HEX_GRID
Routines for a Hexagonal Grid

HEX_GRID is a C++ library 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.

Licensing:

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

Related Data and Programs:

CVT is a C++ library which computes elements of a Centroidal Voronoi Tessellation.

FAURE is a C++ library which computes Faure sequences.

GRID is a C++ library which computes elements of a grid sequence.

HALTON is a C++ library which computes Halton sequences.

HAMMERSLEY is a C++ library which computes Hammersley sequences.

HEX_GRID is available in a C++ version and a FORTRAN90 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 a C++ program 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 C++ library which computes elements of an improved distributed Latin hypercube dataset.

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

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

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

LCVT is a C++ library which computes a latinized Centroidal Voronoi Tessellation.

NIEDERREITER2 is a C++ library which computes elements of a Niederreiter quasirandom sequence using base 2.

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

SOBOL is a C++ library which computes Sobol sequences.

TOMS647 is a FORTRAN77 library which is a version of ACM TOMS algorithm 647, for evaluating Faure, Halton and Sobol quasirandom sequences.

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

VAN_DER_CORPUT is a C++ library which computes elements of a 1D van der Corput sequence.

Source Code:

• hex_grid.C, the source code.
• hex_grid.H, the include file.
• hex_grid.csh, commands to compile the source code.

Examples and Tests:

• hex_grid_prb.C, a sample calling program.
• hex_grid_prb.csh, commands to compile and run the sample program.
• hex_grid_prb_output.txt, the output file.

List of Routines:

• BOX_PRINT_2D prints information about a coordinate box in 2D.
• DIGIT_TO_CH returns the base 10 digit character corresponding to a digit.
• 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.
• I4_LOG_10 returns the whole part of the logarithm base 10 of an integer.
• I4_TO_S converts an integer to a string.
• R8_EPSILON returns the R8 round off unit.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• TIMESTRING returns the current YMDHMS date as a string.

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