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^e3
where the exponents are nonnegative integers.
The information on this web page is 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 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, a C code which computes properties including the centroid, circumsphere, dihedral angles, edge lengths, face angles, face areas, insphere, quality, solid angles, and volume 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.