Two-dimensional interpolation using a cell-based searching procedure

In this paper we present an efficient algorithm for bivariate interpolation, which is based on the use of the partition of unity method for constructing a global interpolant. It is obtained by combining local radial basis function interpolants with locally supported weight functions. In particular, this interpolation scheme is characterized by the construction of a suitable partition of the domain in cells so that the cell structure strictly depends on the dimension of its subdomains. This fact allows us to construct an efficient cell-based searching procedure, which provides a significant reduction of CPU times. Complexity analysis and numerical results show such improvements on the algorithm performances.