TOMS886 Interpolation over the Rectangle, Ellipse, or Triangle

TOMS886, a MATLAB 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.

The text of many ACM TOMS algorithms is available online through ACM: http://calgo.acm.org/ or NETLIB: http://www.netlib.org/toms/index.html.

Languages:

TOMS886 is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

LAGRANGE_INTERP_2D, 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).

PWL_INTERP_2D, a MATLAB library which evaluates a piecewise linear interpolant to data defined on a regular 2D grid.

PWL_INTERP_2D_SCATTERED, a MATLAB library which evaluates a piecewise linear interpolant to data which is available at an irregularly arranged set of points.

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

SHEPARD_INTERP_2D, a MATLAB library which defines and evaluates Shepard interpolants to scattered 2D data, based on inverse distance weighting.

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

VANDERMONDE_INTERP_2D, 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.

Author:

Marco Caliari, Stefano de Marchi, Marco Vianello.

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,
ACM Transactions on Mathematical Software,
Volume 35, Number 3, October 2008, Article 21, 11 pages.
3. Richard Franke,
Scattered Data Interpolation: Tests of Some Methods,
Mathematics of Computation,
Volume 38, Number 157, January 1982, pages 181-200.

Source Code:

• cheb.m, computes normalized Chebyshev polynomials.
• dgemm.m, computes C = alpha * A * B and related operations.
• franke.m, returns the value of the Franke function #1.