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In this paper we propose a fast algorithm for trivariate interpolation, whichis based on the partition of unity method for constructing a global interpolantby blending local radial basis function interpolants and using locallysupported weight functions. The partition of unity algorithm is efficientlyimplemented and optimized by connecting the method with an effectivecube-partition searching procedure. More precisely, we construct a cubestructure, which partitions the domain and strictly depends on the size of itssubdomains, so that the new searching procedure and, accordingly, the resultingalgorithm enable us to efficiently deal with a large number of nodes.Complexity analysis and numerical experiments show high efficiency and accuracyof the proposed interpolation algorithm.

A trivariate interpolation algorithm using a cube-partition searching procedure