tetrahedron01_monte_carlo

tetrahedron01_monte_carlo, an Octave 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
      

        F(X,Y,Z) = X^E(1) * Y^E(2) * Z^E(3)
      

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

tetrahedron01_monte_carlo is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

tetrahedron01_monte_carlo_test

octave_monte_carlo, an Octave code which uses Monte Carlo sampling to estimate areas and integrals.

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:

• monomial_value.m, evaluates a monomial.
• r8vec_uniform_01.m returns a unit pseudorandom R8VEC.
• tetrahedron01_monomial.m, monomial integrals in the interior of the unit tetrahedron in 3D.
• tetrahedron01_sample.m samples points from the interior of the unit tetrahedron in 3D.
• tetrahedron01_volume.m computes the volume of the unit tetrahedron in 3D.