Data dependent triangulations for piecewise linear interpolation

Nira Dyn*, David Levin, Samuel Rippa

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Given a set of data points in R2 and corresponding data values, it is clear that the quality of a piecewise linear interpolation 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 in this paper we suggest that the triangulation should depend on the data values as well. Several data dependent criteria for defining the triangulation are discussed and efficient algorithms for computing these triangulations are presented. It is shown for a variety of test cases that data dependent triangulations can improve significantly the quality of approximation and that long and thin triangles, which are traditionally avoided, are sometimes very suitable.

Original languageEnglish
Pages (from-to)137-154
Number of pages18
JournalIMA Journal of Numerical Analysis
Issue number1
StatePublished - Jan 1990


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