A new algorithm for bivariate interpolation of large sets of scattered and track data is presented. Then, the extension to the sphere is analyzed. The method, whose different versions depend partially on the kind of data, is based on the partition of the interpolation domain in a suitable number of parallel strips, and, starting from these, on the construction for any data point of a local neighbourhood containing a convenient number of data points. Then, the well-known modified Shepard’s formula for surface interpolation is applied with some effective improvements. The method is extended to the sphere using a modified spherical Shepard’s interpolant with the employment of zonal basis functions as local approximants. The proposed algorithms are very fast, owing to the optimal nearest neighbour searching, and achieve a good accuracy. The efficiency and reliability of the algorithms are shown by several numerical tests, performed also by Renka’s algorithms for a comparison

Efficient approximation algorithms. Part II: Scattered data interpolation based on strip searching procedures

ALLASIA, Giampietro;BESENGHI, Renata;CAVORETTO, Roberto;DE ROSSI, Alessandra
2010

Abstract

A new algorithm for bivariate interpolation of large sets of scattered and track data is presented. Then, the extension to the sphere is analyzed. The method, whose different versions depend partially on the kind of data, is based on the partition of the interpolation domain in a suitable number of parallel strips, and, starting from these, on the construction for any data point of a local neighbourhood containing a convenient number of data points. Then, the well-known modified Shepard’s formula for surface interpolation is applied with some effective improvements. The method is extended to the sphere using a modified spherical Shepard’s interpolant with the employment of zonal basis functions as local approximants. The proposed algorithms are very fast, owing to the optimal nearest neighbour searching, and achieve a good accuracy. The efficiency and reliability of the algorithms are shown by several numerical tests, performed also by Renka’s algorithms for a comparison
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http://drna.di.univr.it/
surface modelling; Shepard’s type formulas; local methods; scattered and track data interpolation; radial basis functions; zonal basis functions; interpolation algorithms
G. Allasia; R. Besenghi; R. Cavoretto; A. De Rossi
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/103411
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