PADUA
2D Points for Interpolation or Integration

PADUA is a Python library which returns the coordinates of the 2D Padua points, as well as interpolation weights or quadrature weights, and images of the points in graphics files created by matplotlib.

Licensing:

The computer code and data files made available on this web page are distributed under the GNU LGPL license.

Languages:

PADUA is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

RBF_INTERP_2D, a Python library which defines and evaluates radial basis function (RBF) interpolants to 2D data.

TEST_INTERP_2D, a Python library which defines test problems for interpolation of data z(x,y), depending on a 2D argument.

Reference:

1. Marco Caliari, Stefano de Marchi, Marco Vianello,
   Bivariate interpolation on the square at new nodal sets,
   Applied Mathematics and Computation,
   Volume 165, Number 2, 2005, pages 261-274.
2. Marco Caliari, Stefano de Marchi, Marco Vianello,
   Algorithm 886: Padua2D: Lagrange Interpolation at Padua Points on Bivariate Domains,
   ACM Transactions on Mathematical Software,
   Volume 35, Number 3, October 2008, Article 21, 11 pages.

Source Code:

• padua.py, the source code.
• padua.sh, runs all the tests.
• padua.txt, the output file.

The program creates PNG images of the points.

• padua_0.png, the PNG image.
• padua_1.png, the PNG image.
• padua_2.png, the PNG image.
• padua_3.png, the PNG image.
• padua_4.png, the PNG image.
• padua_5.png, the PNG image.
• padua_6.png, the PNG image.
• padua_7.png, the PNG image.
• padua_8.png, the PNG image.
• padua_9.png, the PNG image.
• padua_10.png, the PNG image.

You can go up one level to the Python source codes.