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<html>
<head>
<title>
VORONOI_PLOT - Plot Voronoi Neighborhoods
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
VORONOI_PLOT <br> Plot Voronoi Neighborhoods
</h1>
<hr>
<p>
<b>VORONOI_PLOT</b>
is a FORTRAN90 program which
plots a set of Voronoi neighborhoods.
</p>
<p>
The user must specify the name of a file containing the X and
Y coordinates of the pointset to be analyzed. The points must
lie in the unit square.
</p>
<p>
The program allows the user to choose the LP norm in which
distances are calculated, with P any positive real value.
In particular
<ul>
<li>
<b>L1</b>: distance = sum of absolute values of differences;
</li>
<li>
<b>L2</b>: distance = square root of sum of squares of differences;
</li>
<li>
<b>Lp</b>: distance = P-th root of sum of absolute values
of P-th powers of differences;
</li>
<li>
<b>Linfinity</b>: distance = maximum of absolute values of differences;
</li>
</ul>
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>voronoi_plot</b> <i>file_name</i> <i>p</i>
</blockquote>
where
<ul>
<li>
<i>file_name</i> is the name of a file containing the points;
</li>
<li>
<i>p</i> chooses the P-norm, with the special value of 0 for
L-infinity.
</li>
</ul>
</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>VORONOI_PLOT</b> is available in
<a href = "../../f_src/voronoi_plot/voronoi_plot.html">a FORTRAN90 version</a> and
<a href = "../../m_src/voronoi_plot/voronoi_plot.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/geompack/geompack.html">
GEOMPACK</a>,
a FORTRAN90 library which
can compute the Voronoi diagram associated with a set of points.
</p>
<p>
<a href = "../../data/ppma/ppma.html">
PPMA</a>,
a file format which
is used for the output graphics files created by <b>VORONOI_PLOT</b>.
</p>
<p>
<a href = "../../f_src/ppma_io/ppma_io.html">
PPMA_IO</a>,
a FORTRAN90 library which
can write out an ASCII PPM file. These routines are used by <b>VORONOI_PLOT</b>.
</p>
<p>
<a href = "../../c_src/qvoronoi/qvoronoi.html">
QVORONOI</a>,
a C program which
can compute the Voronoi diagram associated with a set of points.
</p>
<p>
<a href = "../../f_src/table_voronoi/table_voronoi.html">
TABLE_VORONOI</a>,
a FORTRAN90 program which
can compute the Voronoi diagram associated with a set of points.
</p>
<p>
<a href = "../../c_src/triangle/triangle.html">
TRIANGLE</a>,
a C program which
can compute and display the Voronoi diagram associated with a set of points.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Franz Aurenhammer,<br>
Voronoi diagrams -
a study of a fundamental geometric data structure,<br>
ACM Computing Surveys,<br>
Volume 23, Number 3, pages 345-405, September 1991.
</li>
<li>
Herbert Edelsbrunner,<br>
Geometry and Topology for Mesh Generation,<br>
Cambridge, 2001,<br>
QA377.E36,<br>
ISBN 0-521-79309-2.
</li>
<li>
Joseph O'Rourke,<br>
Computational Geometry,<br>
Cambridge University Press,<br>
Second Edition, 1998,<br>
QA448.D38.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "voronoi_plot.f90">voronoi_plot.f90</a>, the source code.
</li>
<li>
<a href = "voronoi_plot.sh">voronoi_plot.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>DIAMOND_02_00009</b> is a set of 9 points whose Voronoi diagram includes
a "diamond" shaped region. Test files you may copy include:
<ul>
<li>
<a href = "diamond_02_00009.txt">diamond_02_00009.txt</a>,
the 9 points.
</li>
<li>
<a href = "diamond_02_00009_l0.25.png">
diamond_02_00009_l0.25.png</a>,
a PNG image of
the L0.25 neighborhoods.
</li>
<li>
<a href = "diamond_02_00009_l0.5.png">diamond_02_00009_l0.5.png</a>,
a PNG image of
the L0.5 neighborhoods.
</li>
<li>
<a href = "diamond_02_00009_l1.png">diamond_02_00009_l1.png</a>,
a PNG image of
the L1 neighborhoods.
</li>
<li>
<a href = "diamond_02_00009_l2.png">diamond_02_00009_l2.png</a>,
a PNG image of
the L2 neighborhoods.
</li>
<li>
<a href = "diamond_02_00009_l3.png">diamond_02_00009_l3.png</a>,
a PNG image of
the L3 neighborhoods.
</li>
<li>
<a href = "diamond_02_00009_li.png">diamond_02_00009_li.png</a>,
a PNG image of
the LInfinity neighborhoods.
</li>
</ul>
</p>
<p>
<b>UNIFORM_02_00010</b> is a set of 10 points chosen "randomly".
Test files you may copy include:
<ul>
<li>
<a href = "uniform_02_00010.txt">uniform_02_00010.txt</a>,
10 "random" points in the unit square.
</li>
<li>
<a href = "uniform_02_00010_l1.png">uniform_02_00010_l1.png</a>,
a PNG image of
the L1 neighborhoods.
</li>
<li>
<a href = "uniform_02_00010_l2.png">uniform_02_00010_l2.png</a>,
a PNG image of
the L2 neighborhoods.
</li>
<li>
<a href = "uniform_02_00010_l3.png">uniform_02_00010_l3.png</a>,
a PNG image of
the L3 neighborhoods.
</li>
<li>
<a href = "uniform_02_00010_l4.png">uniform_02_00010_l4.png</a>,
a PNG image of
the L4 neighborhoods.
</li>
<li>
<a href = "uniform_02_00010_li.png">uniform_02_00010_li.png</a>,
a PNG image of
the LInfinity neighborhoods.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for VORONOI_PLOT.
</li>
<li>
<b>ANGLE_TO_RGB</b> returns a color on the perimeter of the color hexagon.
</li>
<li>
<b>CH_CAP</b> capitalizes a single character.
</li>
<li>
<b>CH_EQI</b> is a case insensitive comparison of two characters for equality.
</li>
<li>
<b>CH_LOW</b> lowercases a single character.
</li>
<li>
<b>CH_TO_DIGIT</b> returns the integer value of a base 10 digit.
</li>
<li>
<b>DATA_READ</b> reads generator coordinate data from a file.
</li>
<li>
<b>DIGIT_TO_CH</b> returns the character representation of a decimal digit.
</li>
<li>
<b>FILE_COLUMN_COUNT</b> counts the number of columns in the first line of a file.
</li>
<li>
<b>FILE_NAME_EXT_GET</b> determines the "extension" of a file name.
</li>
<li>
<b>FILE_ROW_COUNT</b> counts the number of row records in a file.
</li>
<li>
<b>FIND_CLOSEST_NORM</b> finds the generator closest to a point X in a given norm.
</li>
<li>
<b>GET_UNIT</b> returns a free FORTRAN unit number.
</li>
<li>
<b>I4_LOG_2</b> returns the integer part of the logarithm base 2 of |I|.
</li>
<li>
<b>I4_TO_ANGLE</b> maps integers to points on a circle.
</li>
<li>
<b>I4_TO_RGB</b> maps integers to RGB colors.
</li>
<li>
<b>I4_TO_S_LEFT</b> converts an integer to a left-justified string.
</li>
<li>
<b>PPMA_WRITE</b> writes an ASCII portable pixel map file.
</li>
<li>
<b>PPMA_WRITE_DATA</b> writes the data of a PPMA file.
</li>
<li>
<b>PPMA_WRITE_HEADER</b> writes the header of a PPMA file.
</li>
<li>
<b>R82VEC_DIST_L2</b> returns the L2 distance between a pair of R82VEC's.
</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>REGION_PLOT_PPMA</b> makes a ASCII PPM plot of the CVT regions in the LP norm.
</li>
<li>
<b>S_INDEX_LAST</b> finds the LAST occurrence of a given substring.
</li>
<li>
<b>S_LOW</b> replaces all uppercase letters by lowercase ones.
</li>
<li>
<b>S_TO_I4</b> reads an I4 from a string.
</li>
<li>
<b>S_TO_R8</b> reads an R8 from a string.
</li>
<li>
<b>S_TO_R8VEC</b> reads an R8VEC from a string.
</li>
<li>
<b>S_WORD_COUNT</b> counts the number of "words" in a string.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</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 13 November 2005.
</i>
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