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<html>
<head>
<title>
DELAUNAY_TREE_2D - Delaunay Triangulation of 2D Data
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055" >
<h1 align = "center">
DELAUNAY_TREE_2D <br> Delaunay Triangulation of 2D Data
</h1>
<hr>
<p>
<b>DELAUNAY_TREE_2D</b>
is a C++ program which
reads a file of point coordinates in 2D and produces a PostScript file containing
an image of the Delaunay triangulation of the points,
by Olivier Devillers.
</p>
<p>
<b>Warning:</b> A limitation of the program is that it assumes
that the user's input coordinates are "reasonable" PostScript coordinates!
Reasonable results will be achieved then if both X and Y coordinates
are positive and range from 0 to 1000 or so, say. On the other hand,
a user whose data is in the unit square will get a PostScript
file which actually plots the entire image in a near infinitesimal
and useless box! A reasonable fix is to rescale data so that it
lies between 0 and 612. (The PostScript coordinates, by default,
are in units of 1/72 inch, so 8.5 inches wide = 612.)
</p>
<p>
It would not be hard to correct the code so that the user can
input data with any scaling whatsoever, while the program would
(simple) just rescale it, or (better) insert the appropriate
PostScript scaling commands in the plot file.
</p>
<p>
In any case, the program is more interesting for being a
fairly clean embodiment of a Delaunay triangulation algorithm,
and the author himself suggests that a user might profitably
and easily modify the code to write out the information defining
the triangulation.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<dl>
<dt>
<b>delaunay_tree_2d</b> < <i>data.txt</i> > <i>data.ps</i>
</dt>
<dd>
reads the point coordinates from <i>data.txt</i> and writes
a PostScript image of the Delaunay triangulation to <i>data.ps</i>.
</dd>
</dl>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>DELAUNAY_TREE_2D</b> is available in
<a href = "../../cpp_src/delaunay_tree_2d/delaunay_tree_2d.html">a C++ version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/delaunay_lmap_2d/delaunay_lmap_2d.html">
DELAUNAY_LMAP_2D</a>,
a FORTRAN90 program which
reads in a pointset and
a linear map and writes out the Delaunay triangulation
for the linearly transformed data.
</p>
<p>
<a href = "../../cpp_src/geompack/geompack.html">
GEOMPACK</a>,
a C++ library which
computes the Delaunay triangulation
or Voronoi diagram.
</p>
<p>
<a href = "../../f_src/stripack/stripack.html">
STRIPACK</a>,
a FORTRAN90 library which
can compute the Delaunay
triangulation of a set of points on a sphere.
</p>
<p>
<a href = "../../cpp_src/table_delaunay/table_delaunay.html">
TABLE_DELAUNAY</a>,
a C++ program which
reads a
file of 2d point coordinates and computes the Delaunay triangulation.
</p>
<p>
<a href = "../../cpp_src/table_voronoi/table_voronoi.html">
TABLE_VORONOI</a>,
a C++ program which
can compute information about the
Voronoi diagram of a set of points stored in a file.
</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/tripack/tripack.html">
TRIPACK</a>,
a FORTRAN90 library which
can compute the Delaunay
triangulation of a set of points.
</p>
<h3 align = "center">
Author:
</h3>
<p>
Olivier Devillers
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
<a href = "http://www-sop.inria.fr/prisme/logiciel/index.html.en">
http://www-sop.inria.fr/prisme/logiciel/index.html.en
</a>
a software download site at INRIA.
</li>
<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>
Jean-Daniel Boissonnat, Monique Teillaud,<br>
On the randomized construction of the Delaunay tree,<br>
Theoretetical Computer Science,<br>
Volume 112, pages 339-354, 1993.
</li>
<li>
Olivier Devillers, Stefan Meiser, Monique Teillaud,<br>
Fully dynamic Delaunay triangulation in logarithmic expected
time per operation,<br>
Computational Geometry: Theory and Applications,<br>
Volume 2, Number 2, pages 55-80, 1992.
</li>
<li>
Olivier Devillers,
Robust and efficient implementation of the Delaunay tree,<br>
INRIA Research Report 1619, 1992.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "delaunay_tree_2d.cpp">delaunay_tree_2d.cpp</a>,
the source code;
</li>
<li>
<a href = "delaunay_tree_2d.sh">delaunay_tree_2d.sh</a>,
commands to compile and load the source code;
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>DEVILLERS_02_01000</b> is a set of 1000 points.
<ul>
<li>
<a href = "devillers_02_01000.txt">devillers_02_01000.txt</a>,
the point coordinates;
</li>
<li>
<a href = "devillers_02_01000.png">devillers_02_01000.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the file created by the program from the input data;
</li>
</ul>
</p>
<p>
<b>DIAMOND_02_00009</b> is a set of 9 points. Unfortunately,
the data is scaled to lie in the unit box, so <b>TABLE_SCALE</b>
was called to rescale both X and Y to lie between 0 and 612:
<ul>
<li>
<a href = "diamond_02_00009.txt">devillers_02_00009.txt</a>,
the point coordinates;
</li>
<li>
<a href = "diamond_scaled.txt">devillers_scaled.txt</a>,
the rescaled point coordinates;
</li>
<li>
<a href = "diamond_02_00009.png">diamond_02_00009.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the file created by the program from the input data;
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>"+"</b> is an overloading of the + operator to points.
</li>
<li>
<b>"-"</b> is an overloading of the - operator to points.
</li>
<li>
<b>"*"</b> is an overloading of the * operator to points.
</li>
<li>
<b>"^"</b> is an overloading of the ^ operator to points.
</li>
<li>
<b>DT_list::~DT_list</b> is the annihilator for class DT_list.
</li>
<li>
<b>DT_node::conflict</b> is true if the point is inside the closed circumdisk.
</li>
<li>
<b>point::lineto</b> writes a record to the PostScript file.
</li>
<li>
<b>DT_node::DT_node</b> ( void ) is a creation routine for class DT_node.
</li>
<li>
<b>DT_node::DT_node</b> ( DT_node* root, ind i ) is a creation routines for class DT_node.
</li>
<li>
<b>DT_node::DT_node</b> ( DT_node* f, point *c, ind i ) is a creation routine for class DT_node.
</li>
<li>
<b>DT_node::find_conflict</b> returns an alive node in conflict.
</li>
<li>
<b>DT_node:output</b> ?
</li>
<li>
<b>Delaunay_tree::output</b> outputs the Delaunay triangulation.
</li>
<li>
<b>DT_node::output2</b> ?
</li>
<li>
<b>Delaunay_tree::output2</b> outputs the Delaunay triangulation.
</li>
<li>
<b>Delaunay_tree::Delaunay_tree</b> ( void ) initializes the Delaunay tree.
</li>
<li>
<b>Delaunay_tree::~Delaunay_tree</b> is the destructor for class Delaunay_tree.
</li>
<li>
<b>Delaunay_tree::operator=+</b> is the insertion operator for class Delaunay_tree.
</li>
<li>
<b>MAIN</b> is the main program for delaunay_tree_2d.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 16 March 2006.
</i>
<!-- John Burkardt -->
</body>
</html>