Partition of unity interpolation on multivariate convex domains

In this paper, we present an algorithm for multivariate interpolation of scattered data sets lying in convex domains . To organize the points in a multidimensional space, we build a kd-tree space-partitioning data structure, which is used to efficiently apply a partition of unity interpolant. This global scheme is combined with local radial basis function (RBF) approximants and compactly supported weight functions. A detailed description of the algorithm for convex domains and a complexity analysis of the computational procedures are also considered. Several numerical experiments show the performances of the interpolation algorithm on various sets of Halton data. Finally, an application to topographical data contained in a pentagonal domain is presented.