triangle_symq_rule, a C code which returns symmetric quadrature rules, with exactness up to total degree 50, over the interior of a triangle, 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 ,
The computer code and data files made available on this web page are distributed under the MIT license
triangle_symq_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.
simplex_gm_rule, a C code which defines Grundmann-Moeller quadrature rules over the interior of a simplex in M dimensions.
toms886, a C code which defines the Padua points for interpolation in a 2D region, including the rectangle, triangle, and ellipse, by Marco Caliari, Stefano de Marchi, Marco Vianello. This is a version of ACM TOMS algorithm 886.
triangle_exactness, a C code which investigates the monomial exactness quadrature rule over the interior of a triangle in 2D.
triangle_fekete_rule, a C code which defines a Fekete rule for interpolation or quadrature over the interior of a triangle in 2D.
triangle_felippa_rule, a C code which returns a Felippa quadrature rule for approximating integrals over the interior of a triangle in 2D.
triangle_integrals, a C code which returns the exact value of the integral of any monomial over the interior of the unit triangle in 2D.
triangle_monte_carlo, a C code which uses the Monte Carlo method to estimate the integral of a function over the interior of the unit triangle in 2D.
triangle_ncc_rule, a C code which defines Newton-Cotes Closed (NCC) quadrature rules over the interior of a triangle in 2D.
triangle_nco_rule, a C code which defines Newton-Cotes Open (NCO) quadrature rules over the interior of a triangle in 2D.
triangle_witherden_rule, a C code which returns a symmetric Witherden quadrature rule for the triangle, with exactness up to total degree 20.