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<html>
<head>
<title>
TABLE_DELAUNAY - Triangulate Points in 2D
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TABLE_DELAUNAY <br> Triangulate Points in 2D
</h1>
<hr>
<p>
<b>TABLE_DELAUNAY</b>
is a FORTRAN90 program which
computes the Delaunay triangulation of a set of points in the plane.
</p>
<p>
Specifically, <b>TABLE_DELAUNAY</b> reads a data file of node coordinates,
computes the Delaunay triangulation of those points, and writes a
triangle file listing the indices of nodes that form each triangle.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>table_delaunay</b> <i>prefix</i>
</blockquote>
where <i>prefix</i> is the common prefix for the node and triangle files,
<ul>
<li>
<i>prefix</i><b>_nodes.txt</b>, the node coordinate file (input).
</li>
<li>
<i>prefix</i><b>_elements.txt</b>, the element file (output).
</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_DELAUNAY</b> is available in
<a href = "../../cpp_src/table_delaunay/table_delaunay.html">a C++ version</a> and
<a href = "../../f_src/table_delaunay/table_delaunay.html">a FORTRAN90 version</a> and
<a href = "../../m_src/table_delaunay/table_delaunay.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Programs:
</h3>
<p>
<a href = "../../f_src/delaunay_lmap_2d/delaunay_lmap_2d.html">
DELAUNAY_LMAP_2D</a>,
a FORTRAN90 program which
computes the Delaunay triangulation of points in the plane under a linear mapping.
</p>
<p>
<a href = "../../f_src/geompack/geompack.html">
GEOMPACK</a>,
a FORTRAN90 library which
contains the routines used for computing the Delaunay triangulation, by Barry Joe.
</p>
<p>
<a href = "../../f_src/stripack/stripack.html">
STRIPACK</a>,
a FORTRAN90 library which
can compute the Delaunay triangulation or Voronoi diagram
of points on a sphere.
</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_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_voronoi/table_voronoi.html">
TABLE_VORONOI</a>,
a FORTRAN90 program which
can be used to compute information about
the Voronoi diagram of the points.
</p>
<p>
<a href = "../../cpp_src/triangulation_display_opengl/triangulation_display_opengl.html">
TRIANGULATION_DISPLAY_OPENGL</a>,
a C++ program which
reads files defining a triangulation and displays an image using Open GL.
</p>
<p>
<a href = "../../f_src/triangulation_plot/triangulation_plot.html">
TRIANGULATION_PLOT</a>,
a FORTRAN90 program which
may be used to visualize triangulations.
</p>
<p>
<a href = "../../f_src/tripack/tripack.html">
TRIPACK</a>,
a FORTRAN90 library which
can compute the Delaunay triangulation of points in the plane.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Marc deBerg, Marc Krevald, Mark Overmars,
Otfried Schwarzkopf,<br>
Computational Geometry,<br>
Springer, 2000,<br>
ISBN: 3-540-65620-0,<br>
LC: QA448.D38.C65.
</li>
<li>
Herbert Edelsbrunner,<br>
Geometry and Topology for Mesh Generation,<br>
Cambridge, 2001,<br>
ISBN: 0-521-79309-2,<br>
LC: QA377.E36.
</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>
<li>
Joseph ORourke,<br>
Computational Geometry,<br>
Second Edition,<br>
Cambridge, 1998,<br>
ISBN: 0521649765,<br>
LC: QA448.D38.
</li>
<li>
Per-Olof Persson, Gilbert Strang,<br>
A Simple Mesh Generator in MATLAB,<br>
SIAM Review,<br>
Volume 46, Number 2, pages 329-345, June 2004.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "table_delaunay.f90">table_delaunay.f90</a>, the source code.
</li>
<li>
<a href = "table_delaunay.sh">table_delaunay.sh</a>,
commands to compile, link and load the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>P09</b> is a set of 211 nodes in a region with two hexagonal
holes. When TABLE_DELAUNAY triangulates the data, the holes get
filled in.
<ul>
<li>
<a href = "p09_nodes.txt">
p09_nodes.txt</a>,
the nodes.
</li>
<li>
<a href = "p09_nodes.png">
p09_nodes.png</a>,
a PNG image of the nodes.
</li>
<li>
<a href = "p09_elements.txt">
p09_elements.txt</a>,
the triangulation created by TABLE_DELAUNAY.
</li>
<li>
<a href = "p09_triangulation.png">
p09_triangulation.png</a>,
a PNG image of the triangulation.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for TABLE_DELAUNAY.
</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>I4_MODP</b> returns the nonnegative remainder of I4 division.
</li>
<li>
<b>I4_SIGN</b> evaluates the sign of an I4.
</li>
<li>
<b>I4_WRAP</b> forces an I4 to lie between given limits by wrapping.
</li>
<li>
<b>I4MAT_TRANSPOSE_PRINT_SOME</b> prints some of the transpose of an I4MAT.
</li>
<li>
<b>I4MAT_WRITE</b> writes an I4MAT file.
</li>
<li>
<b>I4VEC_INDICATOR</b> sets an I4VEC to the indicator vector.
</li>
<li>
<b>LRLINE</b> determines if a point is left of, right or, or on a directed line.
</li>
<li>
<b>PERM_CHECK</b> checks that a vector represents a permutation.
</li>
<li>
<b>PERM_INVERSE</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> ascending index heaps 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_SOME</b> prints some of an R8MAT, transposed.
</li>
<li>
<b>S_BLANK_DELETE</b> removes blanks from a string, left justifying the remainder.
</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>VBEDG</b> determines which boundary edges are visible to a point.
</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 01 October 2009.
</i>
<!-- John Burkardt -->
</body>
</html>