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. R. E. Barnhill and 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 P. Alfeld [Computer Aided Geom. Des. 2, 281-296 (1985; Zbl 0585.65014)] and optimizes the local method II due to R. J. Renka and 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. (netlib numeralgo na17)
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References in zbMATH (referenced in 3 articles , 1 standard article )
Showing results 1 to 3 of 3.
- Haber, Jörg; Zeilfelder, Frank; Davydov, Oleg; Seidel, Hans-Peter: Smooth approximation and rendering of large scattered data sets (2008)
- Davydov, Oleg; Zeilfelder, Frank: Scattered data fitting by direct extension of local polynomials to bivariate splines (2004)
- Morandi Cecchi, M.; De Marchi, S.; Fasoli, D.: A package for representing $C^1$ interpolating surfaces: Application to the lagoon of Venice’s bed (1999)