tetrahedron_integrals


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.

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

        0 <= x
        0 <= y
        0 <= z
             x + y + 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:

tetrahedron_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:

python_integrals, a Python code which returns the exact value of the integral of any monomial over the surface or interior of some geometric object, including a line, quadrilateral, box, circle, disk, sphere, ball and others.

tetrahedron_arbq_rule, a Python code which returns quadrature rules, with exactness up to total degree 15, over the interior of a tetrahedron in 3D, by Hong Xiao and Zydrunas Gimbutas.

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.

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

tetrahedron01_monte_carlo, a Python code which uses the Monte Carlo method to estimate integrals over the interior of the unit tetrahedron in 3D.

tetrahedron_witherden_rule, a Python code which returns a symmetric Witherden quadrature rule for the tetrahedron, with exactness up to total degree 10.

Reference:

Source Code:


Last revised on 03 February 2020.