triangle_monte_carlo

triangle_monte_carlo, a FORTRAN90 code which uses the Monte Carlo method to estimate the integral of a function F(X,Y) over the interior of a general triangle in 2D.

The library makes it relatively easy to compare different methods of producing sample points in the triangle, and to vary the triangle over which integration is carried out.

Licensing:

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

Languages:

triangle_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 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 applies a Monte Carlo method to estimate the integral of a function on the circumference of the unit circle in 2D;

DISK_MONTE_CARLO, a FORTRAN90 code which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit disk in 2D;

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;

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 sphere in M dimensions;

RANDOM_DATA, a FORTRAN90 code which generates sample points for various probability distributions, spatial dimensions, and geometries;

SPHERE_MONTE_CARLO, a FORTRAN90 code which uses the Monte Carlo method to estimate integrals over the surface of the unit sphere in 3D.

TETRAHEDRON_MONTE_CARLO, a FORTRAN90 code which uses the Monte Carlo method to estimate integrals over a tetrahedron.

triangle_monte_carlo_test

TRIANGLE01_MONTE_CARLO, a FORTRAN90 code which uses the Monte Carlo method to estimate integrals over the interior of the unit triangle in 2D.

Reference:

  1. Claudio Rocchini, Paolo Cignoni,
    Generating Random Points in a Tetrahedron,
    Journal of Graphics Tools,
    Volume 5, Number 4, 2000, pages 9-12.
  2. Reuven Rubinstein,
    Monte Carlo Optimization, Simulation and Sensitivity of Queueing Networks,
    Krieger, 1992,
    ISBN: 0894647644,
    LC: QA298.R79.
  3. Greg Turk,
    Generating Random Points in a Triangle,
    in Graphics Gems I,
    edited by Andrew Glassner,
    AP Professional, 1990,
    ISBN: 0122861663,
    LC: T385.G697

Source Code:

Last revised on 10 September 2020.