An efficient scattered data approximation using multilevel B-splines based on quasi-interpolants

In this paper, we propose an efficient approximation algorithm using multilevel B-splines based on quasi-interpolants. Multilevel technique uses a coarse to fine hierarchy to generate a sequence of bicubic B-spline functions whose sum approaches the desired interpolation function. To compute a set of control points, quasi-interpolants gives a procedure for deriving local spline approximation methods where a B-spline coefficient only depends on data points taken from the neighborhood of the support corresponding the B-spline. Experimental results show that the smooth surface reconstruction with high accuracy can be obtained from a selected set of scattered or dense irregular samples.