# tetrahedron_arbq_rule

tetrahedron_arbq_rule, an Octave 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.

### Related Data and Programs:

alpert_rule, an Octave code which sets up an Alpert quadrature rule for functions which are regular, log(x) singular, or 1/sqrt(x) singular.

annulus_rule, an Octave code which computes a quadrature rule for estimating integrals of a function over the interior of a circular annulus in 2d.

cube_arbq_rule, an Octave 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_felippa_rule, an Octave code which returns the points and weights of a felippa quadrature rule over the interior of a cube in 3d.

pyramid_felippa_rule, an Octave code which returns felippa's quadratures rules for approximating integrals over the interior of a pyramid in 3d.

simplex_gm_rule, an Octave 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.

square_arbq_rule, an Octave code which returns quadrature rules, with exactness up to total degree 20, over the interior of the symmetric square in 2d, by hong xiao and zydrunas gimbutas.

square_felippa_rule, an Octave code which returns the points and weights of a felippa quadrature rule over the interior of a square in 2d.

square_symq_rule, an Octave code which returns symmetric quadrature rules, with exactness up to total degree 20, over the interior of the symmetric square in 2d, by hong xiao and zydrunas gimbutas.

stroud, an Octave code which defines quadrature rules for a variety of m-dimensional regions, including the interior of the square, cube and hypercube, the pyramid, cone and ellipse, the hexagon, the m-dimensional octahedron, the circle, sphere and hypersphere, the triangle, tetrahedron and simplex, and the surface of the circle, sphere and hypersphere.

tetrahedron, an Octave 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, an Octave code which returns felippa's quadratures rules for approximating integrals over the interior of a tetrahedron in 3d.

tetrahedron_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3d.

tetrahedron_monte_carlo, an Octave code which uses the monte carlo method to estimate the integral of a function over the interior of the unit tetrahedron in 3d.

triangle_fekete_rule, an Octave code which defines fekete rules for quadrature or interpolation over the interior of a triangle in 2d.

triangle_felippa_rule, an Octave code which returns felippa's quadratures rules for approximating integrals over the interior of a triangle in 2d.

triangle_symq_rule, an Octave code which returns efficient symmetric quadrature rules, with exactness up to total degree 50, over the interior of an arbitrary triangle in 2d, by hong xiao and zydrunas gimbutas.

wedge_felippa_rule, an Octave code which returns quadratures rules for approximating integrals over the interior of the unit wedge in 3d.

### 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 03 April 2019.