Fast and accurate interpolation of large scattered data sets on the sphere

Authors:
Roberto Cavoretto;Alessandra De Rossi
Affiliations:
Department of Mathematics, University of Turin, via Carlo Alberto 10, I-10123 Turin, Italy;Department of Mathematics, University of Turin, via Carlo Alberto 10, I-10123 Turin, Italy
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

Citing 14
Cited 1

Multivariate interpolation of large sets of scattered data

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Modified multiquadric methods for scattered data interpolation over a sphere

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Fitting scattered data on sphere-like surfaces using spherical splines

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Strictly positive definite functions on spheres in Euclidean spaces

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Algorithm 773: SSRFPACK: interpolation of scattered data on the surface of a sphere with a surface under tension

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Scattered data fitting on the sphere

Proceedings of the international conference on Mathematical methods for curves and surfaces II Lillehammer, 1997
Error estimates for scattered data interpolation on spheres

Mathematics of Computation
Data Structures for Range Searching

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Radial basis functions for the multivariate interpolation of large scattered data sets

Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
Lp-error estimates for radial basis function interpolation on the sphere

Journal of Approximation Theory
Meshfree Approximation Methods with MATLAB

Meshfree Approximation Methods with MATLAB

A meshless interpolation algorithm using a cell-based searching procedure

Computers & Mathematics with Applications

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Abstract

In this paper a new efficient algorithm for spherical interpolation of large scattered data sets is presented. The solution method is local and involves a modified spherical Shepard's interpolant, which uses zonal basis functions as local approximants. The associated algorithm is implemented and optimized by applying a nearest neighbour searching procedure on the sphere. Specifically, this technique is mainly based on the partition of the sphere in a suitable number of spherical zones, the construction of spherical caps as local neighbourhoods for each node, and finally the employment of a spherical zone searching procedure. Computational cost and storage requirements of the spherical algorithm are analyzed. Moreover, several numerical results show the good accuracy of the method and the high efficiency of the proposed algorithm.