SIMPLEX_GM_RULE is a C library 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.
The user can choose the spatial dimension M, thus defining the region to be a triangle (M = 2), tetrahedron (M = 3) or a general M-dimensional simplex.
The user chooses the index S of the rule. Rules are available with index S = 0 on up. A rule of index S will exactly integrate any polynomial of total degree 2*S+1 or less.
The rules are defined on the unit M-dimensional simplex. A simple linear transformation can be used to map the vertices and weights to an arbitrary simplex, while preserving the accuracy of the rule.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
SIMPLEX_GM_RULE is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.
CUBE_FELIPPA_RULE, a C library which returns the points and weights of a Felippa quadrature rule over the interior of a cube in 3D.
DISK_RULE, a C library which computes quadrature rules over the interior of the unit disk in 2D.
PYRAMID_FELIPPA_RULE, a C library which returns Felippa's quadratures rules for approximating integrals over the interior of a pyramid in 3D.
SIMPLEX_GRID, a C library which generates a regular grid of points over the interior of an arbitrary simplex in M dimensions.
SQUARE_FELIPPA_RULE, a C library which returns the points and weights of a Felippa quadrature rule over the interior of a square in 2D.
TETRAHEDRON_FELIPPA_RULE, a C library which returns Felippa's quadratures rules for approximating integrals over the interior of a tetrahedron in 3D.
TETRAHEDRON_MONTE_CARLO, a C program which uses the Monte Carlo method to estimate integrals over the interior of a tetrahedron in 3D.
TETRAHEDRON_NCC_RULE, a C library which defines Newton-Cotes Closed (NCC) quadrature rules over the interior of a tetrahedron in 3D.
TETRAHEDRON_NCO_RULE, a C library which defines Newton-Cotes Open (NCO) quadrature rules over the interior of a tetrahedron in 3D.
TRIANGLE_FEKETE_RULE, a C library which defines Fekete rules for interpolation or quadrature over the interior of a triangle in 2D.
TRIANGLE_FELIPPA_RULE, a C library which returns Felippa's quadratures rules for approximating integrals over the interior of a triangle in 2D.
TRIANGLE_MONTE_CARLO, a C program which uses the Monte Carlo method to estimate integrals over the interior of a triangle in 2D.
TRIANGLE_NCC_RULE, a C library which defines Newton-Cotes Closed (NCC) quadrature rules over the interior of a triangle in 2D.
TRIANGLE_NCO_RULE, a C library which defines Newton-Cotes Open (NCO) quadrature rules over the interior of a triangle in 2D.
TRIANGLE_SYMQ_RULE, a C library 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, a C library which returns quadratures rules for approximating integrals over the interior of the unit wedge in 3D.
You can go up one level to the C source codes.