TOMS526
Bivariate interpolation of scattered data

TOMS526 is a FORTRAN77 library which interpolates scattered bivariate data, by Hiroshi Akima.

TOMS526 accepts a set of (X,Y) data points scattered in 2D, with associated Z data values, and is able to construct a smooth interpolation function Z(X,Y), which agrees with the given data, and can be evaluated at other points in the plane.

TOMS526 is ACM TOMS Algorithm 526.

The original, true, correct version of ACM TOMS 526 is available in the TOMS subdirectory of the NETLIB web site.

Languages:

TOMS526 is available in a FORTRAN77 version and a FORTRAN90 version.

Related Data and Packages:

RBF_INTERP, a FORTRAN77 library which defines and evaluates radial basis interpolants to multidimensional data.

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

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.

TOMS661, a FORTRAN77 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.

TOMS790 a FORTRAN77 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 FORTRAN77 library which tests functions that interpolate scattered data in the plane; by Robert Renka; this is ACM TOMS algorithm 792.

TOMS886, a FORTRAN77 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:

Hiroshi Akima

Reference:

1. Hiroshi Akima,
   Algorithm 526: A Method of Bivariate Interpolation and Smooth Surface Fitting for Values Given at Irregularly Distributed Points,
   ACM Transactions on Mathematical Software,
   Volume 4, Number 2, June 1978, pages 160-164.
2. Hiroshi Akima,
   On Estimating Partial Derivatives for Bivariate Interpolation of Scattered Data,
   Rocky Mountain Journal of Mathematics,
   Volume 14, Number 1, Winter 1984, pages 41-51.

Source Code:

• toms526.f, the source code.
• toms526.sh, commands to compile the source code.

Examples and Tests:

• toms526_prb.f, a sample problem.
• toms526_prb.sh, commands to compile, link and run the sample problem.
• toms526_prb_output.txt, sample problem output.

List of Routines:

• IDBVIP performs bivariate interpolation of irregular X, Y data.
• IDGRID organizes grid points for surface fitting.
• IDLCTN finds the triangle that contains a point.
• IDPDRV estimates first and second partial derivatives at data points.
• IDPTIP performs interpolation, determining a value of Z given X and Y.
• IDSFFT performs smooth surface fitting when the projections of the
• IDTANG performs triangulation.
• IDXCHG determines whether two triangles should be exchanged.

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