tetrahedron_integrals


tetrahedron_integrals, a MATLAB 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:

matlab_integrals, a MATLAB 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, a MATLAB 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_arbq_rule, a MATLAB 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_exactness, a MATLAB code which investigates the monomial exactness of a quadrature rule over the interior of a tetrahedron in 3d.

tetrahedron_felippa_rule, a MATLAB code which returns a Felippa quadrature rule for approximating integrals over the interior of a tetrahedron in 3d.

tetrahedron_jaskowiec_rule, a MATLAB 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_keast_rule, a MATLAB code which defines ten Keast quadrature rules, with exactness degrees 0 through 8, over the interior of a tetrahedron in 3d.

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

tetrahedron_ncc_rule, a MATLAB code which defines Newton-Cotes closed (NCC) quadrature rules over the interior of a tetrahedron in 3d.

tetrahedron_nco_rule, a MATLAB code which defines Newton-Cotes open (NCO) quadrature rules over the interior of a tetrahedron in 3d.

tetrahedron_witherden_rule, a MATLAB 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 April 2019.