rbf_interp_2d, a MATLAB code which defines and evaluates radial basis function (RBF) interpolants to 2D data.
A radial basis interpolant is a useful, but expensive, technique for definining a smooth function which interpolates a set of function values specified at an arbitrary set of data points.
Given nd multidimensional points xd with function values fd, and a basis function phi(r), the form of the interpolant is
f(x) = sum ( 1 <= i <= nd ) w(i) * phi(||x-xd(i)||)where the weights w have been precomputed by solving
sum ( 1 <= i <= nd ) w(i) * phi(||xd(j)-xd(i)||) = fd(j)
Although the technique is generally applied in a multidimensional setting, in this directory we look specifically at the case involving 2D data. This allows us to easily plot and compare the various results.
Four families of radial basis functions are provided.
RBF_INTERP_2D needs access to the R8LIB library. The test program also needs access to the TEST_INTERP_2D library.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
rbf_interp_2d is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.
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padua, a MATLAB code 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 code which evaluates a piecewise linear interpolant to data defined on a regular 2d grid.
r8lib, a MATLAB code which contains many utility routines, using double precision real (r8) arithmetic.
rbf_interp_1d, a MATLAB code which defines and evaluates radial basis function (rbf) interpolants to 1d data.
rbf_interp_nd, a MATLAB code which defines and evaluates radial basis function (rbf) interpolants to multidimensional data.
shepard_interp_2d, a MATLAB code which defines and evaluates shepard interpolants to 2d data, which are based on inverse distance weighting.
test_interp_2d, a MATLAB code which defines test problems for interpolation of data z(x,y) of a 2d argument.
toms886, a MATLAB code 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.
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