A triangle-based \(C^ 1\) interpolation method (Q1060526)

A software package is described that produces a \(C^ 1\) scattered data interpolant. The interpolation method used is the well-known Clough- Tocher interpolant. This method requires specification of gradients at the data points, and the main part of the paper discusses methods to estimate these gradients. A local estimation scheme is based on fitting a quadratic through neighbors of the point of interest. Two global methods are described that are based on the minimization of certain linear functionals. All methods are compared with each other and other existing methods.