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Article: Local computation of curve interpolation knots with quadratic precision

TitleLocal computation of curve interpolation knots with quadratic precision
Authors
KeywordsInterpolation
Knots
Parametric Curves
Quadratic Polynomial
Issue Date2013
PublisherElsevier Ltd. The Journal's web site is located at http://www.elsevier.com/locate/cad
Citation
CAD Computer Aided Design, 2013, v. 45 n. 4, p. 853-859 How to Cite?
AbstractThere are several prevailing methods for selecting knots for curve interpolation. A desirable criterion for knot selection is whether the knots can assist an interpolation scheme to achieve the reproduction of polynomial curves of certain degree if the data points to be interpolated are taken from such a curve. For example, if the data points are sampled from an underlying quadratic polynomial curve, one would wish to have the knots selected such that the resulting interpolation curve reproduces the underlying quadratic curve; in this case, the knot selection scheme is said to have quadratic precision. In this paper, we propose a local method for determining knots with quadratic precision. This method improves on our previous method that entails the solution of a global equation to produce a knot sequence with quadratic precision. We show that this new knot selection scheme results in better interpolation error than other existing methods, including the chord-length method, the centripetal method and Foley's method, which do not possess quadratic precision. © 2011 Elsevier Ltd. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/152464
ISSN
2014 Impact Factor: 1.801
2014 SCImago Journal Rankings: 1.470
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorZhang, Cen_US
dc.contributor.authorWang, Wen_US
dc.contributor.authorWang, Jen_US
dc.contributor.authorLi, Xen_US
dc.date.accessioned2012-06-26T06:39:26Z-
dc.date.available2012-06-26T06:39:26Z-
dc.date.issued2013en_US
dc.identifier.citationCAD Computer Aided Design, 2013, v. 45 n. 4, p. 853-859en_US
dc.identifier.issn0010-4485en_US
dc.identifier.urihttp://hdl.handle.net/10722/152464-
dc.description.abstractThere are several prevailing methods for selecting knots for curve interpolation. A desirable criterion for knot selection is whether the knots can assist an interpolation scheme to achieve the reproduction of polynomial curves of certain degree if the data points to be interpolated are taken from such a curve. For example, if the data points are sampled from an underlying quadratic polynomial curve, one would wish to have the knots selected such that the resulting interpolation curve reproduces the underlying quadratic curve; in this case, the knot selection scheme is said to have quadratic precision. In this paper, we propose a local method for determining knots with quadratic precision. This method improves on our previous method that entails the solution of a global equation to produce a knot sequence with quadratic precision. We show that this new knot selection scheme results in better interpolation error than other existing methods, including the chord-length method, the centripetal method and Foley's method, which do not possess quadratic precision. © 2011 Elsevier Ltd. All rights reserved.en_US
dc.languageengen_US
dc.publisherElsevier Ltd. The Journal's web site is located at http://www.elsevier.com/locate/caden_US
dc.relation.ispartofCAD Computer Aided Designen_US
dc.subjectInterpolationen_US
dc.subjectKnotsen_US
dc.subjectParametric Curvesen_US
dc.subjectQuadratic Polynomialen_US
dc.titleLocal computation of curve interpolation knots with quadratic precisionen_US
dc.typeArticleen_US
dc.identifier.emailWang, W:wenping@cs.hku.hken_US
dc.identifier.authorityWang, W=rp00186en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1016/j.cad.2011.08.004en_US
dc.identifier.scopuseid_2-s2.0-84875923135en_US
dc.identifier.hkuros208994-
dc.identifier.isiWOS:000317454700006-
dc.publisher.placeUnited Kingdomen_US
dc.identifier.scopusauthoridZhang, C=35197623400en_US
dc.identifier.scopusauthoridWang, W=35147101600en_US
dc.identifier.scopusauthoridWang, J=50263349100en_US
dc.identifier.scopusauthoridLi, X=50262300200en_US

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