Fairing cubic B-spline curves
type: Item
instance of: scholarly article
title: Fairing cubic B-spline curves
zbMATH Open document ID: 0644.65007
DOI: 10.1016/0167-8396(87)90027-6
published in: Computer Aided Geometric Design
publication date: 1987-01-01T00:00:00Z
review text: This paper is concerned with numerical algorithms for locally fairing cubic B-spline curves in order to obtain a fine curvature plot. A mathematical definition of relative fairness of curves is given in terms of the value of the third derivative step discontinuity. The methods discussed are based on \textit{J. A. Kjellander}'s approach to fairing a piecewise cubic curve [Smoothing of cubic parametric splines, Comput. Aided Des. 15, 175-179 (1983)] and on the inversion of \textit{W. Boehm}'s knot inserting algorithm for B-spline curves [Inserting new knots into B- spline curves, Comput. Aided Des. 12, 199-201 (1981)]. Three kinds of knot removal algorithms for fairing are studied with their advantages and difficulties in various cases. Some numerical examples are considered and comparison with other methods is drawn.
reviewed by: Valery V. Kobkov
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 65D10
Mathematics Subject Classification ID: 53A04
zbMATH DE Number: 4050839
zbMATH Keywords: smoothing
zbMATH Keywords: cubic B-spline curves
zbMATH Keywords: curvature plot
zbMATH Keywords: fairness of curves
zbMATH Keywords: knot removal algorithms
zbMATH Keywords: fairing
zbMATH Keywords: numerical examples
zbMATH Keywords: comparison
author: Gerald Farin
author: Gerhard Rein
author: Nickolas S. Sapidis
author: Andrew J. Worsey
MaRDI profile type: Publication
full work available at URL: 0167-8396(87)90027-6
OpenAlex ID: W4376858197
cites work: A survey of curve and surface methods in CAGD
cites work: A practical guide to splines
cites work: Q3319163
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description: scientific article; zbMATH DE number 4050839