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In this paper we propose a new efficient interpolation tool, extremelysuitable for large scattered data sets. The partition of unity method is usedand performed by blending Radial Basis Functions (RBFs) as local approximantsand using locally supported weight functions. In particular we present a newspace-partitioning data structure based on a partition of the underlyinggeneric domain in blocks. This approach allows us to examine only a reducednumber of blocks in the search process of the nearest neighbour points, leadingto an optimized searching routine. Complexity analysis and numericalexperiments in two- and three-dimensional interpolation support our findings.Some applications to geometric modelling are also considered. Moreover, theassociated software package written in \textsc{Matlab} is here discussed andmade available to the scientific community.

Efficient computation of partition of unity interpolants through a block-based searching technique