BIVAR
Bivariate interpolation of scattered data

BIVAR is a FORTRAN90 library which interpolates scattered bivariate data, by Hiroshi Akima.

BIVAR 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.

BIVAR is a FORTRAN90 version of ACM TOMS Algorithm 526.

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

Licensing:

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

Related Data and Packages:

TOMS526, a FORTRAN90 library which is the original version of the algorithm implemented in BIVAR.

TOMS660, a FORTRAN90 library which takes scattered 2D data and produces an interpolating function F(X,Y), this is a FORTRAN90 version of 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 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:

The FORTRAN77 version of BIVAR is by Hiroshi Akima. The translation to FORTRAN90 was done by John Burkardt.

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:

• bivar.f90, the source code.

Examples and Tests:

• bivar_test.f90, a sample problem.
• bivar_test.txt, the output file.

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 FORTRAN90 source codes.