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<html>
<head>
<title>
PADUA - 2D Pointsets for Interpolation or Integration
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
PADUA <br> 2D Pointsets for Interpolation or Integration
</h1>
<hr>
<p>
<b>PADUA</b>
is a C++ library which
returns the coordinates of the 2D Padua points,
as well as interpolation weights or quadrature weights,
and images of the points in gnuplot graphics files.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files 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>PADUA</b> is available in
<a href = "../../c_src/padua/padua.html">a C version</a> and
<a href = "../../cpp_src/padua/padua.html">a C++ version</a> and
<a href = "../../f77_src/padua/padua.html">a FORTRAN77 version</a> and
<a href = "../../f_src/padua/padua.html">a FORTRAN90 version</a> and
<a href = "../../m_src/padua/padua.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/exactness_2d/exactness_2d.html">
EXACTNESS_2D</a>,
a C++ library which
investigates the exactness of 2D quadrature rules that estimate the
integral of a function f(x,y) over a 2D domain.
</p>
<p>
<a href = "../../cpp_src/gnuplot/gnuplot.html">
GNUPLOT</a>,
C++ programs which
illustrate how a program can write data and command files
so that gnuplot can create plots of the program results.
</p>
<p>
<a href = "../../cpp_src/lagrange_interp_2d/lagrange_interp_2d.html">
LAGRANGE_INTERP_2D</a>,
a C++ library which
defines and evaluates the Lagrange polynomial p(x,y)
which interpolates a set of data depending on a 2D argument
that was evaluated on a product grid,
so that p(x(i),y(j)) = z(i,j).
</p>
<p>
<a href = "../../cpp_src/pwl_interp_2d/pwl_interp_2d.html">
PWL_INTERP_2D</a>,
a C++ library which
evaluates a piecewise linear interpolant to data defined on
a regular 2D grid.
</p>
<p>
<a href = "../../cpp_src/quadrature_weights_vandermonde_2d/quadrature_weights_vandermonde_2d.html">
QUADRATURE_WEIGHTS_VANDERMONDE_2D</a>,
a C++ library which
computes the weights of a 2D quadrature rule using the Vandermonde
matrix, assuming that the points have been specified.
</p>
<p>
<a href = "../../cpp_src/rbf_interp_2d/rbf_interp_2d.html">
RBF_INTERP_2D</a>,
a C++ library which
defines and evaluates radial basis function (RBF) interpolants to 2D data.
</p>
<p>
<a href = "../../cpp_src/shepard_interp_2d/shepard_interp_2d.html">
SHEPARD_INTERP_2D</a>,
a C++ library which
defines and evaluates Shepard interpolants to 2D data,
based on inverse distance weighting.
</p>
<p>
<a href = "../../cpp_src/test_interp_2d/test_interp_2d.html">
TEST_INTERP_2D</a>,
a C++ library which
defines test problems for interpolation of data z(x,y),
depending on a 2D argument.
</p>
<p>
<a href = "../../cpp_src/toms886/toms886.html">
TOMS886</a>,
a C++ library which
defines the Padua points for interpolation in a 2D region,
including the rectangle, triangle, and ellipse,
by Marco Caliari, Stefano de Marchi, Marco Vianello.
This is ACM TOMS algorithm 886.
</p>
<p>
<a href = "../../cpp_src/vandermonde_interp_2d/vandermonde_interp_2d.html">
VANDERMONDE_INTERP_2D</a>,
a C++ library which
finds a polynomial interpolant to data z(x,y) of a 2D argument
by setting up and solving a linear system for the polynomial coefficients,
involving the Vandermonde matrix.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Marco Caliari, Stefano de Marchi, Marco Vianello,<br>
Bivariate interpolation on the square at new nodal sets,<br>
Applied Mathematics and Computation,<br>
Volume 165, Number 2, 2005, pages 261-274.
</li>
<li>
Marco Caliari, Stefano de Marchi, Marco Vianello,<br>
Algorithm 886:
Padua2D: Lagrange Interpolation at Padua Points on Bivariate Domains,<br>
ACM Transactions on Mathematical Software,<br>
Volume 35, Number 3, October 2008, Article 21, 11 pages.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "padua.cpp">padua.cpp</a>, the source code.
</li>
<li>
<a href = "padua.hpp">padua.hpp</a>, the include file.
</li>
<li>
<a href = "padua.sh">padua.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "padua_prb.cpp">padua_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "padua_prb.sh">padua_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "padua_prb_output.txt">padua_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<p>
The program creates GNUPLOT command and data files, which can be
used to create a PNG image of the points.
<ul>
<li>
<a href = "padua_00_commands.txt">padua_00_commands.txt</a>,
the command file.
</li>
<li>
<a href = "padua_00_data.txt">padua_00_data.txt</a>,
the data file.
</li>
<li>
<a href = "padua_00.png">padua_00.png</a>,
the PNG image.
</li>
<li>
<a href = "padua_01_commands.txt">padua_01_commands.txt</a>,
the command file.
</li>
<li>
<a href = "padua_01_data.txt">padua_01_data.txt</a>,
the data file.
</li>
<li>
<a href = "padua_01.png">padua_01.png</a>,
the PNG image.
</li>
<li>
<a href = "padua_02_commands.txt">padua_02_commands.txt</a>,
the command file.
</li>
<li>
<a href = "padua_02_data.txt">padua_02_data.txt</a>,
the data file.
</li>
<li>
<a href = "padua_02.png">padua_02.png</a>,
the PNG image.
</li>
<li>
<a href = "padua_03_commands.txt">padua_03_commands.txt</a>,
the command file.
</li>
<li>
<a href = "padua_03_data.txt">padua_03_data.txt</a>,
the data file.
</li>
<li>
<a href = "padua_03.png">padua_03.png</a>,
the PNG image.
</li>
<li>
<a href = "padua_04_commands.txt">padua_04_commands.txt</a>,
the command file.
</li>
<li>
<a href = "padua_04_data.txt">padua_04_data.txt</a>,
the data file.
</li>
<li>
<a href = "padua_04.png">padua_04.png</a>,
the PNG image.
</li>
<li>
<a href = "padua_05_commands.txt">padua_05_commands.txt</a>,
the command file.
</li>
<li>
<a href = "padua_05_data.txt">padua_05_data.txt</a>,
the data file.
</li>
<li>
<a href = "padua_05.png">padua_05.png</a>,
the PNG image.
</li>
<li>
<a href = "padua_06_commands.txt">padua_06_commands.txt</a>,
the command file.
</li>
<li>
<a href = "padua_06_data.txt">padua_06_data.txt</a>,
the data file.
</li>
<li>
<a href = "padua_06.png">padua_06.png</a>,
the PNG image.
</li>
<li>
<a href = "padua_07_commands.txt">padua_07_commands.txt</a>,
the command file.
</li>
<li>
<a href = "padua_07_data.txt">padua_07_data.txt</a>,
the data file.
</li>
<li>
<a href = "padua_07.png">padua_07.png</a>,
the PNG image.
</li>
<li>
<a href = "padua_08_commands.txt">padua_08_commands.txt</a>,
the command file.
</li>
<li>
<a href = "padua_08_data.txt">padua_08_data.txt</a>,
the data file.
</li>
<li>
<a href = "padua_08.png">padua_08.png</a>,
the PNG image.
</li>
<li>
<a href = "padua_09_commands.txt">padua_09_commands.txt</a>,
the command file.
</li>
<li>
<a href = "padua_09_data.txt">padua_09_data.txt</a>,
the data file.
</li>
<li>
<a href = "padua_09.png">padua_09.png</a>,
the PNG image.
</li>
<li>
<a href = "padua_10_commands.txt">padua_10_commands.txt</a>,
the command file.
</li>
<li>
<a href = "padua_10_data.txt">padua_10_data.txt</a>,
the data file.
</li>
<li>
<a href = "padua_10.png">padua_10.png</a>,
the PNG image.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>FILENAME_INC</b> increments a partially numeric file name.
</li>
<li>
<b>PADUA_ORDER</b> returns the size of the Padua set of given level.
</li>
<li>
<b>PADUA_PLOT</b> plots the Padua points of given level.
</li>
<li>
<b>PADUA_POINTS</b> returns the Padua points of order N.
</li>
<li>
<b>PADUA_POINT_SET</b> sets the Padua points.
</li>
<li>
<b>PADUA_WEIGHT_SET</b> sets quadrature weights for the Padua points.
</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>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</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 30 April 2014.
</i>
<!-- John Burkardt -->
</body>
<!-- Initial HTML skeleton created by HTMLINDEX. -->
</html>