# pyramid_grid

pyramid_grid, a MATLAB 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.
```

### Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

### Languages:

pyramid_grid is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

### Related Data and Programs:

ball_grid, a MATLAB code which computes a grid of points over the interior of a ball in 3d.

circle_arc_grid, a MATLAB code which computes a grid of points over the length of a circular arc in 2d;

cube_grid, a MATLAB code which computes a grid of points over the interior of a cube in 3d.

disk_grid, a MATLAB code which computes a grid of points over the interior of a disk in 2d.

ellipse_grid, a MATLAB code which computes a grid of points over the interior of an ellipse in 2d.

ellipsoid_grid, a MATLAB code which computes grid points over the interior of an ellipsoid in 3d.

hypercube_grid, a MATLAB code which computes a grid of points over the interior of a hypercube in m dimensions.

line_grid, a MATLAB code which computes a grid of points over the interior of a line segment in 1d.

polygon_grid, a MATLAB code which generates a grid of points over the interior of a polygon in 2d.

pyramid_exactness, a MATLAB code which investigates the monomial exactness of a quadrature rule over the interior of the unit pyramid in 3d.

pyramid_integrals, a MATLAB code which returns the exact value of the integral of any monomial over the interior of the unit pyramid in 3d.

pyramid_monte_carlo, a MATLAB code which applies a monte carlo method to estimate integrals of a function over the interior of the unit pyramid in 3d;

pyramid_rule, a MATLAB code which computes a quadrature rule over the interior of the unit pyramid in 3d;

simplex_grid, a MATLAB code which generates a grid of points over the interior of a simplex in m dimensions.

sphere_fibonacci_grid, a MATLAB code which uses a fibonacci spiral to create a grid of points on the surface of the unit sphere in 3d.

sphere_grid, a MATLAB code which provides a number of ways of generating grids of points, or of points and lines, or of points and lines and faces, on the surface of the unit sphere in 3d.

sphere_llq_grid, a MATLAB code which uses longitudes and latitudes to create grids of points, lines, and quadrilaterals on the surface of the unit sphere in 3d.

square_grid, a MATLAB code which computes a grid of points over the interior of a square in 2d.

tetrahedron_grid, a MATLAB code which computes a grid of points over the interior of a tetrahedron in 3d.

triangle_grid, a MATLAB code which computes a grid of points over the interior of a triangle in 2d.

wedge_grid, a MATLAB code which computes a grid of points over the interior of the unit wedge in 3d.

### Source Code:

Last revised on 05 March 2019.