Approximate conversion of rational splines
type: Item
instance of: scholarly article
title: Approximate conversion of rational splines
zbMATH Open document ID: 0686.65005
DOI: 10.1016/0167-8396(89)90018-6
author: Nicholas M. Patrikalakis
published in: Computer Aided Geometric Design
publication date: 1989-01-01T00:00:00Z
review text: During exchange of data between different geometric modeling systems, approximate conversions of rational Bézier and B-spline curves and surfaces to lower degree integral B-spline representations are required. Accurate such conversions are required in many modeling environments. The aim of the present paper is to establish an algorithm to approximate non-uniform rational B-spline curves with non-uniform integral B-spline curves of lower degree, which guarantees a prescribed accuracy. A derivation of global error bounds necessary in verifying accurate approximation at all points is presented. The author presents several illustrative examples and recommendations for further research.
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 65D10
Mathematics Subject Classification ID: 65D15
Mathematics Subject Classification ID: 41A15
zbMATH DE Number: 4124880
zbMATH Keywords: degree reduction
zbMATH Keywords: knot refinement
zbMATH Keywords: rational Bézier curves and surfaces
zbMATH Keywords: exchange of data
zbMATH Keywords: geometric modeling
zbMATH Keywords: B-spline curves and surfaces
zbMATH Keywords: conversions
zbMATH Keywords: algorithm
zbMATH Keywords: non-uniform rational B-spline curves
zbMATH Keywords: non-uniform integral B-spline curves
zbMATH Keywords: global error bounds
reviewed by: Dimitrie D. Stancu
MaRDI profile type: Publication
full work available at URL: 0167-8396(89)90018-6
OpenAlex ID: W2066347618
cites work: Approximate conversion of rational B-spline patches
cites work: A survey of curve and surface methods in CAGD
cites work: Algorithms for degree-raising of splines
cites work: Approximate conversion of surface representations with polynomial bases
cites work: On calculating with B-splines
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cites work: Polya’s Urn Model and Computer Aided Geometric Design
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description: scientific article; zbMATH DE number 4124880