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.
ball_integrals, a C code which returns the exact value of the integral of any monomial over the interior of the unit ball in 3D.
circle_integrals, a C code which returns the exact value of the integral of any monomial over the surface of the unit circle in 2D.
cube_integrals, a C code which returns the exact value of the integral of any monomial over the interior of the unit cube in 3D.
disk01_integrals, a C code which returns the exact value of the integral of any monomial over the interior of the unit disk in 2D.
hyperball_integrals, a C code which returns the exact value of the integral of any monomial over the interior of the unit hyperball in M dimensions.
hypercube_integrals, a C code which returns the exact value of the integral of any monomial over the interior of the unit hypercube in M dimensions.
hypersphere_integrals, a C code which returns the exact value of the integral of any monomial over the surface of the unit hypersphere in M dimensions.
line_integrals, a C code which returns the exact value of the integral of any monomial over the length of the unit line in 1D.
polygon_integrals, a C code which returns the exact value of the integral of any monomial over the interior of a polygon in 2D.
pyramid_integrals, a C code which returns the exact value of the integral of any monomial over the interior of the unit pyramid in 3D.
simplex_integrals, a C code which returns the exact value of the integral of any monomial over the interior of the unit simplex in M dimensions.
sphere_integrals, a C code which returns the exact value of the integral of any monomial over the surface of the unit sphere in 3D.
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.
tetrahedron_integrals, a C code which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3D.
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_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_witherden_rule, a C code which returns a symmetric Witherden quadrature rule for the triangle, with exactness up to total degree 20.