pyramid_grid, an Octave code which generates a grid of points over the interior of a pyramid in 3D.
The pyramid has a square base. As it rises, the square cross section smoothly shrinks to a point. Thus there are five vertices, of which four are on the square base, and one is the apex. There are 8 edges, consisting of the four edges of the square, and an edge joining each base vertex to the apex vertex.
The unit pyramid is the set of points (X,Y,Z) such that:
- ( 1 - Z ) <= X <= 1 - Z
- ( 1 - Z ) <= Y <= 1 - Z
0 <= Z <= 1.
The computer code and data files described and made available on this web page are distributed under the MIT license
pyramid_grid 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.
octave_grid, an Octave code which generates a regular grid of points inside a variety of regions in one, two, three or many dimensions.
pyramid_exactness, an Octave code which investigates the monomial exactness of a quadrature rule over the interior of the unit pyramid in 3d.
pyramid_integrals, an Octave code which returns the exact value of the integral of any monomial over the interior of the unit pyramid in 3d.
pyramid_monte_carlo, an Octave code which applies a monte carlo method to estimate integrals of a function over the interior of the unit pyramid in 3d;
pyramid_rule, an Octave code which computes a quadrature rule over the interior of the unit pyramid in 3d;