POLYGON_MONTE_CARLO
Monte Carlo Estimate of Integrals Over Polygon in 2D

POLYGON_MONTE_CARLO is a C++ 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 FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

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 uses the Monte Carlo method to estimate integrals over 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 applies a Monte Carlo method to estimate the integral of a function over the interior of the unit 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;

HYPERBALL_VOLUME_MONTE_CARLO, a C++ program which applies a Monte Carlo method to estimate the volume 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 hypersphere 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_INTEGRALS, a C++ library which returns the exact value of the integral of any monomial over the interior of a polygon in 2D.

POLYGON_PROPERTIES, a C++ 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 C++ 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 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_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 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 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.

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

Source Code:

• polygon_monte_carlo.cpp, the source code.
• polygon_monte_carlo.hpp, the include file.
• polygon_monte_carlo.sh, BASH commands to compile the source code.

Examples and Tests:

• polygon_monte_carlo_prb.cpp, a sample calling program.
• polygon_monte_carlo_prb.sh, BASH commands to compile and run the sample program.
• polygon_monte_carlo_prb_output.txt, the output file.

List of Routines:

• BETWEEN is TRUE if vertex C is between vertices A and B.
• COLLINEAR returns a measure of collinearity for three points.
• DIAGONAL: VERTEX(IM1) to VERTEX(IP1) is a proper internal diagonal.
• DIAGONALIE is true if VERTEX(IM1):VERTEX(IP1) is a proper diagonal.
• IN_CONE is TRUE if the diagonal VERTEX(IM1):VERTEX(IP1) is strictly internal.
• INTERSECT is true if lines VA:VB and VC:VD intersect.
• INTERSECT_PROP is TRUE if lines VA:VB and VC:VD have a proper intersection.
• L4_XOR returns the exclusive OR of two L4's.
• MONOMIAL_VALUE evaluates a monomial.
• POLYGON_AREA determines the area of a polygon.
• POLYGON_INTEGRAL integrates a monomial over a polygon.
• POLYGON_SAMPLE uniformly samples a polygon.
• POLYGON_TRIANGULATE determines a triangulation of a polygon.
• R8_CHOOSE computes the binomial coefficient C(N,K) as an R8.
• R8_UNIFORM_01 returns a pseudorandom R8 scaled to [0,1].
• R8VEC_UNIFORM_01_NEW returns a unit pseudorandom R8VEC.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• TRIANGLE_AREA computes the signed area of a triangle.

You can go up one level to the C++ source codes.