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.
The quadrature rules are described in terms of barycentric coordinates (a,b,c,d), with weights w that sum to 1.
The computer code and data files made available on this web page are distributed under the MIT license
tetrahedron_jaskowiec_rule 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.
tetrahedron_jaskowiec_rule_test
simplex_gm_rule, a MATLAB code which defines Grundmann-Moeller quadrature rules over the interior of a triangle in 2d, a tetrahedron in 3d, or over the interior of the simplex in m dimensions.
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_felippa_rule, a MATLAB code which returns a Felippa quadrature rule for approximating integrals over the interior of a tetrahedron in 3d.
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.
tetrahedron_keast_rule, a MATLAB code which returns a Keast quadrature rule, with exactness between 0 and 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.