A package for representing \(C^1\) interpolating surfaces: Application to the lagoon of Venice's bed
type: Item
instance of: scholarly article
title: A package for representing \(C^1\) interpolating surfaces: Application to the lagoon of Venice's bed
zbMATH Open document ID: 0934.65011
DOI: 10.1023/A:1019103901231
published in: Numerical Algorithms
publication date: 2000-04-03T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 65Y15
Mathematics Subject Classification ID: 65D17
zbMATH DE Number: 1356059
zbMATH Keywords: piecewise polynolmials
zbMATH Keywords: interpolation
zbMATH Keywords: minimization
zbMATH Keywords: computer-aided design
zbMATH Keywords: Powell-Sabin finite elements
zbMATH Keywords: Bézier patches
zbMATH Keywords: Clough-Tocher element
zbMATH Keywords: lagoon of Venice's bed
author: M. Morandi Cecchi
author: Stefano De Marchi
author: Diego Fasoli
reviewed by: H. P. Dikshit
describes a project that uses: TRIPACK
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1356059