**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.

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

**polygon_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 uses the monte carlo method to estimate integrals over 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 hypersphere 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_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of a polygon in 2d.

polygon_properties, a MATLAB code which computes properties of an arbitrary polygon in the plane, defined by a sequence of vertices, including interior angles, area, centroid, containment of a point, convexity, diameter, distance to a point, inradius, lattice area, nearest point in set, outradius, uniform sampling.

polygon_triangulate, a MATLAB code which triangulates a possibly nonconvex polygon, and which can use gnuplot to display the external edges and internal diagonals of the triangulation.

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_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 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 the interior of the unit tetrahedron in 3d.

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.
- polygon_area.m, determines the area of a polygon.
- polygon_monomial_integral.m, integrates a monomial over a polygon.
- polygon_sample.m, uniformly samples a polygon.
- triangle_area.m, returns the area of a triangle.