A trivariate Powell-Sabin interpolant
type: Item
instance of: scholarly article
title: A trivariate Powell-Sabin interpolant
zbMATH Open document ID: 0654.65008
DOI: 10.1016/0167-8396(88)90001-5
author: B. Piper
author: Andrew J. Worsey
published in: Computer Aided Geometric Design
publication date: 1988-01-01T00:00:00Z
review text: We consider the problem of producing a piecewise quadratic C 1 interpolant to positional and gradient information at the vertices of a tessellation in \({\mathbb{R}}^ 3 \)of tetrahedra. By splitting each tetrahedron in an appropriate way we show how the problem may be solved. The solution does rely upon the fact that certain geometric constraints must be satisfied. We consider these, and examine how they might be met through a splitting process which is a generalization of that for the bivariate element studied by \textit{M. J. Powell} and \textit{M. A. Sabin} [ACM Trans. Math. Software 3, 316-325 (1977; Zbl 0375.41010)]. Since the interpolant is piecewise quadratic, it can be contured easily.
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 4068144
zbMATH Keywords: trivariate Powell-Sabin interpolant
zbMATH Keywords: Powell-Sabin splitting process
zbMATH Keywords: piecewise quadratic interpolation
MaRDI profile type: Publication
full work available at URL: 0167-8396(88)90001-5
OpenAlex ID: W2010535246
cites work: Surfaces in computer aided geometric design: A survey with new results
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description: scientific article; zbMATH DE number 4068144