A geometric approach for Hermite subdivision
type: Item
instance of: scholarly article
title: A geometric approach for Hermite subdivision
zbMATH Open document ID: 1198.65043
author: Carla Manni
author: Paolo Costantini
published in: Numerische Mathematik
publication date: 2010-05-21T00:00:00Z
review text: A new approach for the construction of non-uniform and non-stationary Hermite \(C^1\) subdivision schemes is presented. This new approach lies in the geometric interpretation of the subdivision steps using Bernstein-Bézier bases and the related results for general families of spaces. The Hermite interpolating function is expressed in the Bernstein basis and replaced by two new functions from the space of the same family. The subdivision is then described in terms of the transformation matrix which maps the initial four Bézier points in the final set of seven control points corresponding to the two new functions. The presented approach can be considered as the natural extension of the cubic de Casteljau algorithm for more general function spaces. The analytic formulation of the subdivision formulas for Hermite subdivision is a consequence of the geometric constructions. The subdivision scheme for rational functions is described in detail. Numerical and graphical examples are shown in the article, too.
reviewed by: Ivana Linkeová
Mathematics Subject Classification ID: 65D18
Mathematics Subject Classification ID: 65D05
zbMATH DE Number: 5710584
zbMATH Keywords: subdivision scheme
zbMATH Keywords: Hermite interpolation
zbMATH Keywords: Hermite subdivision
zbMATH Keywords: non-stationary subdivision scheme
zbMATH Keywords: non-uniform subdivision scheme
zbMATH Keywords: de Casteljau algorithm
zbMATH Keywords: Bernstein basis
zbMATH Keywords: algorithm
zbMATH Keywords: numerical and graphical examples
MaRDI profile type: Publication
full work available at URL: s00211-009-0280-0
OpenAlex ID: W2067988126
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DOI: 10.1007/S00211-009-0280-0
description: scientific article; zbMATH DE number 5710584