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.
The interior of the unit tetrahedron in 3D is defined by
0 <= x 0 <= y 0 <= z x + y + z <= 1
The integrands are all of the form
f(x,y,z) = x^e1 * y^e2 * z^e3where the exponents are nonnegative integers.
The computer code and data files described and made available on this web page are distributed under the MIT license
tetrahedron_integrals is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB 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_GM_RULE, a C++ code 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.
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_ARBQ_RULE, a C++ code which returns quadrature rules, with exactness up to total degree 15, over the interior of a tetrahedron in 3D, by Hong Xiao and Zydrunas Gimbutas.
TETRAHEDRON_EXACTNESS, a C++ code which investigates the monomial exactness of a quadrature rule over the interior of a tetrahedron in 3D.
TETRAHEDRON_FELIPPA_RULE, a C++ code which returns Felippa's quadratures rules for approximating integrals over the interior of a tetrahedron in 3D.
TETRAHEDRON_KEAST_RULE, a C++ code which defines ten quadrature rules, with exactness degrees 0 through 8, over the interior of a tetrahedron in 3D.
TETRAHEDRON_MONTE_CARLO, a C++ code which uses the Monte Carlo method to estimate the integral of a function over the interior of the unit tetrahedron in 3D.
TETRAHEDRON_NCC_RULE, a C++ code which defines Newton-Cotes Closed (NCC) quadrature rules over the interior of a tetrahedron in 3D.
TETRAHEDRON_NCO_RULE, a C++ code which defines Newton-Cotes Open (NCO) quadrature rules over the interior of a tetrahedron in 3D.
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.
WEDGE_INTEGRALS, a C++ code which returns the exact value of the integral of any monomial over the interior of the unit wedge in 3D.