cube_integrals


cube_integrals, a C++ code which returns the exact value of the integral of any monomial over the interior of the unit cube in 3D.

The interior of the unit cube in 3D is defined by

        0 <= X <= 1,
        0 <= Y <= 1,
        0 <= Z <= 1.
      

The integrands are all of the form

        f(x,y,z) = x^e1 * y^e2 * z^e3.
      
where the exponents are nonnegative integers.

Licensing:

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

Languages:

cube_integrals 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:

cube_integrals_test

cpp_integrals, a C++ code which returns the exact value of the integral of any monomial over a line, square, cube, a polygon, a circle, a disk, a sphere, a ball, a triangle, a tetrahedron, a simplex, and various other geometric regions.

cube_arbq_rule, a C++ code which returns quadrature rules, with exactness up to total degree 15, over the interior of the symmetric cube in 3D, by Hong Xiao and Zydrunas Gimbutas.

cube_exactness, a C++ code which investigates the polynomial exactness of quadrature rules over the interior of a cube in 3D.

cube_felippa_rule, a C++ code which returns the points and weights of a Felippa quadrature rule over the interior of a cube in 3D.

cube_grid, a C++ code which computes a grid of points over the interior of a cube in 3D.

cube_monte_carlo, a C++ code which uses the Monte Carlo method to estimate the integral of a function over the interior of the unit cube in 3D.

Source Code:


Last revised on 23 February 2020.