Grid of Points Inside a Hypercube in M Dimensions

**HYPERCUBE_GRID**
is a MATLAB library 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)

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

**HYPERCUBE_GRID** is available in
a C version and
a C++ version and
a FORTRAN77 version and
a FORTRAN90 version and
a MATLAB version and
a Python version.

BALL_GRID, a MATLAB library which computes a grid of points over the interior of a ball in 3D.

CIRCLE_ARC_GRID, a MATLAB program which computes a grid of points over the length of a circular arc in 2D;

CUBE_GRID, a MATLAB library which computes a grid of points over the interior of a cube in 3D.

DISK_GRID, a MATLAB library which computes a grid of points over the interior of a disk in 2D.

ELLIPSE_GRID, a MATLAB library which computes a grid of points over the interior of an ellipse in 2D.

ELLIPSOID_GRID, a MATLAB library which computes grid points over the interior of an ellipsoid in 3D.

LINE_GRID, a MATLAB library which computes a grid of points over the interior of a line segment in 1D.

POLYGON_GRID, a MATLAB library which generates a grid of points over the interior of a polygon in 2D.

PYRAMID_GRID, a MATLAB library which computes a grid of points over the interior of the unit pyramid in 3D.

SIMPLEX_GRID, a MATLAB library which generates a grid of points over the interior of a simplex in M dimensions.

SPHERE_FIBONACCI_GRID, a MATLAB library which uses a Fibonacci spiral to create a grid of points on the surface of the unit sphere in 3D.

SPHERE_GRID, a MATLAB library 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 library 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 library which computes a grid of points over the interior of a square in 2D.

TETRAHEDRON_GRID, a MATLAB library which computes a grid of points over the interior of a tetrahedron in 3D.

TRIANGLE_GRID, a MATLAB library which computes a grid of points over the interior of a triangle in 2D.

WEDGE_GRID, a MATLAB library which computes a grid of points over the interior of the unit wedge in 3D.

- hypercube_grid.m, grid points over the interior of a hypercube in M dimensions.
- r8mat_transpose_print.m, prints an R8MAT, transposed.
- r8mat_transpose_print_some.m, prints some of an R8MAT, transposed.
- r8vec_direct_product.m, creates a direct product of R8VEC's.
- timestamp.m, prints the current YMDHMS date as a time stamp.

- hypercube_grid_test.m, a sample calling program.
- hypercube_grid_test_output.txt, the output file.
- hypercube_grid_test01.m, makes a sample grid in 2D.
- hypercube_grid_test02.m, makes a 5D grid that uses a different centering in each dimension.
- hypercube_grid_test03.m, makes a 3D grid that uses the same parameters in all dimensions.

You can go up one level to the MATLAB source codes.