HEX_GRID
Routines for a Hexagonal Grid

HEX_GRID is a library of FORTRAN90 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 FORTRAN90 library which computes elements of a Centroidal Voronoi Tessellation.

FAURE is a FORTRAN90 library which computes elements of a Faure quasirandom sequence.

GRID is a FORTRAN90 library which computes elements of a grid dataset.

HALTON is a FORTRAN90 library which computes elements of a Halton quasirandom sequence.

HAMMERSLEY is a FORTRAN90 library which computes elements of a Hammersley quasirandom sequence.

HEX_GRID is also available in a C++ version and a MATLAB 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 FORTRAN90 program, using the HEX_GRID library, which can create a hex grid dataset and write it to a file.

HEX_GRID_TRIANGULATE is an interactive 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 FORTRAN90 library which computes elements of an improved distributed Latin hypercube dataset.

LATIN_CENTER is a FORTRAN90 library which computes elements of a Latin Hypercube dataset, choosing center points.

LATIN_EDGE is a FORTRAN90 library which computes elements of a Latin Hypercube dataset, choosing edge points.

LATIN_RANDOM is a FORTRAN90 library which computes elements of a Latin Hypercube dataset, choosing points at random.

LCVT is a FORTRAN90 library which computes a latinized Centroidal Voronoi Tessellation.

NIEDERREITER2 is a FORTRAN90 library which computes elements of a Niederreiter quasirandom sequence with base 2.

NORMAL is a FORTRAN90 library which computes elements of a sequence of pseudorandom normally distributed values.

SOBOL is a FORTRAN90 library which computes elements of a Sobol quasirandom sequence.

UNIFORM is a FORTRAN90 library which computes elements of a uniform pseudorandom sequence.

VAN_DER_CORPUT is a FORTRAN90 library which computes elements of a van der Corput quasirandom sequence.

Source Code:

• hex_grid.f90, the source code.
• hex_grid.csh, commands to compile the source code.

Examples and Tests:

• hex_grid_prb.f90, a sample calling program.
• hex_grid_prb.csh, commands to compile and run the sample program.
• hex_grid_prb.out, the output from a run of the sample program.

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.

List of Routines:

• BOX_PRINT_2D prints information about a coordinate box in 2D.
• GET_UNIT returns a free FORTRAN unit number.
• HEX_GRID_01_APPROXIMATE_H seeks a unit square hex grid with spacing H.
• HEX_GRID_01_APPROXIMATE_N seeks a unit square hex grid of about N nodes.
• HEX_GRID_01_H computes the unit square hex grid spacings.
• HEX_GRID_01_LAYERS computes the unit square hex grid column width.
• HEX_GRID_01_N computes the number of unit square hex grid points.
• HEX_GRID_01_POINTS returns unit square hex grid points.
• HEX_GRID_APPROXIMATE_H seeks a hex grid with spacing H.
• HEX_GRID_APPROXIMATE_N seeks a hex grid of about N nodes.
• HEX_GRID_H computes the coordinate box hex grid spacings.
• HEX_GRID_LAYERS computes the coordinate box hex grid column width.
• HEX_GRID_N computes the number of coordinate box hex grid points.
• HEX_GRID_POINTS returns coordinate box hex grid points.
• HEX_GRID_WRITE writes a hex grid dataset to a file.
• S_BLANK_DELETE removes blanks from a string, left justifying the remainder.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• TIMESTRING writes the current YMDHMS date into a string.

You can go up one level to the FORTRAN90 source codes.