TOMS660
Interpolation of Scattered Data in the Plane

TOMS660 is a FORTRAN90 library which interpolates scattered 2D data, also called "qshep2d", by Robert Renka.

TOMS660 takes a set of data values ZDAT(XDAT,YDAT), where the points (XDAT,YDAT) are "scattered" in the plane, and constructs an interpolating function Z(X,Y) which matches the given data, and extends smoothly through the plane.

TOMS660 is primarily a FORTRAN90 "translation" of a FORTRAN77 program which was written by Robert Renka and published in the ACM Transactions on Mathematical Software.

TOMS660 is ACM Transactions on Mathematical Software Algorithm number 660. The original text of any ACM TOMS algorithm is available through ACM: http://www.acm.org/pubs/calgo or NETLIB: http://www.netlib.org/toms/index.html

Languages:

TOMS660 is available in a FORTRAN90 version.

Related Data and Programs:

RBF_INTERP_ND, 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 a FORTRAN90 version of ACM TOMS algorithm 526, by Hiroshi Akima;

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

TOMS790, a FORTRAN90 library which computes an interpolating function to a set of scattered data in the plane;
this library is commonly called CSHEP2D;
by Robert Renka;
this is ACM TOMS algorithm 790.

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 660,
   QSHEP2D, Quadratic Shepard method for bivariate interpolation of scattered data,
   ACM Transactions on Mathematical Software,
   Volume 14, 1988, pages 149-150.

Source Code:

• toms660.f90, the source code.

Examples and Tests:

• toms660_prb.f90, a sample problem.
• toms660_prb_output.txt, the output file.

List of Routines:

• GETNP2 seeks the closest unmarked node to a point.
• GIVENS constructs a Givens plane rotation.
• QS2GRD evaluates the interpolant and its first spatial derivatives.
• QSHEP2 computes an interpolant to scattered data in the plane.
• QS2VAL evaluates the interpolant function at a point.
• ROTATE applies a Givens rotation.
• SETUP2 sets up a row of the least squares regression matrix.
• STORE2 creates a cell data structure for the scattered data.

You can go up one level to the FORTRAN90 source codes.