HYPERCUBE_INTEGRALS is a C++ library which returns the exact value of the integral of any monomial over the interior of the unit hypercube in M dimensions.
The interior of the unit hypercube in M dimensions is defined by
0 <= X(1:M) <= 1.
The integrands are all of the form
F(X) = product ( 1 <= I <= M ) X(I)^E(I)where the exponents are nonnegative integers.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
HYPERCUBE_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++ library which returns the exact value of the integral of any monomial over the interior of the unit ball in 3D.
CIRCLE_INTEGRALS, a C++ library which returns the exact value of the integral of any monomial over the circumference of the unit circle in 2D.
CUBE_INTEGRALS, a C++ library which returns the exact value of the integral of any monomial over the interior of the unit cube in 3D.
DISK01_INTEGRALS, a C++ library which returns the exact value of the integral of any monomial over the interior of the unit disk in 2D.
HYPERCUBE_GRID, a C++ library which computes a grid of points over the interior of a hypercube in M dimensions.
HYPERBALL_INTEGRALS, a C++ library which returns the exact value of the integral of any monomial over the interior of the unit hyperball in M dimensions.
HYPERCUBE_MONTE_CARLO, a C++ library which uses the Monte Carlo method to estimate the integral of a function over the interior of the unit hypercube in M dimensions.
HYPERSPHERE_INTEGRALS, a C++ library 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++ library which returns the exact value of the integral of any monomial over the length of the unit line in 1D.
POLYGON_INTEGRALS, a C++ library which returns the exact value of the integral of any monomial over the interior of a polygon in 2D.
PYRAMID_INTEGRALS, a C++ library which returns the exact value of the integral of any monomial over the interior of the unit pyramid in 3D.
SIMPLEX_INTEGRALS, a C++ library 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++ library which returns the exact value of the integral of any monomial over the surface of the unit sphere in 3D.
SQUARE_INTEGRALS, a C++ library which returns the exact value of the integral of any monomial over the interior of the unit square in 2D.
TETRAHEDRON_INTEGRALS, a C++ library which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3D.
TRIANGLE_INTEGRALS, a C++ library which returns the exact value of the integral of any monomial over the interior of the unit triangle in 2D.
WEDGE_INTEGRALS, a C++ library which returns the exact value of the integral of any monomial over the interior of the unit wedge in 3D.
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