triangle_integrals, a C++ code which returns the exact value of the integral of a polynomial over the interior of an arbitrary triangle in 2D.
The information on this web page is distributed under the MIT license.
triangle_integrals 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.
cpp_integrals, a C++ code which returns the exact value of the integral of any monomial over a line, square, cube, a polygon, a circle, a disk, a sphere, a ball, a triangle, a tetrahedron, a simplex, and various other geometric regions.
triangle_analyze, a C++ code which reads a triangle defined in a file, and uses the triangle_properties() library to compute angles, area, centroid, circumcircle, edge lengths, incircle, orientation, orthocenter, and quality.
triangle_dunavant_rule, a C++ code which sets up a Dunavant quadrature rule over the interior of a triangle in 2D.
triangle_fekete_rule, a C++ code which defines a Fekete rule for quadrature or interpolation 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_lyness_rule, a C++ code which returns a Lyness-Jespersen quadrature rule over the interior of a 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 quadrature rules over the interior of a triangle in 2D.
triangle_nco_rule, a C++ code which defines Newton-Cotes open quadrature rules on a triangle.
triangle_symq_rule, a C++ 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.
triangle_wandzura_rule, a C++ code which sets up a Wandzura quadrature rule of exactness 5, 10, 15, 20, 25 or 30 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.