triangle01_monte_carlo


triangle01_monte_carlo, a MATLAB code which uses the Monte Carlo method to estimate the integral of a function F(X,Y) over the interior of the unit triangle in 2D.

The interior of the unit triangle in 2D is defined by the constraints:

        0 <= X
        0 <= Y
             X + Y <= 1
      
The functions F(X,Y) are monomials, having the form
        F(X,Y) = X^E(1) * Y^E(2)
      
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:

triangle01_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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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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triangle_dunavant_rule, a MATLAB code which sets up a dunavant quadrature rule over the interior of a triangle in 2d.

triangle_fekete_rule, a MATLAB code which defines fekete rules for quadrature or interpolation over the interior of a triangle in 2d.

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triangle_lyness_rule, a MATLAB code which returns lyness-jespersen quadrature rules over the interior of a triangle in 2d.

triangle_ncc_rule, a MATLAB code which defines newton-cotes closed quadrature rules on a triangle.

triangle_nco_rule, a MATLAB code which defines newton-cotes open quadrature rules on a triangle.

triangle_symq_rule, a MATLAB code which returns efficient symmetric quadrature rules, with exactness up to total degree 50, over the interior of an arbitrary triangle in 2d, by hong xiao and zydrunas gimbutas.

triangle_wandzura_rule, a MATLAB code which sets up a quadrature rule of exactness 5, 10, 15, 20, 25 or 30 over the interior of a triangle in 2d.

triangle01_monte_carlo_test

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 05 April 2019.