polygon_monte_carlo, a FORTRAN90 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 FORTRAN90 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 FORTRAN90 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 FORTRAN90 code which uses the Monte Carlo method to estimate integrals over the circumference of the unit circle in 2D.
CUBE_MONTE_CARLO, a FORTRAN90 code which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit cube in 3D;
DISK01_MONTE_CARLO, a FORTRAN90 code which uses the Monte Carlo method to estimate integrals over the interior of the unit disk in 2D.
DISK01_QUARTER_MONTE_CARLO, a FORTRAN90 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 FORTRAN90 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 FORTRAN90 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 FORTRAN90 code 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 FORTRAN90 code which applies a Monte Carlo method to estimate the volume of the unit hyperball in M dimensions;
HYPERCUBE_MONTE_CARLO, a FORTRAN90 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 FORTRAN90 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 FORTRAN90 code which uses the Monte Carlo method to estimate integrals over the length of the unit line in 1D.
POLYGON_INTEGRALS, a FORTRAN90 code which returns the exact value of the integral of any monomial over the interior of a polygon in 2D.
POLYGON_PROPERTIES, a FORTRAN90 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 FORTRAN90 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 FORTRAN90 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 FORTRAN90 code which uses the Monte Carlo method to estimate integrals over the interior of the unit simplex in M dimensions.
SPHERE_MONTE_CARLO, a FORTRAN90 code 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 FORTRAN90 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 FORTRAN90 code which uses the Monte Carlo method to estimate integrals over the interior of the unit tetrahedron in 3D.
TRIANGLE_MONTE_CARLO, a FORTRAN90 code which uses the Monte Carlo method to estimate integrals over the interior of a general triangle in 2D.
TRIANGLE01_MONTE_CARLO, a FORTRAN90 code which uses the Monte Carlo method to estimate integrals over the interior of the unit triangle in 2D.
WEDGE_MONTE_CARLO, a FORTRAN90 code which uses the Monte Carlo method to estimate integrals over the interior of the unit wedge in 3D.