# tetrahedron_arbq_rule

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.

The original source code, from which this library was developed, is available from the Courant Mathematics and Computing Laboratory, at https://www.cims.nyu.edu/cmcl/quadratures/quadratures.html ,

### Languages:

tetrahedron_arbq_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.

### Related Data and Programs:

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

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.

tetrahedron_keast_rule, a Python code which defines Keast quadrature rules, with exactness degrees 0 through 8, over the interior of a tetrahedron in 3d.

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

tetrahedron_nco_rule, a Python code which defines Newton-Cotes open (NCO) quadrature rules over the interior of a 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:

1. Hong Xiao, Zydrunas Gimbutas,
A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions,
Computers and Mathematics with Applications,
Volume 59, 2010, pages 663-676.

### Source Code:

Last revised on 06 May 2023.