On optimal interpolation triangle incidences

Abstract

The problem of determining optimal incidences for triangulating a given set of vertices for the model problem of interpolating a convex quadratic surface by piecewise linear functions is studied. An exact expression for the maximum error is derived, and the optimality criterion is minimization of the maximum error. The optimal incidences are shown to be derivable from an associated Delaunay triangulation and hence are computable in $O(N\log N)$ time for N vertices.