Partition of Unity Interpolation on Multivariate Convex Domains

2014/09/19 by Roberto Cavoretto, Cavoretto, Roberto, Alessandra De Rossi +2
Computer Science · #Computational Geometry and Mesh Generation #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1409.5576

openalex publication_date 2014/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we present a new algorithm for multivariate interpolation of scattered data sets lying in convex domains Ω⊆ \RR^N, for any N ≥ 2. 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 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 points contained in Ω, where Ω can be any convex domain like a 2D polygon or a 3D polyhedron.

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