On the evaluation of box splines
type: Item
instance of: scholarly article
title: On the evaluation of box splines
zbMATH Open document ID: 0798.65012
DOI: 10.1007/BF02109280
author: Carl De Boor
published in: Numerical Algorithms
publication date: 1994-10-30T00:00:00Z
review text: The topic of multivariate \(B\)-splines really took off after the appearance of nice recurrence relations for simplex splines due to \textit{C. A. Micchelli} [Rocky Mt. J. Math. 10, 485-497 (1980; Zbl 0456.41003)]. The present paper outlines the procedures to meet the difficulties that arise in evaluation of box splines [for definition and other details see \textit{C. de Boor}, \textit{K. Höllig} and \textit{S. D. Riemenschneider}, Box splines, Springer, Berlin (1993)], when a straightforward use of the simple recurrence relation for such splines is made. It is mentioned that the difficulty is essentially due to the fact that step functions are not computable. A MATLAB program for the (correct) evaluation of a box spline is also given. Since use of the recurrence relation is very time-consuming, various alternative approaches involving use of the idea of subdivision [see \textit{E. Cohen}, \textit{T. Lyche} and \textit{R. Riesenfeld}: Comput. Aided Geom. Des. 1, 131-148 (1984; Zbl 0567.65004) and \textit{W. Dahmen} and \textit{C. A. Micchelli}, ibid. 1, 115- 129 (1984; Zbl 0581.65011)] are also given.
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 510186
zbMATH Keywords: multivariate \(B\)-splines
zbMATH Keywords: recurrence relations
zbMATH Keywords: simplex splines
zbMATH Keywords: box splines
zbMATH Keywords: MATLAB program
zbMATH Keywords: subdivision
reviewed by: H. P. Dikshit
describes a project that uses: na2
describes a project that uses: Matlab
MaRDI profile type: Publication
cites work: A practical guide to splines
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full work available at URL: https://doi.org/10.1007/bf02109280
OpenAlex ID: W2062636705
description: scientific article; zbMATH DE number 510186