simplex_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit simplex in M dimensions.
The interior of the unit simplex in M dimensions is defined by
0 <= X(1:M) sum ( 1 <= I <= M ) X(I) <= 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.
simplex_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 MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit ball in 3d.
circle_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the surface of the unit circle in 2d.
cube_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit cube in 3d.
disk01_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit disk in 2d.
hexagon_integrals, a MATLAB code which returns the exact value of the integral of a monomial over the interior of a hexagon in 2d.
hyperball_integrals, a MATLAB 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 MATLAB 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 MATLAB 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 MATLAB code which returns the exact value of the integral of any monomial over the length of the unit line in 1d.
polygon_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of a polygon in 2d.
pyramid_integrals, a MATLAB 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 MATLAB 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_grid, a MATLAB code which generates a regular grid of points over the interior of an arbitrary simplex in m dimensions.
simplex_monte_carlo, a MATLAB code which uses the monte carlo method to estimate the integral of a function over the interior of the unit simplex in m dimensions.
sphere_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the surface of the unit sphere in 3d.
square_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit square in 2d.
tetrahedron_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit tetrahedron in 3d.
triangle_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit triangle in 2d.
wedge_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit wedge in 3d.