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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 C++ program which
analyzes the triangulation
of a region, and lists those nodes which lie on the boundary
of the triangulation.
</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 'prefix' 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 = "../../cpp_src/mesh_to_xml/mesh_to_xml.html">
MESH_TO_XML</a>,
a C++ program which
reads information defining a 1D, 2D or 3D mesh, namely
a file of node coordinates and a file of elements defined by
node indices, and creates a corresponding XML file for input
to DOLFIN or FENICS.
</p>
<p>
<a href = "../../cpp_src/table_delaunay/table_delaunay.html">
TABLE_DELAUNAY</a>,
a C++ 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 = "../../cpp_src/triangulation/triangulation.html">
TRIANGULATION</a>,
a C++ library which
carries out various operations on order 3 ("linear") or order 6
("quadratic") triangulations.
</p>
<p>
<a href = "../../cpp_src/triangulation_corner/triangulation_corner.html">
TRIANGULATION_CORNER</a>,
a C++ program which
patches triangulations so that no triangle has two sides on the boundary.
</p>
<p>
<a href = "../../cpp_src/triangulation_delaunay_discrepancy/triangulation_delaunay_discrepancy.html">
TRIANGULATION_DELAUNAY_DISCREPANCY</a>,
a C++ program which
measures the amount by which a triangulation fails the local Delaunay test;
</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 = "../../cpp_src/triangulation_histogram/triangulation_histogram.html">
TRIANGULATION_HISTOGRAM</a>,
a C++ program which
computes histograms of data over a triangulation.
</p>
<p>
<a href = "../../cpp_src/triangulation_l2q/triangulation_l2q.html">
TRIANGULATION_L2Q</a>,
a C++ 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 = "../../cpp_src/triangulation_mask/triangulation_mask.html">
TRIANGULATION_MASK</a>,
a C++ program which
takes an existing triangulation and deletes triangles and
their corresponding nodes as requested by the user.
</p>
<p>
<a href = "../../cpp_src/triangulation_node_to_element/triangulation_node_to_element.html">
TRIANGULATION_NODE_TO_ELEMENT</a>,
a C++ program which
reads files describing a set of nodes, their triangulation, and the
value of one or more quantities at each node, and outputs a file
that averages the quantities for each element. This operation
in effect creates an "order1" finite element model of the data.
</p>
<p>
<a href = "../../data/triangulation_order3/triangulation_order3.html">
TRIANGULATION_ORDER3</a>,
a 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 directory which
contains a description and
examples of order 6 triangulations.
</p>
<p>
<a href = "../../cpp_src/triangulation_orient/triangulation_orient.html">
TRIANGULATION_ORIENT</a>,
a C++ 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 = "../../cpp_src/triangulation_plot/triangulation_plot.html">
TRIANGULATION_PLOT</a>,
a C++ program which
reads data defining a triangulation and creates a
PostScript image of the nodes and triangles.
</p>
<p>
<a href = "../../cpp_src/triangulation_q2l/triangulation_q2l.html">
TRIANGULATION_Q2L</a>,
a C++ 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 = "../../cpp_src/triangulation_quad/triangulation_quad.html">
TRIANGULATION_QUAD</a>,
a C++ program which
estimates the integral of a function over a triangulated region.
</p>
<p>
<a href = "../../cpp_src/triangulation_quality/triangulation_quality.html">
TRIANGULATION_QUALITY</a>,
a C++ program which
reads data defining a triangulation and computes a number
of quality measures.
</p>
<p>
<a href = "../../cpp_src/triangulation_rcm/triangulation_rcm.html">
TRIANGULATION_RCM</a>,
a C++ 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 = "../../cpp_src/triangulation_refine/triangulation_refine.html">
TRIANGULATION_REFINE</a>,
a C++ 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 = "../../cpp_src/triangulation_triangle_neighbors/triangulation_triangle_neighbors.html">
TRIANGULATION_TRIANGLE_NEIGHBORS</a>,
a C++ 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.cpp">
triangulation_boundary_nodes.cpp</a>, the source code.
</li>
<li>
<a href = "triangulation_boundary_nodes.sh">
triangulation_boundary_nodes.sh</a>,
commands to compile 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>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for TRIANGULATION_BOUNDARY_NODES.
</li>
<li>
<b>CH_CAP</b> capitalizes a single character.
</li>
<li>
<b>CH_EQI</b> is true if two characters are equal, disregarding case.
</li>
<li>
<b>CH_TO_DIGIT</b> returns the integer value of a base 10 digit.
</li>
<li>
<b>FILE_COLUMN_COUNT</b> counts the columns in the first line of a file.
</li>
<li>
<b>FILE_EXIST</b> reports whether a file exists.
</li>
<li>
<b>FILE_ROW_COUNT</b> counts the number of row records in a file.
</li>
<li>
<b>I4_MAX</b> returns the maximum of two I4's.
</li>
<li>
<b>I4_MIN</b> returns the minimum of two I4's.
</li>
<li>
<b>I4COL_COMPARE</b> compares columns I and J of a integer array.
</li>
<li>
<b>I4COL_SORT_A</b> ascending sorts the columns of an integer array.
</li>
<li>
<b>I4COL_SWAP</b> swaps two columns of an integer array.
</li>
<li>
<b>I4MAT_DATA_READ</b> reads data from an I4MAT file.
</li>
<li>
<b>I4MAT_HEADER_READ</b> reads the header from an I4MAT file.
</li>
<li>
<b>I4MAT_TRANSPOSE_PRINT_SOME</b> prints some of an I4MAT, transposed.
</li>
<li>
<b>R8MAT_DATA_READ</b> reads the 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>R8MAT_WRITE</b> writes an R8MAT file with no header.
</li>
<li>
<b>S_LEN_TRIM</b> returns the length of a string to the last nonblank.
</li>
<li>
<b>S_TO_I4</b> reads an I4 from a string.
</li>
<li>
<b>S_TO_I4VEC</b> reads an I4VEC 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>SORT_HEAP_EXTERNAL</b> externally sorts a list of items into ascending order.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>TRIANGULATION_ORDER3_BOUNDARY_NODE</b> indicates nodes on the boundary.
</li>
<li>
<b>TRIANGULATION_ORDER6_BOUNDARY_NODE</b> indicates nodes on the boundary.
</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 03 December 2010.
</i>
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