Local lagrange interpolation with bivariate splines of arbitrary smoothness
Bivariate interpolation, Splines
We describe a method which can be used to interpolate function values at a set of scattered points in a planar domain using bivariate polynomial splines of any prescribed smoothness. The method starts with an arbitrary given triangulation of the data points, and involves refining some of the triangles with Clough-Tocher splits. The construction of the interpolating splines requires some additional function values at selected points in the domain, but no derivatives are needed at any point. Given n data points and a corresponding initial triangulation, the interpolating spline can be computed in just O(n) operations. The interpolation method is local and stable, and provides optimal order approximation of smooth functions. © 2005 Springer Science+Business Media, Inc.
Department of Mathematics
Original Publication Date
DOI of published version
Nürnberger, Günther; Rayevskaya, Vera; Schumaker, Larry L.; and Zeilfelder, Frank, "Local lagrange interpolation with bivariate splines of arbitrary smoothness" (2005). Faculty Publications. 2906.