TOMS886
Interpolation over the Rectangle, Ellipse, or Triangle

TOMS886 is a FORTRAN77 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 original, true, correct version of ACM TOMS Algorithm 886 is available through ACM: http://www.acm.org/pubs/calgo or NETLIB: http://www.netlib.org/toms/index.html.

Licensing:

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

Languages:

TOMS886 is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

LAGRANGE_INTERP_2D, a FORTRAN77 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 FORTRAN77 library which evaluates a piecewise linear interpolant to data defined on a regular 2D grid.

PWL_INTERP_2D_SCATTERED, a FORTRAN77 library which evaluates a piecewise linear interpolant to data which is available at an irregularly arranged set of points.

RBF_INTERP_2D, a FORTRAN77 library which defines and evaluates radial basis function (RBF) interpolants to 2D data.

SHEPARD_INTERP_2D, a FORTRAN77 library which defines and evaluates Shepard interpolants to scattered 2D data, based on inverse distance weighting.

TEST_INTERP_2D, a FORTRAN77 library which defines test problems for interpolation of regular or scattered data z(x,y), depending on a 2D argument.

TOMS526, a FORTRAN77 library which interpolates scattered bivariate data. This is ACM TOMS algorithm 526, by Hiroshi Akima;

TOMS660, a FORTRAN77 library which takes scattered 2D data and produces an interpolating function F(X,Y). This is ACM TOMS algorithm 660, called qshep2d, by Robert Renka.

TOMS790, a FORTRAN77 library which computes an interpolating function to a set of scattered data in the plane, by Robert Renka; This library is commonly called cshep2d; this is ACM TOMS algorithm 790.

TOMS792, a FORTRAN77 library which tests functions that interpolate scattered data in the plane; by Robert Renka; this is ACM TOMS algorithm 792.

VANDERMONDE_INTERP_2D, a FORTRAN77 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,
   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.
3. Richard Franke,
   Scattered Data Interpolation: Tests of Some Methods,
   Mathematics of Computation,
   Volume 38, Number 157, January 1982, pages 181-200.

Source Code:

• toms886.f, the source code.
• toms886.sh, BASH commands to compile the source code.

Examples and Tests:

ELLIPSE applies the procedure to an ellipse.

• ellipse.f, a sample calling program.
• ellipse.sh, BASH commands to compile and run the sample program.
• ellipse_output.txt, the output file.

RECTANGLE applies the procedure to a rectangle.

• rectangle.f, a sample calling program.
• rectangle.sh, BASH commands to compile and run the sample program.
• rectangle_output.txt, the output file.

TRIANGLE applies the procedure to a triangle.

• triangle.f, a sample calling program.
• triangle.sh, BASH commands to compile and run the sample program.
• triangle_output.txt, the output file.

List of Routines:

• CHEB computes normalized Chebyshev polynomials.
• DGEMM computes C = alpha * A * B and related operations.
• FRANKE returns the value of the Franke function #1.
• PADUA2 computes the Padua interpolation coefficient matrix.
• PD2VAL evaluates the Padua2 interpolant.
• PDPTS returns the points and weights for Padua interpolation.
• R8_HUGE returns a "huge" R8.
• R8VEC_DOT_PRODUCT finds the dot product of a pair of R8VEC's.
• TIMESTAMP prints out the current YMDHMS date as a timestamp.

You can go up one level to the FORTRAN77 source codes.