Monte Carlo Estimate of Sphere Surface Integrals

**SPHERE_MONTE_CARLO**,
a C library 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 GNU LGPL 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 C library 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 C library 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 C library 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 C library 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 C library which uses the Monte Carlo method to estimate integrals over the interior of the general disk in 2D.

DISK01_MONTE_CARLO, a C library which uses the Monte Carlo method to estimate integrals over the interior of the unit disk in 2D.

DISK01_QUARTER_MONTE_CARLO, a C library 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 C library which uses the Monte Carlo method to estimate the value of integrals over the interior of an ellipse in 2D.

ELLIPSOID_MONTE_CARLO a C library 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 C library 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 C library 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 C library 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 C library which uses the Monte Carlo method to estimate integrals over the length of the unit line in 1D.

POLYGON_MONTE_CARLO, a C library 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 C library 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 C library which uses the Monte Carlo method to estimate integrals over the interior of the unit simplex in M dimensions.

SPHERE_TRIANGLE_MONTE_CARLO, a C library 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 C library 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 C library which uses the Monte Carlo method to estimate integrals over the interior of a general tetrahedron.

TETRAHEDRON01_MONTE_CARLO, a C library which uses the Monte Carlo method to estimate integrals over the interior of the unit tetrahedron in 3D.

TRIANGLE_MONTE_CARLO, a C library which uses the Monte Carlo method to estimate integrals over the interior of a triangle in 2D.

TRIANGLE01_MONTE_CARLO, a C library which uses the Monte Carlo method to estimate integrals over the interior of the unit triangle in 2D.

WEDGE_MONTE_CARLO, a C library which uses the Monte Carlo method to estimate integrals over the interior of the unit wedge in 3D.

- sphere_monte_carlo.c, the source code.
- sphere_monte_carlo.sh, compiles the source code.
- sphere_monte_carlo.h, the include file