TOMS790
Bivariate Interpolation of Scattered Data

TOMS790 is a FORTRAN77 library which constructs an interpolant to scattered 2D data, by Robert Renka.

TOMS790 is similar to the algorithm employed in ACM TOMS algorithm 660, but achieves cubic precision (where the previous algorithm was only quadratic) and has C2 continuity.

TOMS790 is ACM TOMS Algorithm 790.

The original, true, correct version of this ACM TOMS algorithm is available in the TOMS subdirectory of the NETLIB web site.

Languages:

TOMS790 is available in a FORTRAN90 version.

Related Data and Programs:

RBF_INTERP, a FORTRAN90 library which defines and evaluates radial basis interpolants to multidimensional data.

TEST_INTERP_ND, a FORTRAN90 library which defines test problems for interpolation of data z(x), depending on an M-dimensional argument.

TOMS526, a FORTRAN90 library which interpolates scattered bivariate data, This is ACM TOMS algorithm 526, by Hiroshi Akima;

TOMS660, a FORTRAN90 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.

TOMS661, a FORTRAN90 library which takes scattered 3D data and produces an interpolating function F(X,Y,Z), this is ACM TOMS algorithm 661, called qshep3d, by Robert Renka.

TOMS792 a FORTRAN90 library which tests functions that interpolate scattered data in the plane; by Robert Renka; this is ACM TOMS algorithm 792.

TOMS886, a FORTRAN90 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.

Author:

Robert Renka

Reference:

1. Richard Franke,
   Scattered Data Interpolation: Tests of Some Methods,
   Mathematics of Computation,
   Volume 38, Number 157, January 1982, pages 181-200.
2. Robert Renka,
   Algorithm 790: CSHEP2D: Cubic Shepard Method for Bivariate Interpolation of Scattered Data,
   ACM Transactions on Mathematical Software,
   Volume 25, Number 1, March 1999, pages 70-73.

Source Code:

• toms790.f, the source code.

Examples and Tests:

TOMS790_TEST1 is a program which can be run interactively, and allows the user to specify the test data to be used, and other parameters.

• toms790_test1.f, a sample calling program.
• toms790_test1_input.txt, the input file.
• toms790_test1.txt, the output file.

TOMS790_TEST2 tests the package using data on a 20 by 20 uniform grid.

• toms790_test2.f, a sample calling program.
• toms790_test2.txt, the output file.

List of Routines:

• CSHEP2 defines a C2 function F(X,Y) interpolating scattered data.
• CS2VAL evaluates an interpolant defined by CSHEP2.
• CS2GRD returns the value and gradients of a function defined by CSHEP2.
• CS2HES returns value, gradients and Hessian of a function defined by CSHEP2.
• GETNP2 gets the closest unmarked node to a specified point.
• GIVENS constructs a Givens plane rotation.
• ROTATE applies a Givens rotation.
• SETUP2 sets a row of a regression matrix to fit a cubic function to data.
• STORE2 creates a closest-point data structure given points in the plane.
• TESTDT returns one of five sets of test nodes.
• TSTFN1 computes one of ten bivariate test functions.

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