# hypercube_grid

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

The M-dimensional hypercube is the set of points (X(1),X(2),...,X(M)) 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:

hypercube_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.

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_grid, a MATLAB code which computes a grid of points 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 01 February 2019.