Optimal approximate conversion of spline curves and spline approximation of offset curves
type: Item
instance of: scholarly article
title: Optimal approximate conversion of spline curves and spline approximation of offset curves
zbMATH Open document ID: 0666.65010
DOI: 10.1016/0010-4485(88)90006-1
author: J. Hoschek
author: N. Wissel
published in: CAD. Computer-Aided Design
publication date: 1988-01-01T00:00:00Z
review text: Parametric polynomial representation with different polynomial bases and maximum polynomial degrees is used for CAD systems for free-form curves and surfaces modelling. This involves conversion from one polynomial base to another. By direct matrix multiplication, one can achieve such a conversion whenever the number of degrees of polynomial terms in both representations are equal. If two systems do not allow for the same maximum polynomial degrees, then approximate conversions of high order function into low order functions or vice versa is inevitable. This causes an approximation error which has to be minimized. This has been achieved by \textit{L. Dannenberg} and \textit{H. Nowacki} [Comput. Aided Geom. Des. 2, 123-131 (1985; Zbl 0577.65005)] using an error estimate due to \textit{C. de Boor} [A practical guide to splines. (1978; Zbl 0406.41003)] and its applications due to \textit{G. Hölzle} [Comput. Aided Des. 15, 295-296 (1983)]. The first author [ibid. 17, 77-82 (1985)] has proposed a conversion method using geometric continuity of orders 1 and 2 and parametric optimization. In the present paper, this method is extended to geometric continuity of orders 3 and 4. A more effective nonlinear optimization algorithm and a spline splitting algorithm are also introduced.
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 65D15
Mathematics Subject Classification ID: 65D05
zbMATH DE Number: 4090667
zbMATH Keywords: Parametric polynomial representation
zbMATH Keywords: CAD systems
zbMATH Keywords: free-form curves and surfaces modelling
zbMATH Keywords: geometric continuity
zbMATH Keywords: nonlinear optimization algorithm
zbMATH Keywords: spline splitting algorithm
reviewed by: H. P. Dikshit
MaRDI profile type: Publication
full work available at URL: 0010-4485(88)90006-1
OpenAlex ID: W1977171665
description: scientific article; zbMATH DE number 4090667