**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;

- pyramid_grid_size.m, sizes a pyramid grid.
- pyramid_unit_grid.m, computes grid points in the unit pyramid.
- pyramid_unit_grid_plot.m, sets up a GNUPLOT plot of a unit pyramid grid.
- pyramid_unit_vertices.m, returns the vertices of the unit pyramid.
- r8_print.m, prints an R8.
- r8mat_transpose_print.m, prints an R8MAT, transposed.
- r8mat_transpose_print_some.m, prints some of an R8MAT, transposed.