Normalized trivariate B-splines on Worsey-Piper split and quasi-interpolants
type: Item
instance of: scholarly article
title: Normalized trivariate B-splines on Worsey-Piper split and quasi-interpolants
zbMATH Open document ID: 1285.65007
published in: BIT
publication date: 2012-03-23T00:00:00Z
review text: In this paper, the problem of producing a trivariate piecewise quadratic \(C^1\) interpolant to positional and gradient information at the vertices of a tetrahedral partition, considered by \textit{A. J. Worsey} and \textit{B. Piper} [Comput. Aided Geom. Des. 5, No. 3, 177--186 (1988; Zbl 0654.65008)] is recalled. The authors consider a regular tetrahedral partition and give an algorithm to construct a normalized B-splines basis of the space of Worsey-Piper splines (these B-splines are all positive, have local support and form a partition of unity), based on a cubic programming problem. In the geometric framework, the problem is equivalent with founding a WP tetrahedron with minimal volume, containing all Bezier points which surround a vertex. The WP-B-spline representation of \(C^1\) trivariate quadratic polynomials or WP splines in terms of their polar forms is also introduced in order to construct discrete quasi-interpolants which have an optimal approximation order.
reviewed by: Nicoleta Breaz
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 65D05
zbMATH DE Number: 6018293
zbMATH Keywords: quasi-interpolant
zbMATH Keywords: Worsey-Piper partition
zbMATH Keywords: normalized quadratic B-splines
author: D. Sbibih
author: A. Serghini
author: A. Tijini
MaRDI profile type: Publication
full work available at URL: s10543-011-0348-y
OpenAlex ID: W2041062263
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DOI: 10.1007/S10543-011-0348-Y
description: scientific article; zbMATH DE number 6018293