Boundary correction for piecewise linear interpolation defined over data-dependent triangulations

Nira Dyn*, David Levin, Samuel Rippa

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

Given a set of data points in R2 and corresponding data values it is clear that the quality of a Piecewise Linear Interpolating Surface (PLIS) over triangles depends on the specific triangulation of the data points. While conventional triangulation methods depend only on the distribution of the data points in R2, the authors (1990) suggested to construct data-dependent triangulations which depend on the data values as well. Numerical examples indicate that this method improves the PLIS only away from the boundary of the triangulation. In this paper we present and test a numerical scheme for boundary correction to be used as a complementary step to the creation of data-dependent triangulations. This scheme adds more points on the boundary edges of "bad" triangles and estimates corresponding function values. Numerical tests show the success of the scheme in improving the PLIS also near the boundary of the triangulation.

Original languageEnglish
Pages (from-to)179-192
Number of pages14
JournalJournal of Computational and Applied Mathematics
Volume39
Issue number2
DOIs
StatePublished - 30 Mar 1992

Keywords

  • Triangulations
  • boundary corrections
  • data-dependent triangulations
  • piecewise linear interpolation

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