A normalized representation of super splines of arbitrary degree on Powell-Sabin triangulations
type: Item
instance of: scholarly article
title: A normalized representation of super splines of arbitrary degree on Powell-Sabin triangulations
zbMATH Open document ID: 1365.41007
author: Jan Grošelj
published in: BIT
publication date: 2016-12-21T00:00:00Z
review text: The paper proposes a family of spline spaces of arbitrary degree \(d\) on Powell-Sabin triangulations, which extends the class of super spline spaces of arbitrary smoothness \(r\) and degree \(d=3r-1\) introduced by \textit{H. Speleers} [Constr. Approx. 37, No. 1, 41--72 (2013; Zbl 1264.41014)]. The new types of spline spaces studied in the paper are of degree \(d=3r-2\) and \(d=3r\) with global smoothness \(r-1\) and \(r\), respectively, and possess some additional super smoothness across certain edges of the Powell-Sabin partition. The paper also details the construction of normalized bases for the proposed family of spaces. It is proved that the resulting B-spline functions have local supports, are nonnegative, and form a partition of unity, which may serve as useful properties in future applications.
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 65D17
zbMATH DE Number: 6667563
zbMATH Keywords: super splines
zbMATH Keywords: smooth splines on Powell-Sabin triangulations
zbMATH Keywords: normalized B-splines
zbMATH Keywords: macro-elements
reviewed by: Aurelian Bejancu
describes a project that uses: FITPACK
MaRDI profile type: Publication
full work available at URL: s10543-015-0600-y
OpenAlex ID: W2275143114
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DOI: 10.1007/S10543-015-0600-Y
description: scientific article; zbMATH DE number 6667563