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<html>
<head>
<title>
TOMS886 - Interpolation over the Rectangle, Ellipse, or Triangle
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TOMS886 <br> Interpolation over the Rectangle, Ellipse, or Triangle
</h1>
<hr>
<p>
<b>TOMS886</b>
is a C++ library which
implements an interpolation procedure based on "Padua points",
defined in the square [-1,+1]^2, whose interpolating power
is especially good. It is possible to map these points to the
general rectangle, ellipse or triangle to do interpolation on these
regions as well.
</p>
<p>
The original, true, correct version of ACM TOMS Algorithm 886
is available through ACM:
<a href = "http://www.acm.org/pubs/calgo/">
http://www.acm.org/pubs/calgo</a>
or NETLIB:
<a href = "http://www.netlib.org/toms/index.html">
http://www.netlib.org/toms/index.html</a>.
</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>TOMS886</b> is available in
<a href = "../../c_src/toms886/toms886.html">a C version</a> and
<a href = "../../cpp_src/toms886/toms886.html">a C++ version</a> and
<a href = "../../f77_src/toms886/toms886.html">a FORTRAN77 version</a> and
<a href = "../../f_src/toms886/toms886.html">a FORTRAN90 version</a> and
<a href = "../../m_src/toms886/toms886.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<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/pwl_interp_2d_scattered/pwl_interp_2d_scattered.html">
PWL_INTERP_2D_SCATTERED</a>,
a C++ library which
evaluates a piecewise linear interpolant to data which is available
at an irregularly arranged set of points.
</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 scattered 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 regular
or scattered data z(x,y), depending on a 2D argument.
</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">
Author:
</h3>
<p>
Marco Caliari, Stefano de Marchi, Marco Vianello.
</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>
<li>
Richard Franke,<br>
Scattered Data Interpolation: Tests of Some Methods,<br>
Mathematics of Computation,<br>
Volume 38, Number 157, January 1982, pages 181-200.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "toms886.cpp">toms886.cpp</a>, the source code.
</li>
<li>
<a href = "toms886.hpp">toms886.hpp</a>, the include file.
</li>
<li>
<a href = "toms886.sh">toms886.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
ELLIPSE applies the procedure to an ellipse.
<ul>
<li>
<a href = "ellipse.cpp">ellipse.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "ellipse.sh">ellipse.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "ellipse_output.txt">ellipse_output.txt</a>,
the output file.
</li>
</ul>
</p>
<p>
RECTANGLE applies the procedure to a rectangle.
<ul>
<li>
<a href = "rectangle.cpp">rectangle.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "rectangle.sh">rectangle.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "rectangle_output.txt">rectangle_output.txt</a>,
the output file.
</li>
</ul>
</p>
<p>
TRIANGLE applies the procedure to a triangle.
<ul>
<li>
<a href = "triangle.cpp">triangle.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "triangle.sh">triangle.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "triangle_output.txt">triangle_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>CHEB</b> computes normalized Chebyshev polynomials.
</li>
<li>
<b>DGEMM</b> computes C = alpha * A * B and related operations.
</li>
<li>
<b>FRANKE</b> returns the value of the Franke function #1.
</li>
<li>
<b>PADUA2</b> computes the Padua interpolation coefficient matrix.
</li>
<li>
<b>PD2VAL</b> evaluates the Padua2 interpolant.
</li>
<li>
<b>PDPTS</b> returns the points and weights for Padua interpolation.
</li>
<li>
<b>R8_HUGE</b> returns a "huge" R8.
</li>
<li>
<b>R8VEC_DOT_PRODUCT</b> finds the dot product of a pair of R8VEC's.
</li>
<li>
<b>TIMESTAMP</b> prints out the current YMDHMS date as a timestamp.
</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 16 February 2014.
</i>
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