TETRAHEDRON01_MONTE_CARLO
Monte Carlo Integral Estimates over the Unit Tetrahedron in 3D


TETRAHEDRON01_MONTE_CARLO, a C++ library which uses the Monte Carlo method to estimate the integral of a function F(X,Y,Z) over the interior of the unit tetrahedron in 3D.

The interior of the unit tetrahedron in 3D is defined by the constraints:

        0 <= X
        0 <= Y
        0 <= Z
             X + Y + Z <= 1
      
The functions F(X,Y,Z) are monomials, having the form
        F(X,Y,Z) = X^E(1) * Y^E(2) * Z^E(3)
      
where the exponents are nonnegative integers.

Licensing:

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

Languages:

TETRAHEDRON01_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 C++ 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 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 general disk in 2D;

DISK01_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;

DISK01_QUARTER_MONTE_CARLO, a C++ 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 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 FORTRAN90 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_MONTE_CARLO, a C++ library which applies a Monte Carlo method to estimate the integral of a function over the interior of a polygon in 2D.

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 uses the Monte Carlo method to estimate integrals 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 general tetrahedron in 3D.

tetrahedron01_monte_carlo_test

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

TRIANGLE01_MONTE_CARLO, a C++ library which uses the Monte Carlo method to estimate integrals over the interior of the unit 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.

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 30 April 2020.