# wedge_monte_carlo

wedge_monte_carlo, a MATLAB code which uses the Monte Carlo method to estimate the integral of a function over the interior of the unit wedge in 3D

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

```        0 <= X
0 <= Y
X + Y <= 1
-1 <= Z <= +1
```

### Languages:

wedge_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 MATLAB code 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 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;

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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;

ellipse_monte_carlo a MATLAB code which uses the Monte Carlo method to estimate the value of integrals over the interior of an ellipse in 2D.

ellipsoid_monte_carlo a MATLAB code 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 MATLAB code which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit hyperball in M dimensions;

hypercube_monte_carlo, a MATLAB code 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 MATLAB code which applies a Monte Carlo method to estimate the integral of a function on the surface of the unit sphere in M dimensions;

line_monte_carlo, a MATLAB code which applies a Monte Carlo method to estimate the integral of a function over the length of the unit line in 1D;

polygon_monte_carlo, a MATLAB code 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 MATLAB code 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 MATLAB code which uses the Monte Carlo method to estimate integrals over the interior of the unit simplex in M dimensions.

sphere_monte_carlo, a MATLAB code which uses the Monte Carlo method to estimate integrals over the surface of the unit sphere in 3D.

sphere_triangle_monte_carlo, a MATLAB code which applies a Monte Carlo method to estimate the integral of a function over a spherical triangle on the surface of the unit sphere in 3D;

square_monte_carlo, a MATLAB code which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit square in 2D;

tetrahedron_monte_carlo, a MATLAB code which uses the Monte Carlo method to estimate integrals over the interior of the unit tetrahedron in 3D.

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_exactness, a MATLAB code which investigates the monomial exactness of a quadrature rule over the interior of the unit wedge in 3D.

wedge_felippa_rule, a MATLAB code which returns quadratures rules for approximating integrals over the interior of the unit wedge in 3D.

wedge_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit wedge in 3D.

### Reference:

1. Carlos Felippa,
A compendium of FEM integration formulas for symbolic work,
Engineering Computation,
Volume 21, Number 8, 2004, pages 867-890.

### Source Code:

Last revised on 07 February 2019.