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<html>
<head>
<title>
TRIANGULATION_BOUNDARY_NODES - Boundary Nodes of a Triangulation
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TRIANGULATION_BOUNDARY_NODES <br> Boundary Nodes of a Triangulation
</h1>
<hr>
<p>
<b>TRIANGULATION_BOUNDARY_NODES</b>
is a MATLAB program which
analyzes the triangulation
of a region, and identifies each boundary node with the label "1".
</p>
<p>
Either a 3-node or 6-node triangulation may be used.
</p>
<p>
Although this boundary information is useful, it would be more
useful to divide the boundary nodes up, if the boundary consists
of more than one connected segment. Moreover, it would also be
useful to report the sequence of nodes necessary to trace out
a connected segment of the boundary. I imagine I will come back
to work on those projects later!
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>triangulation_boundary_nodes</b> ( <i>'prefix'</i> )
</blockquote>
where <i>prefix</i> is the common filename prefix:
<ul>
<li>
<i>prefix</i><b>_nodes.txt</b> contains the node coordinates,
</li>
<li>
<i>prefix</i><b>_elements.txt</b> contains the element definitions.
</li>
<li>
<i>prefix</i><b>_boundary_nodes.txt</b> will contain a 0 for each internal
node, and a 1 for each boundary node.
</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>TRIANGULATION_BOUNDARY_NODES</b> is available in
<a href = "../../cpp_src/triangulation_boundary_nodes/triangulation_boundary_nodes.html">a C++ version</a> and
<a href = "../../f_src/triangulation_boundary_nodes/triangulation_boundary_nodes.html">a FORTRAN90 version</a> and
<a href = "../../m_src/triangulation_boundary_nodes/triangulation_boundary_nodes.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Programs:
</h3>
<p>
<a href = "../../f_src/table_delaunay/table_delaunay.html">
TABLE_DELAUNAY</a>,
a FORTRAN90 program which
triangulates a set of nodes whose coordinates are stored in a file.
</p>
<p>
<a href = "../../c_src/triangle/triangle.html">
TRIANGLE</a>,
a C program which
computes a triangulation of a geometric region.
</p>
<p>
<a href = "../../m_src/triangulation/triangulation.html">
TRIANGULATION</a>,
a MATLAB library which
carries out various operations on order 3 ("linear") or order 6
("quadratic") triangulations.
</p>
<p>
<a href = "../../m_src/triangulation_boundary_edges/triangulation_boundary_edges.html">
TRIANGULATION_BOUNDARY_EDGES</a>,
a MATLAB program which
reads data defining a triangulation, determines which edges
lie on the boundary, organizes them into connected components,
and writes this information to a file.
</p>
<p>
<a href = "../../m_src/triangulation_corner/triangulation_corner.html">
TRIANGULATION_CORNER</a>,
a MATLAB program which
patches triangulations so that no triangle has two sides on the boundary.
</p>
<p>
<a href = "../../m_src/triangulation_delaunay_discrepancy/triangulation_delaunay_discrepancy.html">
TRIANGULATION_DELAUNAY_DISCREPANCY</a>,
a MATLAB program which
measures the amount by which a triangulation fails the local Delaunay test;
</p>
<p>
<a href = "../../m_src/triangulation_display/triangulation_display.html">
TRIANGULATION_DISPLAY</a>,
a MATLAB program which
displays the nodes and elements of a triangulation on the MATLAB graphics screen;
</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 = "../../m_src/triangulation_histogram/triangulation_histogram.html">
TRIANGULATION_HISTOGRAM</a>,
a MATLAB program which
computes histograms of data over a triangulation.
</p>
<p>
<a href = "../../m_src/triangulation_l2q/triangulation_l2q.html">
TRIANGULATION_L2Q</a>,
a MATLAB program which
reads data defining a 3-node triangulation and generates
midside nodes and writes out the corresponding 6-node triangulation.
</p>
<p>
<a href = "../../m_src/triangulation_mask/triangulation_mask.html">
TRIANGULATION_MASK</a>,
a MATLAB program which
takes an existing triangulation and deletes triangles and
their corresponding nodes as requested by the user.
</p>
<p>
<a href = "../../data/triangulation_order3/triangulation_order3.html">
TRIANGULATION_ORDER3</a>,
a data directory which
contains a description and
examples of order 3 triangulations.
</p>
<p>
<a href = "../../data/triangulation_order6/triangulation_order6.html">
TRIANGULATION_ORDER6</a>,
a data directory which
contains a description and examples of order 6 triangulations.
</p>
<p>
<a href = "../../m_src/triangulation_orient/triangulation_orient.html">
TRIANGULATION_ORIENT</a>,
a MATLAB program which
reads data defining a triangulation, makes sure that
every triangle has positive orientation, and if not, writes a
corrected triangle file.
</p>
<p>
<a href = "../../m_src/triangulation_plot/triangulation_plot.html">
TRIANGULATION_PLOT</a>,
a MATLAB program which
reads data defining a triangulation and creates a
PostScript image of the nodes and triangles.
</p>
<p>
<a href = "../../m_src/triangulation_q2l/triangulation_q2l.html">
TRIANGULATION_Q2L</a>,
a MATLAB program which
reads data defining a 6-node triangulation, and subdivides
each triangle into 4 3-node triangles, writing the resulting
triangulation to a file.
</p>
<p>
<a href = "../../m_src/triangulation_quad/triangulation_quad.html">
TRIANGULATION_QUAD</a>,
a MATLAB program which
estimates the integral of a function over a triangulated region.
</p>
<p>
<a href = "../../m_src/triangulation_quality/triangulation_quality.html">
TRIANGULATION_QUALITY</a>,
a MATLAB program which
reads data defining a triangulation and computes a number
of quality measures.
</p>
<p>
<a href = "../../m_src/triangulation_rcm/triangulation_rcm.html">
TRIANGULATION_RCM</a>,
a MATLAB program which
reads data defining a triangulation, determines an ordering
of the nodes that will reduce the bandwidth of the adjacency
matrix, and writes the new triangulation information to a file.
</p>
<p>
<a href = "../../m_src/triangulation_refine/triangulation_refine.html">
TRIANGULATION_REFINE</a>,
a MATLAB program which
reads data defining a triangulation, replaces each triangle
by four congruent smaller ones, and writes the new triangulation
information to a file.
</p>
<p>
<a href = "../../m_src/triangulation_triangle_neighbors/triangulation_triangle_neighbors.html">
TRIANGULATION_TRIANGLE_NEIGHBORS</a>,
a MATLAB program which
reads data defining a triangulation, determines the neighboring
triangles of each triangle, and writes that information to a file.
</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.
</li>
<li>
Joseph ORourke,<br>
Computational Geometry,<br>
Second Edition,<br>
Cambridge, 1998,<br>
ISBN: 0521649765,<br>
LC: QA448.D38.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "triangulation_boundary_nodes.m">triangulation_boundary_nodes.m</a>
is the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>ELBOW</b> is a curved region, looking like an elbow, that lies inside
the unit square. It is triangulated using order 3 triangles. There are
320 nodes and 568 triangles. There are 66 nodes on the boundary.
<ul>
<li>
<a href = "elbow_nodes.txt">elbow_nodes.txt</a>,
the node file.
</li>
<li>
<a href = "elbow_nodes.png">elbow_nodes.png</a>,
a PNG image of the nodes.
</li>
<li>
<a href = "elbow_elements.txt">elbow_elements.txt</a>,
the triangles.
</li>
<li>
<a href = "elbow_output.txt">elbow_output.txt</a>,
the printed output from a run of the sample program.
</li>
<li>
<a href = "elbow_boundary_nodes.txt">
elbow_boundary_nodes.txt</a>,
the boundary node file.
</li>
<li>
<a href = "elbow_boundary_nodes.png">
elbow_boundary_nodes.png</a>,
a PNG image of the boundary nodes.
</li>
</ul>
</p>
<p>
<b>LAKE</b> is an irregular lake-shaped region with an "island".
It is triangulated using order 3 triangles.
<ul>
<li>
<a href = "lake_nodes.txt">lake_nodes.txt</a>,
the node file.
</li>
<li>
<a href = "lake_nodes.png">lake_nodes.png</a>,
a PNG image of the nodes.
</li>
<li>
<a href = "lake_elements.txt">lake_elements.txt</a>,
the triangles.
</li>
<li>
<a href = "lake_output.txt">lake_output.txt</a>,
the printed output from a run of the sample program.
</li>
<li>
<a href = "lake_boundary_nodes.txt">
lake_boundary_nodes.txt</a>,
the boundary node file.
</li>
<li>
<a href = "lake_boundary_nodes.png">
lake_boundary_nodes.png</a>,
a PNG image of the boundary nodes.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 02 December 2010.
</i>
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