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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 MATLAB library which
returns the coordinates of the 2D Padua points,
as well as interpolation weights or quadrature weights,
and images of the points in MATLAB 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 = "../../m_src/exactness_2d/exactness_2d.html">
EXACTNESS_2D</a>,
a MATLAB 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 = "../../m_src/lagrange_interp_2d/lagrange_interp_2d.html">
LAGRANGE_INTERP_2D</a>,
a MATLAB 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 = "../../m_src/pwl_interp_2d/pwl_interp_2d.html">
PWL_INTERP_2D</a>,
a MATLAB library which
evaluates a piecewise linear interpolant to data defined on
a regular 2D grid.
</p>
<p>
<a href = "../../m_src/quadrature_weights_vandermonde_2d/quadrature_weights_vandermonde_2d.html">
QUADRATURE_WEIGHTS_VANDERMONDE_2D</a>,
a MATLAB 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 = "../../m_src/rbf_interp_2d/rbf_interp_2d.html">
RBF_INTERP_2D</a>,
a MATLAB library which
defines and evaluates radial basis function (RBF) interpolants to 2D data.
</p>
<p>
<a href = "../../m_src/shepard_interp_2d/shepard_interp_2d.html">
SHEPARD_INTERP_2D</a>,
a MATLAB library which
defines and evaluates Shepard interpolants to 2D data,
based on inverse distance weighting.
</p>
<p>
<a href = "../../m_src/test_interp_2d/test_interp_2d.html">
TEST_INTERP_2D</a>,
a MATLAB library which
defines test problems for interpolation of data z(x,y),
depending on a 2D argument.
</p>
<p>
<a href = "../../m_src/toms886/toms886.html">
TOMS886</a>,
a MATLAB 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 = "../../m_src/vandermonde_interp_2d/vandermonde_interp_2d.html">
VANDERMONDE_INTERP_2D</a>,
a MATLAB 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 = "filename_inc.m">filename_inc.m</a>,
increments a partially numeric filename.
</li>
<li>
<a href = "padua_order.m">padua_order.m</a>,
returns the size of the Padua set of given level.
</li>
<li>
<a href = "padua_plot.m">padua_plot.m</a>,
plots the Padua points of given level.
</li>
<li>
<a href = "padua_points_set.m">padua_points_set.m</a>,
looks up the Padua points, for levels 0 through 10.
</li>
<li>
<a href = "padua_points.m">padua_points.m</a>,
computes the Padua points, for any level.
</li>
<li>
<a href = "padua_weights_set.m">padua_weights_set.m</a>,
looks up quadrature weights for Padua points, for levels 0 through 10.
</li>
<li>
<a href = "padua_weights.m">padua_weights.m</a>,
computes the quadrature weights for Padua points, for any level.
</li>
<li>
<a href = "r8mat_transpose_print.m">r8mat_transpose_print.m</a>,
prints an R8MAT, transposed.
</li>
<li>
<a href = "r8mat_transpose_print_some.m">
r8mat_transpose_print_some.m</a>,
prints some of an R8MAT, transposed.
</li>
<li>
<a href = "r8vec_reverse.m">r8vec_reverse.m</a>,
reverses the order of entries in an R8VEC.
</li>
<li>
<a href = "timestamp.m">timestamp.m</a>,
prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "padua_test.m">padua_test.m</a>,
a sample calling program.
</li>
<li>
<a href = "padua_test_output.txt">padua_test_output.txt</a>,
the output file.
</li>
<li>
<a href = "padua_test01.m">padua_test01.m</a>,
tests padua_order().
</li>
<li>
<a href = "padua_test02.m">padua_test02.m</a>,
tests padua_points().
</li>
<li>
<a href = "padua_test03.m">padua_test03.m</a>,
tests padua_plot();
</li>
<li>
<a href = "padua_test04.m">padua_test04.m</a>,
compares padua_points() and padua_points_set().
</li>
<li>
<a href = "padua_test05.m">padua_test05.m</a>,
compares padua_weights() and padua_weights_set().
</li>
</ul>
</p>
<p>
The program creates PNG images of the points.
<ul>
<li>
<a href = "padua_00.png">padua_00.png</a>,
the PNG image.
</li>
<li>
<a href = "padua_01.png">padua_01.png</a>,
the PNG image.
</li>
<li>
<a href = "padua_02.png">padua_02.png</a>,
the PNG image.
</li>
<li>
<a href = "padua_03.png">padua_03.png</a>,
the PNG image.
</li>
<li>
<a href = "padua_04.png">padua_04.png</a>,
the PNG image.
</li>
<li>
<a href = "padua_05.png">padua_05.png</a>,
the PNG image.
</li>
<li>
<a href = "padua_06.png">padua_06.png</a>,
the PNG image.
</li>
<li>
<a href = "padua_07.png">padua_07.png</a>,
the PNG image.
</li>
<li>
<a href = "padua_08.png">padua_08.png</a>,
the PNG image.
</li>
<li>
<a href = "padua_09.png">padua_09.png</a>,
the PNG image.
</li>
<li>
<a href = "padua_10.png">padua_10.png</a>,
the PNG image.
</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 10 June 2014.
</i>
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