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Scattered Data Interpolation with Multilevel Splines
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
, 1997
"... This paper describes a fast algorithm for scattered data interpolation and approximation. Multilevel Bsplines are introduced to compute a C²continuous surface through a set of irregularly spaced points. The algorithm makes use of a coarsetofine hierarchy of control lattices to generate a sequen ..."
Abstract

Cited by 106 (9 self)
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This paper describes a fast algorithm for scattered data interpolation and approximation. Multilevel Bsplines are introduced to compute a C²continuous surface through a set of irregularly spaced points. The algorithm makes use of a coarsetofine hierarchy of control lattices to generate a sequence of bicubic Bspline functions whose sum approaches the desired interpolation function. Large performance gains are realized by using Bspline refinement to reduce the sum of these functions into one equivalent Bspline function. Experimental results demonstrate that highfidelity reconstruction is possible from a selected set of sparse and irregular samples.
Efficient approximation algorithms. Part II: Scattered data interpolation based on strip searching procedures
"... 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 ..."
Abstract
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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 wellknown 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. Keywords: surface modelling, Shepard’s type formulas, local methods, scattered and track data interpolation, radial basis functions, zonal basis functions, interpolation algorithms. AMS Subject classification[2010]: 65D05, 65D15, 65D17. 1