SHEPARD_INTERP_2D
Shepard Interpolation of 2D Data

SHEPARD_INTERP_2D is a MATLAB 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 MATLAB 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).

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

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

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

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

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

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

VANDERMONDE_INTERP_2D, a MATLAB 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.m, evaluates a Shepard interpolant to 2D data.

Examples and Tests:

Running these tests requires access to the test_interp_2d library. Should that library be available in a directory at the same level, this can be accomplished with the command "addpath ( '../test_interp_2d' )".

• shepard_interp_2d_test.m, calls all the tests;
• shepard_interp_2d_test_output.txt, the output file.
• shepard_interp_2d_test01.m, tests a particular set of data and a particular value of the exponent.

The code generates some plots of the data and approximants.

• p01_data.png, the data for problem p01 with a linear interpolant.
• p01_power1.png, the Shepard interpolant for problem p01 with P = 1.0.
• p01_power2.png, the Shepard interpolant for problem p01 with P = 2.0.
• p01_power4.png, the Shepard interpolant for problem p01 with P = 4.0.
• p01_power8.png, the Shepard interpolant for problem p01 with P = 8.0.
• p02_data.png, the data for problem p02 with a linear interpolant.
• p02_power1.png, the Shepard interpolant for problem p02 with P = 1.0.
• p02_power2.png, the Shepard interpolant for problem p02 with P = 2.0.
• p02_power4.png, the Shepard interpolant for problem p02 with P = 4.0.
• p02_power8.png, the Shepard interpolant for problem p02 with P = 8.0.
• p03_data.png, the data for problem p03 with a linear interpolant.
• p03_power1.png, the Shepard interpolant for problem p03 with P = 1.0.
• p03_power2.png, the Shepard interpolant for problem p03 with P = 2.0.
• p03_power4.png, the Shepard interpolant for problem p03 with P = 4.0.
• p03_power8.png, the Shepard interpolant for problem p03 with P = 8.0.
• p04_data.png, the data for problem p04 with a linear interpolant.
• p04_power1.png, the Shepard interpolant for problem p04 with P = 1.0.
• p04_power2.png, the Shepard interpolant for problem p04 with P = 2.0.
• p04_power4.png, the Shepard interpolant for problem p04 with P = 4.0.
• p04_power8.png, the Shepard interpolant for problem p04 with P = 8.0.
• p05_data.png, the data for problem p05 with a linear interpolant.
• p05_power1.png, the Shepard interpolant for problem p05 with P = 1.0.
• p05_power2.png, the Shepard interpolant for problem p05 with P = 2.0.
• p05_power4.png, the Shepard interpolant for problem p05 with P = 4.0.
• p05_power8.png, the Shepard interpolant for problem p05 with P = 8.0.
• p06_data.png, the data for problem p06 with a linear interpolant.
• p06_power1.png, the Shepard interpolant for problem p06 with P = 1.0.
• p06_power2.png, the Shepard interpolant for problem p06 with P = 2.0.
• p06_power4.png, the Shepard interpolant for problem p06 with P = 4.0.
• p06_power8.png, the Shepard interpolant for problem p06 with P = 8.0.
• p07_data.png, the data for problem p07 with a linear interpolant.
• p07_power1.png, the Shepard interpolant for problem p07 with P = 1.0.
• p07_power2.png, the Shepard interpolant for problem p07 with P = 2.0.
• p07_power4.png, the Shepard interpolant for problem p07 with P = 4.0.
• p07_power8.png, the Shepard interpolant for problem p07 with P = 8.0.
• p08_data.png, the data for problem p08 with a linear interpolant.
• p08_power1.png, the Shepard interpolant for problem p08 with P = 1.0.
• p08_power2.png, the Shepard interpolant for problem p08 with P = 2.0.
• p08_power4.png, the Shepard interpolant for problem p08 with P = 4.0.
• p08_power8.png, the Shepard interpolant for problem p08 with P = 8.0.
• p09_data.png, the data for problem p09 with a linear interpolant.
• p09_power1.png, the Shepard interpolant for problem p09 with P = 1.0.
• p09_power2.png, the Shepard interpolant for problem p09 with P = 2.0.
• p09_power4.png, the Shepard interpolant for problem p09 with P = 4.0.
• p09_power8.png, the Shepard interpolant for problem p09 with P = 8.0.
• p10_data.png, the data for problem p10 with a linear interpolant.
• p10_power1.png, the Shepard interpolant for problem p10 with P = 1.0.
• p10_power2.png, the Shepard interpolant for problem p10 with P = 2.0.
• p10_power4.png, the Shepard interpolant for problem p10 with P = 4.0.
• p10_power8.png, the Shepard interpolant for problem p10 with P = 8.0.
• p11_data.png, the data for problem p11 with a linear interpolant.
• p11_power1.png, the Shepard interpolant for problem p11 with P = 1.0.
• p11_power2.png, the Shepard interpolant for problem p11 with P = 2.0.
• p11_power4.png, the Shepard interpolant for problem p11 with P = 4.0.
• p11_power8.png, the Shepard interpolant for problem p11 with P = 8.0.
• p12_data.png, the data for problem p12 with a linear interpolant.
• p12_power1.png, the Shepard interpolant for problem p12 with P = 1.0.
• p12_power2.png, the Shepard interpolant for problem p12 with P = 2.0.
• p12_power4.png, the Shepard interpolant for problem p12 with P = 4.0.
• p12_power8.png, the Shepard interpolant for problem p12 with P = 8.0.
• p13_data.png, the data for problem p13 with a linear interpolant.
• p13_power1.png, the Shepard interpolant for problem p13 with P = 1.0.
• p13_power2.png, the Shepard interpolant for problem p13 with P = 2.0.
• p13_power4.png, the Shepard interpolant for problem p13 with P = 4.0.
• p13_power8.png, the Shepard interpolant for problem p13 with P = 8.0.

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