rbf_interp_2d, a FORTRAN90 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.
The code needs access to the R8LIB library. The test code 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 MIT 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.
LAGRANGE_INTERP_2D, a FORTRAN90 code 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 FORTRAN90 code which evaluates a piecewise linear interpolant to data defined on a regular 2D grid.
R8LIB, a FORTRAN90 code which contains many utility routines, using double precision real (R8) arithmetic.
RBF_INTERP_1D, a FORTRAN90 code which defines and evaluates radial basis function (RBF) interpolants to 1D data.
RBF_INTERP_ND, a FORTRAN90 code which defines and evaluates radial basis function (RBF) interpolants to multidimensional data.
SHEPARD_INTERP_2D, a FORTRAN90 code which defines and evaluates Shepard interpolants to 2D data, based on inverse distance weighting.
TEST_INTERP_2D, a FORTRAN90 code which defines test problems for interpolation of data z(x,y) of a 2D argument.
TOMS886, a FORTRAN90 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 ACM TOMS algorithm 886.
VANDERMONDE_INTERP_2D, a FORTRAN90 code 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.