# cube_grid

cube_grid, an Octave code which generates a grid of points over the interior of a cube in 3D.

The 3D cube is the set of points (X(1),X(2),X(3)) such that:

```         A(I) <= X(I) <= B(I)
```

For each dimension I, a set of parameters is input:

• NS(I), the number of points along the I-th coordinate direction;
• A(I), B(I), the left and right endpoints of the I-th coordinate.
• C(I), one of 5 choices for centering the grid in the I-th coordinate.

The centering options allow the user to control the centering of the equally spaced points. This is easiest to illustrate if we look at a 1 dimensional case and assume A = 0 and B = 1. Then, using NS = 4, the centering options will produce 4 equally spaced points as follows:

• 1: 0, 1/3, 2/3, 1 (include endpoints)
• 2: 1/5, 2/5, 3/5, 4/5 (do not include endpoints)
• 3: 0, 1/4, 2/4, 3/4 (do not include right endpoint)
• 4: 1/4, 2/4, 3/4, 1 (do not include left endpoint)
• 5: 1/8, 3/8, 5/8, 7/8 (half spacing at the ends)

### Languages:

cube_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.

### Related Data and Programs:

ball_grid, an Octave code which computes a grid of points over the interior of a ball in 3D.

circle_arc_grid, an Octave code which computes a grid of points over the length of a circular arc in 2D;

line_grid, an Octave code which computes a grid of points over the interior of a line segment in 1D.

simplex_grid, an Octave code which generates a regular grid of points over the interior of an arbitrary simplex in M dimensions.

### Source Code:

Last revised on 13 November 2022.