SHEPARD_INTERP_2D
Shepard Interpolation of 2D Data

SHEPARD_INTERP_2D is a FORTRAN90 library which defines and evaluates Shepard interpolants to 2D data, based on inverse distance weighting.

SHEPARD_INTERP_2D needs the R8LIB library. The test also needs the TEST_INTERP_2D library.

Licensing:

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

Languages:

SHEPARD_INTERP_2D is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

LAGRANGE_INTERP_2D, a FORTRAN77 library which defines and evaluates the Lagrange polynomial p(x,y) which interpolates a set of data depending on a 2D argument that was evaluated on a product grid, so that p(x(i),y(j)) = z(i,j).

PADUA, a FORTRAN77 library which returns the points and weights for Padu sets, useful for interpolation in 2D. GNUPLOT is used to plot the points.

PWL_INTERP_2D, a FORTRAN77 library which evaluates a piecewise linear interpolant to data defined on a regular 2D grid.

R8LIB, a FORTRAN77 library which contains many utility routines using double precision real (R8) arithmetic.

RBF_INTERP_2D, a FORTRAN77 library which defines and evaluates radial basis function (RBF) interpolants to 2D data.

SHEPARD_INTERP_1D, a FORTRAN77 library which defines and evaluates Shepard interpolants to 1D data, based on inverse distance weighting.

SHEPARD_INTERP_ND, a FORTRAN77 library which defines and evaluates Shepard interpolants to multidimensional data, based on inverse distance weighting.

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

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.

VANDERMONDE_INTERP_2D, a FORTRAN77 library which finds a polynomial interpolant to data z(x,y) of a 2D argument by setting up and solving a linear system for the polynomial coefficients, involving the Vandermonde matrix.

Reference:

1. Richard Franke,
   Scattered Data Interpolation: Tests of Some Methods,
   Mathematics of Computation,
   Volume 38, Number 157, January 1982, pages 181-200.
2. Donald Shepard,
   A two-dimensional interpolation function for irregularly spaced data,
   ACM '68: Proceedings of the 1968 23rd ACM National Conference,
   ACM, pages 517-524, 1969.

Source Code:

• shepard_interp_2d.f, the source code.
• shepard_interp_2d.sh, BASH commands to compile the source code.

Examples and Tests:

• shepard_interp_2d_prb.f, a sample calling program.
• shepard_interp_2d_prb.sh, BASH commands to compile and run the sample program.
• shepard_interp_2d_prb_output.txt, the output file.

List of Routines:

• SHEPARD_INTERP_2D evaluates a 2D Shepard interpolant.

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