Data Dependent Triangulations for Piecewise Linear Interpolation

Given a set of data points in R² and corresponding data values,it is clear that the quality of a piecewise linear interpolationover triangles depends on the specific triangulation of thedata points. While conventional triangulation methods dependonly on the distribution of the data points in R² in this paperwe suggest that the triangulation should depend on the datavalues as well. Several data dependent criteria for definingthe triangulation are discussed and efficient algorithms forcomputing these triangulations are presented. It is shown fora variety of test cases that data dependent triangulations canimprove significantly the quality of approximation and thatlong and thin triangles, which are traditionally avoided, aresometimes very suitable.