Scattered Data Fitting

The problem of approximating or interpolating scattered data values f_k at the points P_k=(x_k,y_k), k=1,..,N inequally distributed in the plane has been dealt with by many authors in the years.

Our contribution in this area were both in approximating than in interpolating; more precisely in the first case we proposed a polyalgorithm based on a Mean Weighted Method and on L-spline functions. In this latter case we used tensor product natural L-splines defining a grid domain containing the data and applying a least square fitting.

In the interpolating approach all the methods consists of three different steps: At the moment of our research in this topics all the known methods worked quite well on relatively smooth data sets, but they failed for rapidly varying data. In this case the reconstructed surface exhibited unwanted oscillations near step gradients. Our proposal, published as ACM Algorithm 677, resolved this problem giving to the user the means for controlling the behaviour of the interpolating surface.

fitting data example