# HEX_GRID_ANGLE Angled Hexagonal Grids

HEX_GRID_ANGLE is a MATLAB library which produces a hexagonal grid of points in the unit square or an arbitrary box, allowing the user to specify an arbitrary center, angle, and grid density.

Specifically, the grid begins with a single point called CENTER, whose location in the unit square or box is specified by the user. The next "layer" of points is produced by stepping out H units in a user-specified direction ANGLE, and marking off points on the hexagon. Further layers of points are added until a layer is reached that lies entirely outside the region.

HEX_GRID_ANGLE was developed to allow more flexibility than the HEX_GRID library provided. In particular, that library always starts the grid at the origin, always runs the first grid line along the X-axis, and always requires that the first grid line terminate exactly with at point at X = 1. By contrast, the HEX_GRID_ANGLE library allows the user total freedom to specify the center, angle, and spacing of the hexagonal grid.

One reason for developing this library was to try to see whether you could always force 100 points of the hexagonal grid to fall into the unit square simply by choosing a spacing H that guaranteed that the Voronoi region around each point (also a hexagon) had an area of 1/100. We finally realized that this cannot be guaranteed, since the hexagonal and Cartesian coordinate systems are "incommensurable". They only match up asymptotically. So, even though we carefully chose the spacing H, it is only on average that we found 100 points in a unit square, but also found squares with 98, 99, or 104 points as well.

Moreover, it will not be possible to choose a hexagonal grid with the property that it is equivalent to the tessellation generated by the the intersection of the hexagonal grid with a single unit square.

### Languages:

HEX_GRID_ANGLE is available in a FORTRAN90 version and a MATLAB version.

### Related Data and Programs:

CVT, a MATLAB library which computes elements of a Centroidal Voronoi Tessellation.

FAURE, a MATLAB library which computes elements of a Faure quasirandom sequence.

GRID, a MATLAB library which computes elements of a grid dataset.

HALTON, a MATLAB library which computes elements of a Halton quasirandom sequence.

HAMMERSLEY, a MATLAB library which computes elements of a Hammersley quasirandom sequence.

HEX_GRID, a MATLAB library which computes elements of a hexagonal grid dataset.

IHS, a MATLAB library which computes elements of an improved distributed Latin hypercube dataset.

LATIN_CENTER, a MATLAB library which computes elements of a Latin Hypercube dataset, choosing center points.

LATIN_EDGE, a MATLAB library which computes elements of a Latin Hypercube dataset, choosing edge points.

LATIN_RANDOM, a MATLAB library which computes elements of a Latin Hypercube dataset, choosing points at random.

LCVT, a MATLAB library which computes a latinized Centroidal Voronoi Tessellation.

NIEDERREITER2, a MATLAB library which computes elements of a Niederreiter quasirandom sequence with base 2.

NORMAL, a MATLAB library which computes elements of a sequence of pseudorandom normally distributed values.

SOBOL, a MATLAB library which computes elements of a Sobol quasirandom sequence.

UNIFORM, a MATLAB library which computes elements of a uniform pseudorandom sequence.

VAN_DER_CORPUT, a MATLAB library which computes elements of a van der Corput quasirandom sequence.

### Examples and Tests:

HEX_GRID_ANGLE_01_DATASET is a set of points on a hexagonal grid in the unit square.

HEX_GRID_ANGLE_DATASET is a set of points on a hexagonal grid in a box with corners (10,2) and (12,2.5) (aspect ratio = 4).

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

Last revised on 24 October 2006.