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<html>
<head>
<title>
MESHLESS - Meshless Voronoi Basis Functions
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
MESHLESS <br> Meshless Voronoi Basis Functions
</h1>
<hr>
<p>
<b>MESHLESS</b>
is a FORTRAN90 program which
generates a set of local basis functions, without the use of a mesh,
by Lili Ju.
</p>
<p>
If <b>N</b> basis functions are desired
in an arbitrary region, then <b>N</b> basis points are chosen at random
in the region. Each point in the region is assigned to the nearest
basis point. The basis points are then adjusted by taking the
average of the associated points. If this process is repeated, the
basis points will arrange themselves into generators of a centroidal
Voronoi tessellation of the region.
</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">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/cvt/cvt.html">
CVT</a>,
a FORTRAN90 library which
computes points that
form a Centroidal Voronoi Tessellation, which can be used by
<b>MESHLESS</b> to assign node locations.
</p>
<p>
<a href = "../../f_src/halton/halton.html">
HALTON</a>,
a FORTRAN90 library which
computes quasirandom
Halton points, which can be used by <b>MESHLESS</b> to
assign node locations.
</p>
<p>
<a href = "../../f_src/ps_write/ps_write.html">
PS_WRITE</a>,
a FORTRAN90 library which
implements some PostScript graphics commands.
</p>
<h3 align = "center">
Author:
</h3>
<p>
Lili Ju
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Qiang Du, Vance Faber, Max Gunzburger,<br>
Centroidal Voronoi Tessellations: Applications and Algorithms,<br>
SIAM Review, Volume 41, 1999, pages 637-676.
</li>
<li>
Qiang Du, Max Gunzburger, Lili Ju,<br>
Meshfree, Probabilistic Determination of Point Sets and Support
Regions for Meshfree Computing,<br>
Computer Methods in Applied Mechanics in Engineering,<br>
Volume 191, 2002, pages 1349-1366;
</li>
<li>
Lili Ju, Qiang Du, Max Gunzburger,<br>
Probabilistic Methods for Centroidal Voronoi Tessellations and
their Parallel Implementations,<br>
Parallel Computing, Volume 28, 2002, pages 1477-1500.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "meshless.f90">meshless.f90</a>, the source code.
</li>
<li>
<a href = "meshless.sh">meshless.sh</a>, commands
to compile and load the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "meshless_input.txt">meshless_input.txt</a>,
a set of sample input commands.
</li>
<li>
<a href = "meshless_output.txt">meshless_output.txt</a>,
the printed responses.
</li>
<li>
<a href = "basis.dat">basis.dat</a>,
a file of basis points written by the program.
</li>
<li>
<a href = "basis.png">basis.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the basis points.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for the meshless basis function routines.
</li>
<li>
<b>BASIS_BOX</b> finds a box that contains all the basis functions.
</li>
<li>
<b>BASIS_OVERLAP</b> counts the number of basis functions with overlapping support.
</li>
<li>
<b>BASIS_PLOT</b> plots the basis functions in the region.
</li>
<li>
<b>BASIS_READ</b> reads basis data from a file.
</li>
<li>
<b>BASIS_WRITE</b> writes the basis data to a file.
</li>
<li>
<b>CH_CAP</b> capitalizes a single character.
</li>
<li>
<b>CENTER_PLOT</b> plots the center in the region.
</li>
<li>
<b>CVT_MAKE</b> computes centroidal Voronoi tessellation generators.
</li>
<li>
<b>CVT_READ</b> reads the CVT data from a file.
</li>
<li>
<b>CVT_WRITE</b> writes the CVT data to a file.
</li>
<li>
<b>DENSITY</b> evaluates the density function.
</li>
<li>
<b>EPS_FILE_HEAD</b> writes header information to an encapsulated PostScript file.
</li>
<li>
<b>EPS_FILE_TAIL</b> writes trailer information to an encapsulated PostScript file.
</li>
<li>
<b>FILE_COLUMN_COUNT</b> counts the number of columns in the first line of a file.
</li>
<li>
<b>FILE_LINE_COUNT</b> counts the number of lines in a file.
</li>
<li>
<b>FIND_CLOSEST</b> finds the center point CENTER(1:M,IC) closest to Y(1:M).
</li>
<li>
<b>FIND_RE</b> finds the number of center points near a given point.
</li>
<li>
<b>GET_UNIT</b> returns a free FORTRAN unit number.
</li>
<li>
<b>HALTON_GENERATE</b> generates a Halton dataset.
</li>
<li>
<b>HALTON_READ</b> reads Halton data from a file.
</li>
<li>
<b>HALTON_WRITE</b> writes a Halton dataset to a file.
</li>
<li>
<b>I4_SWAP</b> swaps two integer values.
</li>
<li>
<b>I4_TO_HALTON</b> computes an element of a Halton sequence.
</li>
<li>
<b>POINT_INSIDE_BOX_2D</b> determines if a point is inside a box in 2D.
</li>
<li>
<b>PRIME</b> returns any of the first PRIME_MAX prime numbers.
</li>
<li>
<b>PS_CIRCLE</b> draws a circle.
</li>
<li>
<b>PS_COLOR_FILL_SET</b> sets the fill color.
</li>
<li>
<b>PS_COLOR_LINE</b> handles the line color.
</li>
<li>
<b>PS_COLOR_LINE_SET</b> sets the line color.
</li>
<li>
<b>PS_COMMENT</b> inserts a comment into the PostScript file.
</li>
<li>
<b>PS_DEFAULT</b> sets the internal settings to their default values
</li>
<li>
<b>PS_FILE_CLOSE</b> closes a PostScript file.
</li>
<li>
<b>PS_FILE_HEAD</b> writes header information to a PostScript file.
</li>
<li>
<b>PS_FILE_OPEN</b> opens a new version of a PostScript file with a given name.
</li>
<li>
<b>PS_FILE_TAIL</b> writes trailer information to a PostScript file.
</li>
<li>
<b>PS_GRID_CARTESIAN</b> draws a cartesian grid.
</li>
<li>
<b>PS_LINE_CLOSED</b> adds the graph of a closed line to a PostScript file.
</li>
<li>
<b>PS_LINETO</b> draws a line from the current point to the given point.
</li>
<li>
<b>PS_MARK_CIRCLES</b> marks points with a small open circle.
</li>
<li>
<b>PS_MARK_DISK</b> marks a point with a small filled disk.
</li>
<li>
<b>PS_MARKER_SIZE</b> sets the marker size.
</li>
<li>
<b>PS_MOVETO</b> "moves to" a new point, which becomes the current point.
</li>
<li>
<b>PS_PAGE_HEAD</b> writes header information on a new page.
</li>
<li>
<b>PS_PAGE_TAIL</b> writes tail information at the end of a page.
</li>
<li>
<b>PS_SETTING_INT</b> sets, gets, or prints integer internal PS_WRITE parameters.
</li>
<li>
<b>PS_SETTING_REAL</b> sets, gets, or prints real internal PS_WRITE parameters.
</li>
<li>
<b>R8_SWAP</b> swaps two real values.
</li>
<li>
<b>RADIUS_MAKE_1</b> uses algorithm 1 to determine a suitable radius for each center.
</li>
<li>
<b>RADIUS_MAKE_2</b> uses algorithm 2 to determine a suitable radius for each center.
</li>
<li>
<b>RANDOM_GENERATOR</b> returns a random point Z(1:M) in [A(1:M),B(1:M)].
</li>
<li>
<b>S_BLANK_DELETE</b> removes blanks from a string, left justifying the remainder.
</li>
<li>
<b>S_EQI</b> is a case insensitive comparison of two strings for equality.
</li>
<li>
<b>S_TO_I4</b> reads an I4 from a string.
</li>
<li>
<b>S_WORD_COUNT</b> counts the number of "words" in a string.
</li>
<li>
<b>SET_RANDOM_SEED</b> initializes the FORTRAN 90 random number generator.
</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>
<li>
<b>UNIFORM_MAKE</b> sets up the uniform random data points.
</li>
<li>
<b>UNIFORM_READ</b> reads uniform random data from a file.
</li>
<li>
<b>UNIFORM_WRITE</b> writes the uniform random data to a file.
</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 12 November 2006.
</i>
<!-- John Burkardt -->
</body>
</html>