the unit circle in 2d;

cube_monte_carlo, a MATLAB code which applies a monte carlo method to estimate the integral of a function over the interior of the unit cube in 3d.

disk_monte_carlo, a MATLAB code which uses the monte carlo method to estimate integrals over the interior of the general disk in 2d.

disk01_monte_carlo, a MATLAB code which uses the monte carlo method to estimate integrals over the interior of the unit disk in 2d.

disk01_quarter_monte_carlo, a MATLAB code which applies a monte carlo method to estimate the integral of a function over the interior of the unit quarter disk in 2d;

ellipse_monte_carlo a MATLAB code which uses the monte carlo method to estimate the value of integrals over the interior of an ellipse in 2d.

ellipsoid_monte_carlo a MATLAB code which uses the monte carlo method to estimate the value of integrals over the interior of an ellipsoid in m dimensions.

hyperball_monte_carlo, a MATLAB code which applies a monte carlo method to estimate the integral of a function over the interior of the unit hyperball in m dimensions;

hypercube_monte_carlo, a MATLAB code which applies a monte carlo method to estimate the integral of a function over the interior of the unit hypercube in m dimensions.

hypersphere_monte_carlo, a MATLAB code which applies a monte carlo method to estimate the integral of a function on the surface of the unit sphere in m dimensions;

line_monte_carlo, a MATLAB code which uses the monte carlo method to estimate integrals over the length of the unit line in 1d.

polygon_monte_carlo, a MATLAB code which applies a monte carlo method to estimate the integral of a function over the interior of a polygon in 2d.

pyramid_monte_carlo, a MATLAB code which applies a monte carlo method to estimate integrals of a function over the interior of the unit pyramid in 3d;

simplex_monte_carlo, a MATLAB code which uses the monte carlo method to estimate integrals over the interior of the unit simplex in m dimensions.

sphere_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the surface of the unit sphere in 3d.

sphere_triangle_monte_carlo, a MATLAB code which applies a monte carlo method to estimate the integral of a function over a spherical triangle on the surface of the unit sphere in 3d;

square_monte_carlo, a MATLAB code which applies a monte carlo method to estimate the integral of a function over the interior of the unit square in 2d.

tetrahedron_monte_carlo, a MATLAB code which uses the monte carlo method to estimate integrals over a tetrahedron.

triangle_monte_carlo, a MATLAB code which uses the monte carlo method to estimate integrals over the interior of a triangle in 2d.

triangle01_monte_carlo, a MATLAB code which uses the monte carlo method to estimate integrals over the interior of the unit triangle in 2d.

wedge_monte_carlo, a MATLAB code which uses the monte carlo method to estimate integrals over the interior of the unit wedge in 3d.

- monomial_value.m, evaluates a monomial.
- sphere01_area.m, returns the area of the unit sphere.
- sphere01_monomial_integral.m, integrates a monomial on a sphere.
- sphere01_sample.m, maps uniform points onto the unit sphere.