POLYGON_MONTE_CARLO
Monte Carlo Estimate of Integrals Over Polygon in 2D

POLYGON_MONTE_CARLO, a MATLAB library which applies a Monte Carlo method to estimate the integral of a function over the interior of a polygon in 2D.

Licensing:

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

Languages:

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.

Related Data and Programs:

ANNULUS_MONTE_CARLO a MATLAB 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 MATLAB 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 MATLAB library which uses the Monte Carlo method to estimate integrals over the circumference of the unit circle in 2D.

CUBE_MONTE_CARLO, a MATLAB 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 MATLAB library which uses the Monte Carlo method to estimate integrals over the interior of the general disk in 2D.

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

DISK01_QUARTER_MONTE_CARLO, a MATLAB 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 MATLAB 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 MATLAB 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 MATLAB library which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit hyperball in M dimensions;

HYPERBALL_VOLUME_MONTE_CARLO, a MATLAB program which applies a Monte Carlo method to estimate the volume of the unit hyperball in M dimensions;

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

POLYGON_INTEGRALS, a MATLAB library which returns the exact value of the integral of any monomial over the interior of a polygon in 2D.

polygon_monte_carlo_test

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

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

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

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

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

Source Code:

• 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.
• r8_choose.m, computes the binomial coefficient C(N,K) as an R8.
• r8_uniform_01.m, returns a pseudorandom unit R8.
• r8vec_uniform_01.m, returns a pseudorandom unit R8VEC.
• timestamp.m, prints the current YMDHMS date as a time stamp.
• triangle_area.m, returns the area of a triangle.