In this paper,we present an algorithm for multivariate interpolation of scattered data sets lying in convex domainsΩ⊆R^(N),for any N≥2.To organize the points in a multidimensional space,we build a kd-tree space-parti...In this paper,we present an algorithm for multivariate interpolation of scattered data sets lying in convex domainsΩ⊆R^(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(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 points contained inΩ,whereΩcan be any convex domain,like a 2D polygon or a 3D polyhedron.Finally,an application to topographical data contained in a pentagonal domain is presented.展开更多
文摘In this paper,we present an algorithm for multivariate interpolation of scattered data sets lying in convex domainsΩ⊆R^(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(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 points contained inΩ,whereΩcan be any convex domain,like a 2D polygon or a 3D polyhedron.Finally,an application to topographical data contained in a pentagonal domain is presented.
