shepard_interp_2d

shepard_interp_2d, a Python code which defines and evaluates Shepard interpolants to scattered 2D data, based on inverse distance weighting.

The test also needs the test_interp_2d() library.

Licensing:

The information on this web page is distributed under the MIT 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 and an Octave version and a Python version.

Related Data and Programs:

padua, a Python code which returns the points and weights for Padua sets, useful for interpolation in 2d.

pwl_interp_2d, a Python code which evaluates a piecewise linear interpolant to data defined on a regular 2d grid.

rbf_interp_2d, a Python code which defines and evaluates radial basis function (RBF) interpolants to 2d data.

shepard_interp_1d, a Python code which defines and evaluates Shepard interpolants to 1d data, based on inverse distance weighting.

test_interp_2d, a Python code which defines test problems for interpolation of data z(x,y)), depending on a 2d 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_2d.py, the source code.
• shepard_interp_2d.sh, runs all the tests;
• shepard_interp_2d.txt, the output file.

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.