# 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.

### 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.

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### 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.