Basis functions for scattered data quasi-interpolation

Nira Gruberger*, David Levin

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Given scattered data of a smooth function in IRd, we consider quasi-interpolation operators for approximating the function. In order to use these operators for the derivation of useful schemes for PDE solvers, we would like the quasi-interpolation operators to be of compact support and of high approximation power. The quasi-interpolation operators are generated through known quasi-interpolation operators on uniform grids, and the resulting basis functions are represented by finite combinations of box-splines. A special attention is given to point-sets of varying density. We construct basis functions with support sizes and approximation power related to the local density of the data points. These basis functions can be used in Finite Elements and in Isogeometric Analysis in cases where a non-uniform mesh is required, the same as T-splines are being used as basis functions for introducing local refinements in flow problems.

Original languageEnglish
Title of host publicationCurves and Surfaces - 8th International Conference, Revised Selected Papers
EditorsAlbert Cohen, Olivier Gibaru, Jean-Daniel Boissonnat, Marie-Laurence Mazure, Christian Gout, Tom Lyche, Larry L. Schumaker
PublisherSpringer Verlag
Number of pages9
ISBN (Print)9783319228037
StatePublished - 2015
Event8th International Conference on Curves and Surfaces, 2014 - Paris, France
Duration: 12 Jun 201418 Jun 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference8th International Conference on Curves and Surfaces, 2014


  • Box-splines
  • Quasi-interpolation
  • Scattered data


Dive into the research topics of 'Basis functions for scattered data quasi-interpolation'. Together they form a unique fingerprint.

Cite this