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<html>
<head>
<title>
HEX_GRID_ANGLE - Angled Hexagonal Grids
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
HEX_GRID_ANGLE <br> Angled Hexagonal Grids
</h1>
<hr>
<p>
<b>HEX_GRID_ANGLE</b>
is a FORTRAN90 library 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.
</p>
<p>
Specifically, the grid begins with a single point called <b>CENTER</b>,
whose location in the unit square or box is specified by the user. The
next "layer" of points is produced by stepping out <b>H</b> units
in a user-specified direction <b>ANGLE</b>, and marking off points
on the hexagon. Further layers of points are added until a layer
is reached that lies entirely outside the region.
</p>
<p>
<b>HEX_GRID_ANGLE</b> was developed to allow more flexibility
than the <a href = "../hex_grid/hex_grid.html">HEX_GRID</a>
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 <b>HEX_GRID_ANGLE</b> library allows the user total freedom
to specify the center, angle, and spacing of the hexagonal grid.
</p>
<p>
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 <b>H</b> 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 <b>H</b>, 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.
</p>
<p>
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.
</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_ANGLE</b> is available in
<a href = "../../f90_src/hex_grid_angle/hex_grid_angle.html">a FORTRAN90 version</a> and
<a href = "../../m_src/hex_grid_angle/hex_grid_angle.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 = "../../f_src/hex_grid/hex_grid.html">
HEX_GRID</a>,
a FORTRAN90 library which
computes elements of a hexagonal grid dataset.
</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_angle.f90">hex_grid_angle.f90</a>, the source code.
</li>
<li>
<a href = "hex_grid_angle.sh">hex_grid_angle.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_angle_prb.f90">hex_grid_angle_prb.f90</a>,
a sample calling program.
</li>
<li>
<a href = "hex_grid_angle_prb.sh">hex_grid_angle_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "hex_grid_angle_prb_output.txt">hex_grid_angle_prb_output.txt</a>,
the output from a run of the sample program.
</li>
<li>
<a href = "hex_grid_angle_01_dataset.txt">
hex_grid_angle_01_dataset.txt</a>,
a set of points on a hexagonal grid in the unit square.
</li>
<li>
<a href = "hex_grid_angle_01_dataset.png">
hex_grid_angle_01_dataset.png</a>,
a PNG image of
a set of points on a
hexagonal grid in the unit square.
</li>
<li>
<a href = "hex_grid_angle_dataset.txt">
hex_grid_angle_dataset.txt</a>,
a set of points on a hexagonal grid in a box
with corners (10,2) and (12,2.5) (aspect ratio = 4).
</li>
<li>
<a href = "hex_grid_angle_dataset.png">
hex_grid_angle_dataset.png</a>,
a PNG image of
a set of points on a
hexagonal grid in a box.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>BOX_01_CONTAINS_POINT_2D</b> determines if a point is inside the unit box in 2D.
</li>
<li>
<b>BOX_CONTAINS_POINT_2D</b> determines if a point is inside a box in 2D.
</li>
<li>
<b>COS_DEG</b> returns the cosine of an angle given in degrees.
</li>
<li>
<b>DEGREES_TO_RADIANS</b> converts an angle measure from degrees to radians.
</li>
<li>
<b>GET_UNIT</b> returns a free FORTRAN unit number.
</li>
<li>
<b>HEX_GRID_ANGLE_01</b> sets the points in an angled hex grid in the unit box.
</li>
<li>
<b>HEX_GRID_ANGLE_01_SIZE</b> counts the points in an angled hex grid in the unit box.
</li>
<li>
<b>HEX_GRID_ANGLE_01_WRITE</b> writes an angled hex grid dataset to a file.
</li>
<li>
<b>HEX_GRID_ANGLE</b> sets the points in an angled hex grid in a box.
</li>
<li>
<b>HEX_GRID_ANGLE_SIZE</b> counts the points in an angled hex grid in a box.
</li>
<li>
<b>HEX_GRID_ANGLE_WRITE</b> writes an angled hex grid dataset in a box to a file.
</li>
<li>
<b>R8_MODP</b> returns the nonnegative remainder of R8 division.
</li>
<li>
<b>R8_UNIFORM_01</b> returns a unit pseudorandom R8.
</li>
<li>
<b>R8MAT_TRANSPOSE_PRINT</b> prints an R8MAT, transposed.
</li>
<li>
<b>R8MAT_TRANSPOSE_PRINT_SOME</b> prints some of an R8MAT, transposed.
</li>
<li>
<b>SIN_DEG</b> returns the sine of an angle given in degrees.
</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 21 October 2006.
</i>
<!-- John Burkardt -->
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</html>