Using Least Squares to Construct Improved Clough-Tocher Interpolant

Abstract

In this thesis, a quartic Clough-Tocher interpolation scheme is introduced, and additional modifications, to adjust the macro-boundary and the order of continuity across domain triangles, are provided to improve both the mathematical and the visual quality of the resulting surface. Furthermore, a proof is given to show the convergence of the interpolation scheme under some specific constraints.