Article: Local computation of curve interpolation knots with quadratic precision

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TitleLocal computation of curve interpolation knots with quadratic precision
AuthorsZhang, C
Wang, W
Wang, J
Li, X
KeywordsInterpolation
Knots
Parametric Curves
Quadratic Polynomial
Issue Date2013
PublisherElsevier Ltd. The Journal's web site is located at http://www.elsevier.com/locate/cad
CitationCAD Computer Aided Design, 2013, v. 45 n. 4, p. 853-859 [How to Cite?]
DOI: http://dx.doi.org/10.1016/j.cad.2011.08.004
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.
ISSN0010-4485
2011 Impact Factor: 1.234
2011 SCImago Journal Rankings: 0.054
DOIhttp://dx.doi.org/10.1016/j.cad.2011.08.004
DC Field
Value
dc.contributor.authorZhang, C
dc.contributor.authorWang, W
dc.contributor.authorWang, J
dc.contributor.authorLi, X
dc.date.accessioned2012-06-26T06:39:26Z
dc.date.available2012-06-26T06:39:26Z
dc.date.issued2013
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.
dc.description.natureLink_to_subscribed_fulltext
dc.identifier.citationCAD Computer Aided Design, 2013, v. 45 n. 4, p. 853-859 [How to Cite?]
DOI: http://dx.doi.org/10.1016/j.cad.2011.08.004
dc.identifier.doihttp://dx.doi.org/10.1016/j.cad.2011.08.004
dc.identifier.hkuros208994
dc.identifier.issn0010-4485
2011 Impact Factor: 1.234
2011 SCImago Journal Rankings: 0.054
dc.identifier.scopuseid_2-s2.0-84875923135
dc.identifier.urihttp://hdl.handle.net/10722/152464
dc.languageeng
dc.publisherElsevier Ltd. The Journal's web site is located at http://www.elsevier.com/locate/cad
dc.publisher.placeUnited Kingdom
dc.relation.ispartofCAD Computer Aided Design
dc.subjectInterpolation
dc.subjectKnots
dc.subjectParametric Curves
dc.subjectQuadratic Polynomial
dc.titleLocal computation of curve interpolation knots with quadratic precision
dc.typeArticle