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<html>
<head>
<title>
HEX_GRID - Routines for a Hexagonal Grid
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
HEX_GRID <br> Routines for a Hexagonal Grid
</h1>
<hr>
<p>
<b>HEX_GRID</b>
is a FORTRAN90 library which
computes points on a hexagonal grid.
</p>
<p>
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].
</p>
<p>
All nodes of the grid lie on one of <b>LAYERS</b> 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 <b>HY</b> units higher.
</p>
<p>
On all the odd numbered lines, there are <b>NODES_PER_LAYER</b> points,
equally spaced from 0 to 1 or A to B, with a spacing of <b>HX</b>.
</p>
<p>
On the even numbered lines, there are <b>NODES_PER_LAYER</b>-1 points,
whose values are the midpoints of successive intervals on
an odd numbered line. (The grid is staggered).
</p>
<p>
In order to maintain the hexagonal structure, the following relationship
is required between <b>HX</b> and <b>HY</b>:
<pre>
<b>HY</b> = <b>HX</b> * sqrt ( 3 ) / 2.
</pre>
</p>
<p>
Here is an image of a hexagonal grid with <b>NODES_PER_ROW</b> = 21
and <b>LAYERS</b> = 24, and a total of <b>N</b> = 492 nodes.
<img src = "../../datasets/hex_grid/hex_grid_01_21_24_492.png"
height = "400"
width = "400">
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>HEX_GRID</b> is available in
<a href = "../../cpp_src/hex_grid/hex_grid.html">a C++ version</a> and
<a href = "../../f_src/hex_grid/hex_grid.html">a FORTRAN90 version</a> and
<a href = "../../m_src/hex_grid/hex_grid.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/cvt/cvt.html">
CVT</a>,
a FORTRAN90 library which
computes elements of a Centroidal Voronoi Tessellation.
</p>
<p>
<a href = "../../f_src/faure/faure.html">
FAURE</a>,
a FORTRAN90 library which
computes elements of a Faure quasirandom sequence.
</p>
<p>
<a href = "../../f_src/grid/grid.html">
GRID</a>,
a FORTRAN90 library which
computes elements of a grid dataset.
</p>
<p>
<a href = "../../f_src/halton/halton.html">
HALTON</a>,
a FORTRAN90 library which
computes elements of a Halton quasirandom sequence.
</p>
<p>
<a href = "../../f_src/hammersley/hammersley.html">
HAMMERSLEY</a>,
a FORTRAN90 library which
computes elements of a Hammersley quasirandom sequence.
</p>
<p>
<a href = "../../datasets/hex_grid/hex_grid.html">
HEX_GRID</a>,
a dataset collection which
contains examples of hexagonal grids.
</p>
<p>
<a href = "../../f_src/hex_grid_angle/hex_grid_angle.html">
HEX_GRID_ANGLE</a>,
a FORTRAN90 library which
computes elements of an angled hexagonal grid dataset.
</p>
<p>
<a href = "../../f_src/hex_grid_dataset/hex_grid_dataset.html">
HEX_GRID_DATASET</a>,
a FORTRAN90 program which
can create a hex grid dataset and write it to a file.
</p>
<p>
<a href = "../../f_src/hex_grid_triangulate/hex_grid_triangulate.html">
HEX_GRID_TRIANGULATE</a>,
a FORTRAN90 program which
uses the <b>HEX_GRID</b> library and
finds points on a hex grid that lie within a given arbitrary region.
</p>
<p>
<a href = "../../f_src/ihs/ihs.html">
IHS</a>,
a FORTRAN90 library which
computes elements of an improved distributed Latin hypercube dataset.
</p>
<p>
<a href = "../../f_src/latin_center/latin_center.html">
LATIN_CENTER</a>,
a FORTRAN90 library which
computes elements of a Latin Hypercube dataset, choosing center points.
</p>
<p>
<a href = "../../f_src/latin_edge/latin_edge.html">
LATIN_EDGE</a>,
a FORTRAN90 library which
computes elements of a Latin Hypercube dataset, choosing edge points.
</p>
<p>
<a href = "../../f_src/latin_random/latin_random.html">
LATIN_RANDOM</a>,
a FORTRAN90 library which
computes elements of a Latin Hypercube dataset, choosing
points at random.
</p>
<p>
<a href = "../../f_src/lattice_rule/lattice_rule.html">
LATTICE_RULE</a>,
a FORTRAN90 library which
approximates multidimensional integrals using lattice rules.
</p>
<p>
<a href = "../../f_src/lcvt/lcvt.html">
LCVT</a>,
a FORTRAN90 library which
computes a latinized Centroidal Voronoi Tessellation.
</p>
<p>
<a href = "../../f_src/niederreiter2/niederreiter2.html">
NIEDERREITER2</a>,
a FORTRAN90 library which
computes elements of a Niederreiter quasirandom sequence with base 2.
</p>
<p>
<a href = "../../f_src/normal/normal.html">
NORMAL</a>,
a FORTRAN90 library which
computes elements of a
sequence of pseudorandom normally distributed values.
</p>
<p>
<a href = "../../f_src/sobol/sobol.html">
SOBOL</a>,
a FORTRAN90 library which
computes elements of a Sobol quasirandom sequence.
</p>
<p>
<a href = "../../f_src/triangle_grid/triangle_grid.html">
TRIANGLE_GRID</a>,
a FORTRAN90 library which
computes a triangular grid of points.
</p>
<p>
<a href = "../../f_src/uniform/uniform.html">
UNIFORM</a>,
a FORTRAN90 library which
computes elements of a uniform pseudorandom sequence.
</p>
<p>
<a href = "../../f_src/van_der_corput/van_der_corput.html">
VAN_DER_CORPUT</a>,
a FORTRAN90 library which
computes elements of a van der Corput quasirandom sequence.
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "hex_grid.f90">hex_grid.f90</a>, the source code.
</li>
<li>
<a href = "hex_grid.sh">hex_grid.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "hex_grid_prb.f90">hex_grid_prb.f90</a>,
a sample calling program.
</li>
<li>
<a href = "hex_grid_prb.sh">hex_grid_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "hex_grid_prb_output.txt">hex_grid_prb_output.txt</a>,
the output from a run of the sample program.
</li>
</ul>
</p>
<p>
You may copy grid files defined for the unit square
[0,1] x [0,1]:
<ul>
<li>
<a href = "../../datasets/hex_grid/hex_grid_01_1_1_1.txt">
hex_grid_01_1_1_1.txt</a>.
</li>
<li>
<a href = "../../datasets/hex_grid/hex_grid_01_2_2_3.txt">
hex_grid_01_2_2_3.txt</a>.
</li>
<li>
<a href = "../../datasets/hex_grid/hex_grid_01_3_3_8.txt">
hex_grid_01_3_3_8.txt</a>.
</li>
<li>
<a href = "../../datasets/hex_grid/hex_grid_01_4_4_14.txt">
hex_grid_01_4_4_14.txt</a>.
</li>
<li>
<a href = "../../datasets/hex_grid/hex_grid_01_5_5_23.txt">
hex_grid_01_5_5_23.txt</a>.
</li>
<li>
<a href = "../../datasets/hex_grid/hex_grid_01_6_6_33.txt">
hex_grid_01_6_6_33.txt</a>.
</li>
<li>
<a href = "../../datasets/hex_grid/hex_grid_01_7_7_46.txt">
hex_grid_01_7_7_46.txt</a>.
</li>
<li>
<a href = "../../datasets/hex_grid/hex_grid_01_8_9_68.txt">
hex_grid_01_8_9_68.txt</a>.
</li>
<li>
<a href = "../../datasets/hex_grid/hex_grid_01_9_10_85.txt">
hex_grid_01_9_10_85.txt</a>.
</li>
<li>
<a href = "../../datasets/hex_grid/hex_grid_01_10_11_105.txt">
hex_grid_01_10_11_105.txt</a>.
</li>
<li>
<a href = "../../datasets/hex_grid/hex_grid_01_11_12_126.txt">
hex_grid_01_11_12_126.txt</a>.
</li>
<li>
<a href = "../../datasets/hex_grid/hex_grid_01_21_24_492.txt">
hex_grid_01_21_24_492.txt</a>.
</li>
<li>
<a href = "../../datasets/hex_grid/hex_grid_01_41_47_1904.txt">
hex_grid_01_41_47_1904.txt</a>.
</li>
<li>
<a href = "../../datasets/hex_grid/hex_grid_01_81_93_7487.txt">
hex_grid_01_81_93_7487.txt</a>.
</li>
<li>
<a href = "../../datasets/hex_grid/hex_grid_01_101_116_11658.txt">
hex_grid_01_101_101_11658.txt</a>.
</li>
</ul>
</p>
<p>
You may copy grid files defined for the coordinate box
[1,4] x [2,7]:
<ul>
<li>
<a href = "../../datasets/hex_grid/hex_grid_1_1_1.txt">
hex_grid_1_1_1.txt</a>.
</li>
<li>
<a href = "../../datasets/hex_grid/hex_grid_2_2_3.txt">
hex_grid_2_2_3.txt</a>.
</li>
<li>
<a href = "../../datasets/hex_grid/hex_grid_3_4_10.txt">
hex_grid_3_4_10.txt</a>.
</li>
<li>
<a href = "../../datasets/hex_grid/hex_grid_4_6_21.txt">
hex_grid_4_6_21.txt</a>.
</li>
<li>
<a href = "../../datasets/hex_grid/hex_grid_5_8_36.txt">
hex_grid_5_8_36.txt</a>.
</li>
<li>
<a href = "../../datasets/hex_grid/hex_grid_6_10_55.txt">
hex_grid_6_10_55.txt</a>.
</li>
<li>
<a href = "../../datasets/hex_grid/hex_grid_7_12_78.txt">
hex_grid_7_12_78.txt</a>.
</li>
<li>
<a href = "../../datasets/hex_grid/hex_grid_8_14_105.txt">
hex_grid_8_14_105.txt</a>.
</li>
<li>
<a href = "../../datasets/hex_grid/hex_grid_9_16_136.txt">
hex_grid_9_16_136.txt</a>.
</li>
<li>
<a href = "../../datasets/hex_grid/hex_grid_10_18_171.txt">
hex_grid_10_18_171.txt</a>.
</li>
<li>
<a href = "../../datasets/hex_grid/hex_grid_11_20_210.txt">
hex_grid_11_20_210.txt</a>.
</li>
<li>
<a href = "../../datasets/hex_grid/hex_grid_21_39_800.txt">
hex_grid_21_39_800.txt</a>.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>BOX_PRINT_2D</b> prints information about a coordinate box in 2D.
</li>
<li>
<b>GET_UNIT</b> returns a free FORTRAN unit number.
</li>
<li>
<b>HEX_GRID_01_APPROXIMATE_H</b> seeks a unit square hex grid with spacing H.
</li>
<li>
<b>HEX_GRID_01_APPROXIMATE_N</b> seeks a unit square hex grid of about N nodes.
</li>
<li>
<b>HEX_GRID_01_H</b> computes the unit square hex grid spacings.
</li>
<li>
<b>HEX_GRID_01_LAYERS</b> computes the unit square hex grid column width.
</li>
<li>
<b>HEX_GRID_01_N</b> computes the number of unit square hex grid points.
</li>
<li>
<b>HEX_GRID_01_POINTS</b> returns unit square hex grid points.
</li>
<li>
<b>HEX_GRID_APPROXIMATE_H</b> seeks a hex grid with spacing H.
</li>
<li>
<b>HEX_GRID_APPROXIMATE_N</b> seeks a hex grid of about N nodes.
</li>
<li>
<b>HEX_GRID_H</b> computes the coordinate box hex grid spacings.
</li>
<li>
<b>HEX_GRID_LAYERS</b> computes the coordinate box hex grid column width.
</li>
<li>
<b>HEX_GRID_N</b> computes the number of coordinate box hex grid points.
</li>
<li>
<b>HEX_GRID_POINTS</b> returns coordinate box hex grid points.
</li>
<li>
<b>HEX_GRID_WRITE</b> writes a hex grid dataset to a file.
</li>
<li>
<b>S_BLANK_DELETE</b> removes blanks from a string, left justifying the remainder.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>TIMESTRING</b> writes the current YMDHMS date into a string.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 30 August 2005.
</i>
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