Local derivative estimation for scattered data interpolation

摘要

In scattered data interpolation a surface through the given data points is constructed. A class of methods requires triangulation of the domain with the data points at the vertices and definition of a local interpolant over each triangle. In order to construct a smooth surface, it is usual to employ certain derivative values at the vertices. If these are not given, they can be prescribed by estimating the derivatives using the data points. We present here a method of derivative estimation by using a convex combination of all derivatives on related triangular planes. The method has comparable accuracy to the existing method of least-squares minimization but with less computation.