SHEPARD_INTERP_ND
Shepard Interpolation of Multidimensional Data

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

SHEPARD_INTERP_ND needs the R8LIB library. The test needs the TEST_INTERP_ND 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_ND 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_ND, a MATLAB library which defines and evaluates the Lagrange polynomial p(x) which interpolates a set of data depending on a multidimensional argument x that was evaluated on a product grid, so that p(x(i)) = z(i).

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

RBF_INTERP_ND, a MATLAB library which defines and evaluates radial basis function (RBF) interpolants to multidimensional data.

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

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

SPARSE_INTERP_ND a MATLAB library which can be used to define a sparse interpolant to a function f(x) of a multidimensional argument.

TEST_INTERP_ND, a MATLAB library which defines test problems for interpolation of data z(x), depending on an M-dimensional argument.

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_nd.m, evaluates a Shepard interpolant to multidimensional data.

Examples and Tests:

Running these tests requires access to the test_interp_nd library. Should that library be available in a directory at the same level, this can be accomplished with the command "addpath ( '../test_interp_nd' )".

• shepard_interp_nd_test.m, calls all the tests;
• shepard_interp_nd_test_output.txt, the output file.
• shepard_interp_nd_test01.m, tests a particular set of data and a particular value of the exponent using an irregular grid.
• shepard_interp_nd_test02.m, tests a particular set of data and a particular value of the exponent using a regular product grid.

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