A 3D Efficient Procedure for Shepard Interpolants on Tetrahedra
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The need of scattered data interpolation methods in the multivariate framework and, in particular, in the trivariate case, motivates the generalization of the fast algorithm for triangular Shepard method. A block-based partitioning structure procedure was already applied to make the method very fast in the bivariate setting. Here the searching algorithm is extended, it allows to partition the domain and nodes in cubic blocks and to find the nearest neighbor points that need to be used in the tetrahedral Shepard interpolation.
KeywordsScattered data interpolation Tetrahedral Shepard operator Fast algorithms Approximation algorithms
The authors acknowledge support from the Department of Mathematics “Giuseppe Peano” of the University of Torino via Project 2019 “Mathematics for applications”. Moreover, this work was partially supported by INdAM – GNCS Project 2019 “Kernel-based approximation, multiresolution and subdivision methods and related applications”. This research has been accomplished within RITA (Research ITalian network on Approximation).
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