A 3D Efficient Procedure for Shepard Interpolants on Tetrahedra

  • Roberto Cavoretto
  • Alessandra De RossiEmail author
  • Francesco Dell’Accio
  • Filomena Di Tommaso
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11973)


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.


Scattered 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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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Mathematics “Giuseppe Peano”University of TurinTurinItaly
  2. 2.Department of Mathematics and Computer ScienceUniversity of CalabriaRende (CS)Italy

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