hexagon_monte_carlo

hexagon_monte_carlo, an Octave code which applies a Monte Carlo method to estimate the integral of a function over the interior of a hexagon.

The code currently only looks at the special case of the unit hexagon, although this can be easily extended to more general sizes, shapes, and orientations.

Licensing:

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

Languages:

hexagon_monte_carlo is available in a MATLAB version and an Octave version..

Related Data and Programs:

hexagon_monte_carlo_test

annulus_monte_carlo an Octave 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, an Octave 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, an Octave code which uses the Monte Carlo method to estimate integrals over the circumference of the unit circle in 2D.

cube_monte_carlo, an Octave 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, an Octave code which uses the Monte Carlo method to estimate integrals over the interior of the general disk in 2D.

disk01_monte_carlo, an Octave code which uses the Monte Carlo method to estimate integrals over the interior of the unit disk in 2D.

disk01_quarter_monte_carlo, an Octave 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 an Octave code which uses the Monte Carlo method to estimate the value of integrals over the interior of an ellipse in 2D.

ellipsoid_monte_carlo an Octave code which uses the Monte Carlo method to estimate the value of integrals over the interior of an ellipsoid in M dimensions.

line_monte_carlo, an Octave code which uses the Monte Carlo method to estimate integrals over the length of the unit line in 1D.

simplex_monte_carlo, an Octave code which uses the Monte Carlo method to estimate integrals over the interior of the unit simplex in M dimensions.

Source Code:

• hexagon01_area.m, determines the area of the unit hexagon.
• hexagon01_integral.m, evaluates a monomial integral in the unit hexagon.
• hexagon01_monte_carlo.m, applies the Monte Carlo method to estimate the integral of a function f(x,y) over the interior of the unit hexagon.
• hexagon01_sample.m, uniformly samples the unit hexagon.
• moment_polygon.m, computes an unnormalized moment of a polygon.
• monomial_value_2d.m, evaluates a monomial.