tetrahedron01_monte_carlo


tetrahedron01_monte_carlo, a MATLAB code 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:

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ball_monte_carlo, a MATLAB 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 MATLAB code which applies a monte carlo method to estimate the integral of a function on the circumference of the unit circle in 2d;

cube_monte_carlo, a MATLAB code 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 code which uses the monte carlo method to estimate integrals over the interior of the general disk in 2d.

disk01_monte_carlo, a MATLAB code which uses the monte carlo method to estimate integrals over the interior of the unit disk in 2d.

disk01_quarter_monte_carlo, a MATLAB code which applies a monte carlo method to estimate the integral of a function over the interior of the unit quarter disk in 2d;

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tetrahedron_arbq_rule, a MATLAB code which returns quadrature rules, with exactness up to total degree 15, over the interior of a tetrahedron in 3d, by hong xiao and zydrunas gimbutas.

tetrahedron_exactness, a MATLAB code which investigates the monomial exactness of a quadrature rule over the interior of a tetrahedron in 3d.

tetrahedron_felippa_rule, a MATLAB code which returns felippa's quadratures rules for approximating integrals over the interior of a tetrahedron in 3d.

tetrahedron_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3d.

tetrahedron_keast_rule, a MATLAB code which defines ten quadrature rules, with exactness degrees 0 through 8, over the interior of a tetrahedron in 3d.

tetrahedron_ncc_rule, a MATLAB code which defines newton-cotes closed (ncc) quadrature rules over the interior of a tetrahedron in 3d.

tetrahedron_nco_rule, a MATLAB code which defines newton-cotes open (nco) quadrature rules over the interior of a tetrahedron in 3d.

tetrahedron01_monte_carlo_test

triangle_monte_carlo, a MATLAB code which uses the monte carlo method to estimate integrals over the interior of a general triangle in 2d.

triangle01_monte_carlo, a MATLAB code which uses the monte carlo method to estimate integrals over the interior of the unit triangle in 2d.

wedge_monte_carlo, a MATLAB code 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 03 April 2019.