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<html>
<head>
<title>
TRIANGULATION_T3_TO_T4 - Convert T3 Mesh to T4 Mesh
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TRIANGULATION_T3_TO_T4 <br> Convert T3 Mesh to T4 Mesh
</h1>
<hr>
<p>
<b>TRIANGULATION_T3_TO_T4</b>
is a FORTRAN90 program which
reads information
describing a triangulation of a set of points using 3-node
"T3" triangles, and creates a 4-node "T4"
triangulation.
</p>
<p>
The same number of triangles are used, but each triangle
is given one extra node at the centroid. The coordinates of
these nodes are determined by averaging the coordinates of
the vertices of the triangles.
</p>
<p>
The input and output files use the simple
<a href = "../../data/table/table.html">TABLE format</a>;
comment lines begin with a "#" character. Otherwise, each line
of the file contains one set of information, either the coordinates
of a node (for a node file), or the indices of nodes that make up
a triangle, (for a triangle file).
</p>
<p>
The input file <i>prefix</i>_nodes.txt contains the node information
for the 3-node triangulation. Each data line contains the X and
Y coordinates of a single node.
</p>
<p>
The input file <i>prefix</i>_elements.txt contains the triangle information
for the 3-node triangulation. Each line contains the indices of three
nodes that form a triangle, in counterclockwise order.
</p>
<p>
The output file <i>prefix</i>_t4_nodes.txt contains the node information
for the 4-node triangulation. It begins with the node information
from <i>prefix</i>_nodes.txt, followed by the coordinates of the new nodes.
</p>
<p>
The output file <i>prefix</i>_t4_triangles.txt contains the triangle
information for the 4-node triangulation. There are exactly
as many triangles as before, but now each triangle uses four nodes.
Each line of the file contains the indices of 4 nodes that form the
triangle. The first three indices are the vertices, in counterclockwise
order. The fourth index is the centroid node..
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>triangulation_t3_to_t4</b> <i>prefix</i>
</blockquote>
where <i>prefix</i> is the common filename prefix:
<ul>
<li>
<i>prefix</i>_nodes.txt contains the node coordinates,
</li>
<li>
<i>prefix</i>_elements.txt contains the element definitions.
</li>
<li>
<i>prefix</i>_t4_nodes.txt is the T4 node coordinates,
</li>
<li>
<i>prefix</i>_t4_elements.txt contains the T4 element definitions.
</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_T3_TO_T4</b> is available in
<a href = "../../cpp_src/triangulation_t3_to_t4/triangulation_t3_to_t4.html">a C++ version</a> and
<a href = "../../f_src/triangulation_t3_to_t4/triangulation_t3_to_t4.html">a FORTRAN90 version</a> and
<a href = "../../m_src/triangulation_t3_to_t4/triangulation_t3_to_t4.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/fem_basis_t3_display/fem_basis_t3_display.html">
FEM_BASIS_T3_DISPLAY</a>,
a MATLAB program which
displays a basis function associated with a 4-node triangle "T3" mesh.
</p>
<p>
<a href = "../../m_src/fem_basis_t4_display/fem_basis_t4_display.html">
FEM_BASIS_T4_DISPLAY</a>,
a MATLAB program which
displays a basis function associated with a 4-node triangle "T4" mesh.
</p>
<p>
<a href = "../../f_src/table_delaunay/table_delaunay.html">
TABLE_DELAUNAY</a>,
a FORTRAN90 program which
computes the triangulation
of 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 = "../../f_src/triangulation/triangulation.html">
TRIANGULATION</a>,
a FORTRAN90 library which
carries out various operations on order 3 ("linear") or order 6
("quadratic") triangulations.
</p>
<p>
<a href = "../../f_src/triangulation_boundary_nodes/triangulation_boundary_nodes.html">
TRIANGULATION_BOUNDARY_NODES</a>,
a FORTRAN90 program which
reads data defining a triangulation, determines which nodes
lie on the boundary, and writes their coordinates to a file.
</p>
<p>
<a href = "../../f_src/triangulation_corner/triangulation_corner.html">
TRIANGULATION_CORNER</a>,
a FORTRAN90 program which
patches triangulations so that no triangle has two sides on the boundary.
</p>
<p>
<a href = "../../f_src/triangulation_delaunay_discrepancy/triangulation_delaunay_discrepancy.html">
TRIANGULATION_DELAUNAY_DISCREPANCY</a>,
a FORTRAN90 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 = "../../f_src/triangulation_histogram/triangulation_histogram.html">
TRIANGULATION_HISTOGRAM</a>,
a FORTRAN90 program which
computes histograms of data over a triangulation.
</p>
<p>
<a href = "../../f_src/triangulation_l2q/triangulation_l2q.html">
TRIANGULATION_L2Q</a>,
a FORTRAN90 program which
reads data defining a 3-node triangulation, and adds midside nodes to
create a 6-node triangulation.
</p>
<p>
<a href = "../../f_src/triangulation_mask/triangulation_mask.html">
TRIANGULATION_MASK</a>,
a FORTRAN90 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 directory which
contains a description and
examples of order 3 triangulations.
</p>
<p>
<a href = "../../data/triangulation_order4/triangulation_order4.html">
TRIANGULATION_ORDER4</a>,
a directory which
contains a description and
examples of order 4 triangulations.
</p>
<p>
<a href = "../../f_src/triangulation_orient/triangulation_orient.html">
TRIANGULATION_ORIENT</a>,
a FORTRAN90 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 = "../../f_src/triangulation_plot/triangulation_plot.html">
TRIANGULATION_PLOT</a>,
a FORTRAN90 program which
reads data defining a triangulation and creates a
PostScript image of the nodes and triangles.
</p>
<p>
<a href = "../../f_src/triangulation_quad/triangulation_quad.html">
TRIANGULATION_QUAD</a>,
a FORTRAN90 program which
estimates the integral of a function over a triangulated region.
</p>
<p>
<a href = "../../f_src/triangulation_quality/triangulation_quality.html">
TRIANGULATION_QUALITY</a>,
a FORTRAN90 program which
reads data defining a triangulation and computes a number
of quality measures.
</p>
<p>
<a href = "../../f_src/triangulation_rcm/triangulation_rcm.html">
TRIANGULATION_RCM</a>,
a FORTRAN90 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 = "../../f_src/triangulation_refine/triangulation_refine.html">
TRIANGULATION_REFINE</a>,
a FORTRAN90 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 = "../../f_src/triangulation_triangle_neighbors/triangulation_triangle_neighbors.html">
TRIANGULATION_TRIANGLE_NEIGHBORS</a>,
a FORTRAN90 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_t3_to_t4.f90">triangulation_t3_to_t4.f90</a>,
the source code.
</li>
<li>
<a href = "triangulation_t3_to_t4.sh">triangulation_t3_to_t4.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>EXAMPLE</b> is a simple set of example data:
<ul>
<li>
<a href = "example_nodes.txt">example_nodes.txt</a>,
the nodes for the 3-node triangulation.
</li>
<li>
<a href = "example_nodes.png">example_nodes.png</a>,
a PNG image of the nodes.
</li>
<li>
<a href = "example_elements.txt">example_elements.txt</a>,
the triangles for the 3-node triangulation.
</li>
<li>
<a href = "example.png">example.png</a>,
a PNG image of the elements.
</li>
<li>
<a href = "example_t4_nodes.txt">example_t4_nodes.txt</a>,
the nodes for the 4-node triangulation.
</li>
<li>
<a href = "example_t4_nodes.png">example_t4_noes.png</a>,
a PNG image of the nodes.
</li>
<li>
<a href = "example_t4_elements.txt">example_t4_elements.txt</a>,
the triangles for the 4-node triangulation.
</li>
<li>
<a href = "example_t4.png">examples_t4.png</a>,
a PNG image of the elements.
</li>
<li>
<a href = "example_output.txt">example_output.txt</a>
the output file.
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for TRIANGULATION_T3_TO_T4.
</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 ( kind = 4 ) value of a base 10 digit.
</li>
<li>
<b>DTABLE_CLOSE_WRITE</b> closes a file used to write a DTABLE.
</li>
<li>
<b>DTABLE_DATA_READ</b> reads data from a double precision table file.
</li>
<li>
<b>DTABLE_DATA_WRITE</b> writes data to a double precision table file.
</li>
<li>
<b>DTABLE_HEADER_READ</b> reads the header from a double precision table file.
</li>
<li>
<b>DTABLE_HEADER_WRITE</b> writes the header to a double precision table file.
</li>
<li>
<b>DTABLE_OPEN_WRITE</b> opens a file to write a DTABLE.
</li>
<li>
<b>DTABLE_WRITE</b> writes a DTABLE to a file.
</li>
<li>
<b>FILE_COLUMN_COUNT</b> counts the number of columns in the first line of a file.
</li>
<li>
<b>FILE_NAME_EXT_GET</b> determines the "extension" of a file name.
</li>
<li>
<b>FILE_NAME_EXT_SWAP</b> replaces the current "extension" of a file name.
</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>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>ITABLE_CLOSE_WRITE</b> closes a file used to write an ITABLE.
</li>
<li>
<b>ITABLE_DATA_READ</b> reads data from an integer ( kind = 4 ) table file.
</li>
<li>
<b>ITABLE_DATA_WRITE</b> writes data to an integer ( kind = 4 ) table file.
</li>
<li>
<b>ITABLE_HEADER_READ</b> reads the header from an integer ( kind = 4 ) table file.
</li>
<li>
<b>ITABLE_HEADER_WRITE</b> writes the header to an integer ( kind = 4 ) table file.
</li>
<li>
<b>ITABLE_WRITE</b> writes an ITABLE file.
</li>
<li>
<b>ITABLE_OPEN_WRITE</b> opens a file to write ITABLE data.
</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_BLANK_DELETE</b> removes blanks from a string, left justifying the remainder.
</li>
<li>
<b>S_INDEX_LAST</b> finds the LAST occurrence of a given substring.
</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>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>TIMESTRING</b> writes the current YMDHMS date into a string.
</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 14 March 2009.
</i>
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