Trivariate near-best blending spline quasi-interpolation operators
type: Item
instance of: scholarly article
title: Trivariate near-best blending spline quasi-interpolation operators
zbMATH Open document ID: 1400.41008
author: M. J. Ibáñez
author: D. Barrera
author: Catterina Dagnino
author: Sara Remogna
published in: Numerical Algorithms
publication date: 2018-05-23T00:00:00Z
review text: This paper deals with the construction of trivariate quasi-interpolation operators based on the blending of univariate B-spline and bivariate box-spline quasi-interpolation operators. The proposed quasi-interpolation method can be used for building non-discrete models from discrete data on volumetric grids, as required, for example, in scientific visualization, medical imaging, or computer graphics. The coefficients of the proposed linear functionals are computed to minimize an objective function constructed from the Bernstein-Bézier coefficients of the fundamental function of the resulting operator. In the case of blending \(C^1\) quadratic B-splines and box-splines, it is shown that the minimization problem has infinitely many solutions depending on a parameter. Further, a specific value of the parameter is determined numerically that yields very favorable results. The paper also treats the case of blending the quartic B-spline with each of the quartic box-splines \(M_{2,1}\) and \(M_{1,2}\). The corresponding minimization problem now has a unique solution, which is computed exactly.
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 65D07
zbMATH DE Number: 6871986
zbMATH Keywords: blending quasi-interpolation
zbMATH Keywords: minimal norm
zbMATH Keywords: Bernstein-Bézier coefficients
reviewed by: Aurelian Bejancu
MaRDI profile type: Publication
full work available at URL: s11075-017-0373-2
OpenAlex ID: W2731893597
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DOI: 10.1007/S11075-017-0373-2
description: scientific article; zbMATH DE number 6871986