ball_monte_carlo

ball_monte_carlo, a MATLAB code which estimates the integral of F(X,Y,Z) over the interior of the unit ball in 3D.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

ball_monte_carlo 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.

Related Data and Programs:

ball_monte_carlo_test

ball_grid, a MATLAB code which computes grid points that lie inside the unit ball in 3D.

ball_integrals, a MATLAB code which defines test functions for integration over the interior of the unit ball in 3D.

matlab_monte_carlo, a MATLAB code which uses Monte Carlo sampling to estimate areas and integrals.

Reference:

1. Gerald Folland,
   How to Integrate a Polynomial Over a Sphere,
   American Mathematical Monthly,
   Volume 108, Number 5, May 2001, pages 446-448.

Source Code:

• ball01_monomial_integral.m, returns monomial integrals in the unit ball.
• ball01_sample.m, uniformly samples points from the unit ball.
• ball01_volume.m, returns the volume of the unit ball.
• monomial_value.m, evaluates a monomial.