A Quartic Clough-Tocher Interpolant

摘要

In this paper we present a quartic version of the Clough-Tocher scheme for Hermite interpolation of functional data. This variation uses least squares to minimize discontinuities across the macro-patch boundaries, as well as adjusting one of the macro-boundary control points. The resulting surfaces have significantly better shape than a cubic version of Clough-Tocher that also used least squares to minimize discontinuities across patch boundaries. We compare our method to this cubic version of Clough-Tocher using shaded images and Gaussian curvature plots.