A package for representing \(C^1\) interpolating surfaces: Application to the lagoon of Venice's bed
The problem of representing a \(C^1\) piecewise polynomial intepolating surface over Delaunay triangulation is studied. The polynomial patches could be \(Q_{18}\) elements [cf. \textit{R. E. Barnhill} and \textit{G. Farin}, Int. J. Numer. Methods Eng. 17, 1763-1778 (1981; Zbl 0477.65009)], the Clough-Tocher or Powell-Sabin finite elements or Bézier patches. The required estimates for the derivative are supplied by the minimization on a suitable domain of the energy functional associated with the Clough-Tocher element. This specializes the global method by \textit{P. Alfeld} [Computer Aided Geom. Des. 2, 281-296 (1985; Zbl 0585.65014)] and optimizes the local method II due to \textit{R. J. Renka} and \textit{A. K. Cline} [Rocky Mt. J. Math. 14, 223-237 (1984; Zbl 0568.65006)]. A brief description of the software modules together with some graphical results of parts of the lagoon of Venice's bed are also presented.
scientific article; zbMATH DE number 1356059