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).
PADUA,
a MATLAB library which
returns the points and weights for Padu sets, useful for interpolation
in 2D. MATLAB graphics are used to plot the points.
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.
TOMS886,
a MATLAB 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 a MATLAB version of ACM TOMS algorithm 886.
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:

Richard Franke,
Scattered Data Interpolation: Tests of Some Methods,
Mathematics of Computation,
Volume 38, Number 157, January 1982, pages 181200.

Donald Shepard,
A twodimensional interpolation function for irregularly spaced data,
ACM '68: Proceedings of the 1968 23rd ACM National Conference,
ACM, pages 517524, 1969.
Source Code:
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' )".
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.
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the MATLAB source codes.
Last modified on 04 August 2012.