HEX_GRID
Routines for a Hexagonal Grid

HEX_GRID is a set of MATLAB routines, using double precision arithmetic, which computes points on a hexagonal grid.

For one set of routines, the hexagonal grid is defined in the unit square [0,1] x [0,1]. For a matching set of routines, the hexagonal grid is defined on a coordinate box [A,B] x [C,D].

All nodes of the grid lie on one of LAYERS horizontal lines. The first of these lines is the X axis (for grids in the unit square) or the line from (A,C) to (B,C), for grids in a coordinate box. Each successive line is HY units higher.

On all the odd numbered lines, there are NODES_PER_LAYER points, equally spaced from 0 to 1 or A to B, with a spacing of HX.

On the even numbered lines, there are NODES_PER_LAYER-1 points, whose values are the midpoints of successive intervals on an odd numbered line. (The grid is staggered).

In order to maintain the hexagonal structure, the following relationship is required between HX and HY:

        HY = HX * sqrt ( 3 ) / 2.
      

Here is an image of a hexagonal grid with NODES_PER_ROW = 21 and LAYERS = 24, and a total of N = 492 nodes.

Related Data and Programs:

CVT is a MATLAB program which computes elements of a Centroidal Voronoi Tessellation.

FAURE is a MATLAB program which computes elements of a Faure quasirandom sequence.

GRID is a MATLAB program which computes elements of a grid dataset.

HALTON is a MATLAB program which computes elements of a Halton quasirandom sequence.

HAMMERSLEY is a MATLAB program which computes elements of a Hammersley quasirandom sequence.

HEX_GRID is also available in a C++ version and a FORTRAN90 version.

HEX_GRID is a dataset collection which contains examples of hexagonal grids.

HEX_GRID_ANGLE is a FORTRAN90 library which computes elements of an angled hexagonal grid dataset.

HEX_GRID_DATASET is an interactive MATLAB program, using the HEX_GRID library, which can create a hex grid dataset and write it to a file.

HEX_GRID_TRIANGULATE is a FORTRAN90 program which uses the HEX_GRID library and finds points on a hex grid that lie within a given arbitrary region.

IHS is a MATLAB program which computes elements of an improved distributed Latin hypercube dataset.

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

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

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

LCVT is a MATLAB program which computes a latinized Centroidal Voronoi Tessellation.

NIEDERREITER2 is a MATLAB program which computes elements of a Niederreiter quasirandom sequence with base 2.

SOBOL is a MATLAB program which computes elements of a Sobol quasirandom sequence.

UNIFORM is a MATLAB program which computes elements of a uniform pseudorandom sequence.

VAN_DER_CORPUT is a MATLAB program which computes elements of a van der Corput quasirandom sequence.

Tar File:

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_m_src.tar.csh the commands used to create the GZIP'ed TAR file.
• hex_grid_m_src.tar.gz the GZIP'ed TAR file.

Source Code:

• box_print_2d.m, prints information about a coordinate box in 2D.
• hex_grid_01_approximate_h.m, seeks a unit square hex grid with spacing H.
• hex_grid_01_approximate_n.m, seeks a unit square hex grid of about N nodes.
• hex_grid_01_h.m, computes the unit square hex grid spacings.
• hex_grid_01_layers.m, computes the unit square hex grid column width.
• hex_grid_01_n.m, computes the number of unit square hex grid points.
• hex_grid_01_points.m, returns unit square hex grid points.
• hex_grid_approximate_h.m, seeks a hex grid with spacing H.
• hex_grid_approximate_n.m, seeks a hex grid of about N nodes.
• hex_grid_h.m, computes the coordinate box hex grid spacings.
• hex_grid_layers.m, computes the coordinate box hex grid column width.
• hex_grid_n.m, computes the number of coordinate box hex grid points.
• hex_grid_points.m, returns coordinate box hex grid points.
• hex_grid_write.m, writes a hex grid dataset to a file.
• r8_epsilon.m, returns the R8 machine precision.
• s_blank_delete.m, removes blanks from a string, left justifying the remainder.
• timestamp.m, prints the current YMDHMS date as a time stamp.
• timestring.m, writes the current YMDHMS date into a string.

Examples and Tests:

• hex_grid_test.m, a sample calling program.
• hex_grid_test.out, the output from a run of the sample program.
• hex_grid_test01.m, tests HEX_GRID_01_LAYERS.
• hex_grid_test02.m, tests HEX_GRID_01_H.
• hex_grid_test03.m, tests HEX_GRID_01_N.
• hex_grid_test04.m, tests HEX_GRID_01_POINTS.
• hex_grid_test05.m, tests HEX_GRID_01_APPROXIMATE_N.
• hex_grid_test06.m, tests HEX_GRID_01_APPROXIMATE_H.
• hex_grid_test07.m, tests HEX_GRID_LAYERS.
• hex_grid_test08.m, tests HEX_GRID_H.
• hex_grid_test09.m, tests HEX_GRID_N.
• hex_grid_test10.m, tests HEX_GRID_POINTS.
• hex_grid_test11.m, tests HEX_GRID_APPROXIMATE_N.
• hex_grid_test12.m, tests HEX_GRID_APPROXIMATE_H.

You may copy grid files defined for the unit square [0,1] x [0,1]:

• hex_grid_01_1_1_1.txt.
• hex_grid_01_2_2_3.txt.
• hex_grid_01_3_3_8.txt.
• hex_grid_01_4_4_14.txt.
• hex_grid_01_5_5_23.txt.
• hex_grid_01_6_6_33.txt.
• hex_grid_01_7_7_46.txt.
• hex_grid_01_8_9_68.txt.
• hex_grid_01_9_10_85.txt.
• hex_grid_01_10_11_105.txt.
• hex_grid_01_11_12_126.txt.
• hex_grid_01_21_24_492.txt.
• hex_grid_01_41_47_1904.txt.
• hex_grid_01_81_93_7487.txt.
• hex_grid_01_101_101_11658.txt.

You may copy grid files defined for the coordinate box [1,4] x [2,7]:

• hex_grid_1_1_1.txt.
• hex_grid_2_2_3.txt.
• hex_grid_3_4_10.txt.
• hex_grid_4_6_21.txt.
• hex_grid_5_8_36.txt.
• hex_grid_6_10_55.txt.
• hex_grid_7_12_78.txt.
• hex_grid_8_14_105.txt.
• hex_grid_9_16_136.txt.
• hex_grid_10_18_171.txt.
• hex_grid_11_20_210.txt.
• hex_grid_21_39_800.txt.

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