square_arbq_rule, a C code which returns quadrature rules, with exactness up to total degree 30, over the interior of the symmetric square in 2D, 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 information on this web page is distributed under the MIT license.
square_arbq_rule is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version.
c_rule, a C code which computes a quadrature rule which estimates the integral of a function f(x), which might be defined over a one dimensional region (a line) or more complex shapes such as a circle, a triangle, a quadrilateral, a polygon, or a higher dimensional region, and which might include an associated weight function w(x).
square_grid, a C code which computes a grid of points over the interior of a square in 2D.
square_integrals, a C code which returns the exact value of the integral of any monomial over the interior of the unit square in 2D.
square_monte_carlo, a C code which uses the Monte Carlo method to estimate the integral of a function over the interior of the unit square in 2D.
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.