tetrahedron_monte_carlo, a Python code which estimates the integral of a function over a general tetrahedron using the Monte Carlo method.
The library makes it relatively easy to compare different methods of producing sample points in the tetrahedron, and to vary the tetrahedron over which integration is carried out.
The computer code and data files described and made available on this web page are distributed under the MIT license
tetrahedron_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.
annulus_monte_carlo a Python 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 Python 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 Python 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 Python 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 Python code which uses the Monte Carlo method to estimate integrals over the interior of the general disk in 2D.
disk01_monte_carlo, a Python code which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit disk in 2d;
disk01_quarter_monte_carlo, a Python 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 Python 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 Python 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 Python 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 Python 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 Python 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 Python code which uses the Monte Carlo method to estimate integrals over the length of the unit line in 1D.
polygon_monte_carlo, a Python 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 Python 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 Python code which uses the Monte Carlo method to estimate integrals over the interior of the unit simplex in m dimensions.
sphere_monte_carlo, a Python code which applies a Monte Carlo method to estimate the integral of a function over the surface of the unit sphere in 3d;
square_monte_carlo, a Python code which applies a Monte Carlo method to estimate the integral of a function over the interior of the unit square in 2D.
tetrahedron, a Python code which carries out geometric calculations involving a general tetrahedron, including solid and facial angles, face areas, point containment, distances to a point, circumsphere and insphere, measures of shape quality, centroid, barycentric coordinates, edges and edge lengths, random sampling, and volumes.
tetrahedron_integrals, a Python code which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3d.
tetrahedron_jaskowiec_rule, a Python code which returns quadrature rules, with exactness up to total degree 20, over the interior of a tetrahedron in 3D, by Jan Jaskowiec, Natarajan Sukumar.
tetrahedron01_monte_carlo, a Python code which uses the Monte Carlo method to estimate integrals over the interior of the unit tetrahedron in 3D.
triangle_monte_carlo, a Python code which uses the Monte Carlo method to estimate integrals over the interior of a triangle.
triangle01_monte_carlo, a Python code which uses the Monte Carlo method to estimate integrals over the interior of the unit triangle in 2D.
wedge_monte_carlo, a Python code which uses the Monte Carlo method to estimate integrals over the interior of the unit wedge in 3D.