pyramid_integrals, a Python 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 information on this web page is 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.
python_integrals, a Python code which returns the exact value of the integral of any monomial over the surface or interior of some geometric object, including a line, quadrilateral, box, circle, disk, sphere, ball and others.
pyramid_grid, a Python code which computes a grid of points over the interior of the unit pyramid in 3d;
pyramid_jaskowiec_rule, a Python code which returns symmetric quadrature rules, with exactness up to total degree 20, over the interior of a pyramid in 3D, by Jan Jaskowiec, Natarajan Sukumar.
pyramid_monte_carlo, a Python code which applies a Monte Carlo method to estimate integrals of a function over the interior of the unit pyramid in 3d;
pyramid_witherden_rule, a Python code which returns a Witherden quadrature rule, with exactness up to total degree 10, over the interior of a pyramid.