Scattered data interpolation using Clough-Tocher type interpolants

In many applications in science and engineering, the only available information about a physical phenomenon are discrete, scalar-valued measurements at arbitrarily located data sites. For analysis and visualization purposes it is then often necessary to construct an interpolating smooth function from the given information. The goal of the proposed research is to gain a better understanding of the problem of scattered data interpolation using the Clough-Tocher type methods. The proposed methods are local and employ piecewise defined Bernstein-Bezier interpolants over triangular regions of the domain. Surface quality is improved by increasing the continuity of the interpolant across triangle boundaries. An integrated approach to the generation of surfaces is adopted, where in all steps that lead to its generation are optimized by one single tool. The quality of surfaces so generated is scrutinized by using different visualization and interrogation tools which are developed for these kinds of surfaces.