pyramid_integrals, an Octave code which returns the exact value of the integral of any monomial x^i y^j z^k over the interior of the unit pyramid in 3D.
The unit pyramid has a square base of area 4, and a height of 1. Specifically, the integration region is:
- ( 1 - Z ) <= X <= 1 - Z - ( 1 - Z ) <= Y <= 1 - Z 0 <= Z <= 1.The volume of the unit pyramid is 4/3.
The computer code and data files described and made available on this web page are distributed under the MIT license
pyramid_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, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit ball in 3d.
circle_integrals, an Octave code which returns the exact value of the integral of any monomial over the circumference of the unit circle in 2d.
cube_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit cube in 3d.
disk01_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit disk in 2d.
hexagon_integrals, an Octave code which returns the exact value of the integral of a monomial over the interior of a hexagon in 2d.
hyperball_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit hyperball in m dimensions.
hypercube_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit hypercube in m dimensions.
hypersphere_integrals, an Octave code which returns the exact value of the integral of any monomial over the surface of the unit hypersphere in m dimensions.
line_integrals, an Octave code which returns the exact value of the integral of any monomial over the unit line segment in 1d.
polygon_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of a polygon in 2d.
simplex_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit simplex in m dimensions.