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<html>
<head>
<title>
TABLE_VORONOI - Voronoi Diagram Data
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TABLE_VORONOI <br> Voronoi Diagram Data
</h1>
<hr>
<p>
<b>TABLE_VORONOI</b>
is a FORTRAN90 program which
reads in a dataset
describing a 2D pointset, and prints out information defining
the Voronoi diagram of the pointset.
</p>
<p>
<b>TABLE_VORONOI</b> is based on the
<a href = "../../f_src/geompack/geompack.html">GEOMPACK</a> library of
Barry Joe, which computes the Delaunay triangulation. The
main work that <b>TABLE_VORONOI</b> does is to analyze that
Delaunay information and work out the location of the Voronoi
vertices, and their specific arrangement around each of the
original data nodes.
</p>
<p>
<b>TABLE_VORONOI</b> is a work in progress; the output is
currently simply printed, which is not very useful except for
toy problems; printed output is of very little use for big problems.
To handle big, interesting problems, I have to think about how
to store this information in a useful and accessible data structure.
</p>
<p>
Moreover, I haven't thought enough about how to deal with the
inevitable "infinite" Voronoi cells.
</p>
<p>
The program begins with the pointset, of which a typical element
is a point <b>G</b>. Each <b>G</b> generates a Voronoi polygon (or
semi-infinite region, which we will persist in calling a polygon).
A typical vertex of the polygon is called <b>V</b>. For the semi-infinite
regions, we have a vertex at infinity, but it's really not helpful to
store a vertex (Inf,Inf), since we have lost information about the
direction from which we reach that infinite vertex. We will have to
treat these special regions with a little extra care.
</p>
<p>
We are interested in computing the following quantities:
<ul>
<li>
<b>G_DEGREE</b>, for generator <b>G</b>, the degree (number of
vertices) of the Voronoi polygon;
</li>
<li>
<b>G_START</b>, for generator <b>G</b>, the index of the first
Voronoi vertex in a traversal of the sides of the Voronoi polygon;
</li>
<li>
<b>G_FACE</b>, for all generators <b>G</b>, the sequence of Voronoi
vertices in a traversal of the sides of the Voronoi polygon.
A traversal of a semi-infinite polygon begins at an "infinite"
vertex, lists the finite vertices, and then ends with a
(different) infinite vertex. Infinite vertices are given
negative indexes.
</li>
<li>
<b>V_NUM</b>, the number of (finite) Voronoi vertices <b>V</b>;
</li>
<li>
<b>V_XY</b>, for each finite Voronoi vertex <b>V</b>,
the XY coordinates.
</li>
<li>
<b>I_NUM</b>, the number of Voronoi vertices at infinity;
</li>
<li>
<b>I_XY</b>, the "direction" associated with each Voronoi vertex
at infinity.
</li>
</ul>
</p>
<p>
So if we have to draw a semi-infinite region, we start at infinity.
We then need to draw a line from infinity to vertex #2. We do so
by drawing a line in the appropriate direction, stored in I_XY.
Having safely reached finite vertex #2, we can connect the finite
vertices, until it is time to draw another line to infinity, this
time in another direction, also stored in I_XY.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>table_voronoi</b> <i>file_name.xy</i>
</blockquote>
where
<ul>
<li>
<i>file_name.xy</i> is a file containing the (x,y) coordinates of points.
</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>TABLE_VORONOI</b> is available in
<a href = "../../cpp_src/table_voronoi/table_voronoi.html">a C++ version</a> and
<a href = "../../f_src/table_voronoi/table_voronoi.html">a FORTRAN90 version</a> and
<a href = "../../m_src/table_voronoi/table_voronoi.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
supplies the routines used to compute the Voronoi
information.
</p>
<p>
<a href = "../../f_src/table_barplot_ppma/table_barplot_ppma.html">
TABLE_BARPLOT_PPMA</a>,
a FORTRAN90 program which
reads a table file and creates a
PPMA bargraph of the data.
</p>
<p>
<a href = "../../f_src/table_border/table_border.html">
TABLE_BORDER</a>,
a FORTRAN90 program which
can be used to add a border (of zero values) to a table file.
</p>
<p>
<a href = "../../f_src/table_columns/table_columns.html">
TABLE_COLUMNS</a>,
a FORTRAN90 program which
can extract specific columns of data from a table file.
</p>
<p>
<a href = "../../f_src/table_columns_permute/table_columns_permute.html">
TABLE_COLUMNS_PERMUTE</a>,
a FORTRAN90 program which
permutes the columns of a table file.
</p>
<p>
<a href = "../../f_src/table_delaunay/table_delaunay.html">
TABLE_DELAUNAY</a>,
a FORTRAN90 program which
computes the Delaunay triangulation of a set
of points.
</p>
<p>
<a href = "../../f_src/table_histogram/table_histogram.html">
TABLE_HISTOGRAM</a>,
a FORTRAN90 program which
can make a histogram of a set of points stored in a table file.
</p>
<p>
<a href = "../../f_src/table_io/table_io.html">
TABLE_IO</a>,
a FORTRAN90 library which
supplies the routines used to read the TABLE file.
</p>
<p>
<a href = "../../f_src/table_latinize/table_latinize.html">
TABLE_LATINIZE</a>,
a FORTRAN90 program which
reads a file of points and creates a "latinized" version by adjusting the data.
</p>
<p>
<a href = "../../f_src/table_merge/table_merge.html">
TABLE_MERGE</a>,
a FORTRAN90 program which
reads a file of
points, and removes duplicates, and points that are close to each other.
</p>
<p>
<a href = "../../f_src/table_orthonormalize/table_orthonormalize.html">
TABLE_ORTHONORMALIZE</a>,
a FORTRAN90 program which
reads a file of points and orthonormalizes the columns.
</p>
<p>
<a href = "../../f_src/table_quality/table_quality.html">
TABLE_QUALITY</a>,
a FORTRAN90 program which
reads a file of
points and computes the quality of dispersion.
</p>
<p>
<a href = "../../m_src/table_read/table_read.html">
TABLE_READ</a>,
a MATLAB program which
can read in a TABLE file.
</p>
<p>
<a href = "../../f_src/table_record_match/table_record_match.html">
TABLE_RECORD_MATCH</a>,
a FORTRAN90 program which
can be used to find close records in a table file.
</p>
<p>
<a href = "../../f_src/table_scale/table_scale.html">
TABLE_SCALE</a>,
a FORTRAN90 program which
can be used to multiply the entries of a table file
by a scale vector.
</p>
<p>
<a href = "../../f_src/table_shift/table_shift.html">
TABLE_SHIFT</a>,
a FORTRAN90 program which
can be used to shift the entries of a table file
by a shift vector.
</p>
<p>
<a href = "../../f_src/table_stats/table_stats.html">
TABLE_STATS</a>,
a FORTRAN90 program which
can read a table file and compute certain statistics.
</p>
<p>
<a href = "../../f_src/table_tet_mesh/table_tet_mesh.html">
TABLE_TET_MESH</a>,
a FORTRAN90 program which
can read a table file of 3D data, and compute a tetrahedral mesh.
</p>
<p>
<a href = "../../f_src/table_top/table_top.html">
TABLE_TOP</a>,
a FORTRAN90 program which
can read a table file of M-dimensional data and
make a table of plots of all pairs of coordinates.
</p>
<p>
<a href = "../../f_src/table_unborder/table_unborder.html">
TABLE_UNBORDER</a>,
a FORTRAN90 program which
can be used to remove the border from a table file.
</p>
<p>
<a href = "../../f_src/table_uniform_noise/table_uniform_noise.html">
TABLE_UNIFORM_NOISE</a>,
a FORTRAN90 program which
can be used to add a uniform noise term to the data in a table file.
</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>
Jacob Goodman, Joseph ORourke, editors,<br>
Handbook of Discrete and Computational Geometry,<br>
Second Edition,<br>
CRC/Chapman and Hall, 2004,<br>
ISBN: 1-58488-301-4,<br>
LC: QA167.H36.
</li>
<li>
Barry Joe, <br>
GEOMPACK - a software package for the generation of meshes
using geometric algorithms, <br>
Advances in Engineering Software,<br>
Volume 13, pages 325-331, 1991.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "table_voronoi.f90">table_voronoi.f90</a>,
the source code.
</li>
<li>
<a href = "table_voronoi.sh">table_voronoi.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "diamond_02_00009.xy">diamond_02_00009.xy</a>,
a simple data file of 9 points.
</li>
<li>
<a href = "diamond_02_00009_output.txt">diamond_02_00009_output.txt</a>,
the output from the program.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for TABLE_VORONOI.
</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_TO_DIGIT</b> returns the integer value of a base 10 digit.
</li>
<li>
<b>DIAEDG</b> chooses a diagonal edge.
</li>
<li>
<b>DTRIS2</b> constructs a Delaunay triangulation of 2D vertices.
</li>
<li>
<b>FILE_COLUMN_COUNT</b> counts the number of columns in the first line of a file.
</li>
<li>
<b>FILE_ROW_COUNT</b> counts the number of row records in a file.
</li>
<li>
<b>GET_UNIT</b> returns a free FORTRAN unit number.
</li>
<li>
<b>HANDLE_FILE</b> computes Voronoi information for a given set of data.
</li>
<li>
<b>I4_MODP</b> returns the nonnegative remainder of I4 division.
</li>
<li>
<b>I4_WRAP</b> forces an I4 to lie between given limits by wrapping.
</li>
<li>
<b>I4MAT_TRANSPOSE_PRINT</b> prints an I4MAT, transposed.
</li>
<li>
<b>I4MAT_TRANSPOSE_PRINT_SOME</b> prints some of the transpose of an I4MAT.
</li>
<li>
<b>I4VEC_INDICATOR</b> sets an I4VEC to the indicator vector.
</li>
<li>
<b>I4VEC_PRINT</b> prints an I4VEC.
</li>
<li>
<b>LINE_EXP_NORMAL_2D</b> computes the unit normal vector to a line in 2D.
</li>
<li>
<b>LRLINE</b> determines if a point is left of, right or, or on a directed line.
</li>
<li>
<b>PERM_INV</b> inverts a permutation "in place".
</li>
<li>
<b>R82VEC_PERMUTE</b> permutes an R82VEC in place.
</li>
<li>
<b>R82VEC_SORT_HEAP_INDEX_A</b> does an indexed heap ascending sort of an R82VEC.
</li>
<li>
<b>R8MAT_DATA_READ</b> reads data from an R8MAT file.
</li>
<li>
<b>R8MAT_HEADER_READ</b> reads the header from an R8MAT file.
</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>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>SWAPEC</b> swaps diagonal edges until all triangles are Delaunay.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>TRI_AUGMENT</b> augments the triangle data using vertices at infinity.
</li>
<li>
<b>TRIANGLE_AREA_2D</b> computes the area of a triangle in 2D.
</li>
<li>
<b>TRIANGLE_CIRCUMCENTER_2D</b> computes the circumcenter of a triangle in 2D.
</li>
<li>
<b>VBEDG</b> determines which boundary edges are visible to a point.
</li>
<li>
<b>VORONOI_DATA</b> returns data defining the Voronoi diagram.
</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 28 December 2010.
</i>
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