Interpolation of Scattered Data in 3D

TOMS661 is a FORTRAN90 library which interpolates scattered 3D data, also known as "qshep3d", by Robert Renka.

TOMS661 takes a set of data values WDAT(XDAT,YDAT,ZDAT), where the points (XDAT,YDAT,ZDAT) are "scattered" in 3D, and constructs an interpolating function W(X,Y,Z) which matches the given data and extends smoothly through 3D space.

TOMS661 is primarily a FORTRAN90 "translation" of a FORTRAN77 program which was written by Robert Renka and published in the ACM Transactions on Mathematical Software.

TOMS661 is ACM Transactions on Mathematical Software Algorithm number 661. The original text of any ACM TOMS algorithm is available through ACM: or NETLIB:


TOMS661 is available in a FORTRAN77 version and 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;

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.

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.


Robert Renka


  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 661: QSHEP3D, Quadratic Shepard method for trivariate interpolation of scattered data,
    ACM Transactions on Mathematical Software,
    Volume 14, 1988, pages 151-152.

Source Code:

Examples and Tests:

List of Routines:

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

Last revised on 21 February 2006.