HEX_GRID_ANGLE is a MATLAB library, using double precision arithmetic, 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.
CVT is a MATLAB library which computes elements of a Centroidal Voronoi Tessellation.
FAURE is a MATLAB library which computes elements of a Faure quasirandom sequence.
GRID is a MATLAB library which computes elements of a grid dataset.
HALTON is a MATLAB library which computes elements of a Halton quasirandom sequence.
HAMMERSLEY is a MATLAB library which computes elements of a Hammersley quasirandom sequence.
HEX_GRID is a MATLAB library which computes elements of a hexagonal grid dataset.
HEX_GRID_ANGLE is also available in a FORTRAN90 version.
IHS is a MATLAB library which computes elements of an improved distributed Latin hypercube dataset.
LATIN_CENTER is a MATLAB library which computes elements of a Latin Hypercube dataset, choosing center points.
LATIN_EDGE is a MATLAB library which computes elements of a Latin Hypercube dataset, choosing edge points.
LATIN_RANDOM is a MATLAB library which computes elements of a Latin Hypercube dataset, choosing points at random.
LCVT is a MATLAB library which computes a latinized Centroidal Voronoi Tessellation.
NIEDERREITER2 is a MATLAB library which computes elements of a Niederreiter quasirandom sequence with base 2.
NORMAL is a MATLAB library which computes elements of a sequence of pseudorandom normally distributed values.
SOBOL is a MATLAB library which computes elements of a Sobol quasirandom sequence.
UNIFORM is a MATLAB library which computes elements of a uniform pseudorandom sequence.
VAN_DER_CORPUT is a MATLAB library which computes elements of a van der Corput quasirandom sequence.
A GZIP'ed TAR file of the contents of this directory is available. This is only done as a convenience for users who want ALL the files, and don't want to download them individually. This is not a convenience for me, so don't be surprised if the tar file is somewhat out of date.
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.
