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Article: Local computation of curve interpolation knots with quadratic precision
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TitleLocal computation of curve interpolation knots with quadratic precision
 
AuthorsZhang, C1 3
Wang, W2
Wang, J3
Li, X1
 
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
2013 Impact Factor: 1.515
2013 SCImago Journal Rankings: 1.148
 
DOIhttp://dx.doi.org/10.1016/j.cad.2011.08.004
 
ISI Accession Number IDWOS:000317454700006
 
DC FieldValue
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.isiWOS:000317454700006
 
dc.identifier.issn0010-4485
2013 Impact Factor: 1.515
2013 SCImago Journal Rankings: 1.148
 
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
 
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<contributor.author>Wang, W</contributor.author>
<contributor.author>Wang, J</contributor.author>
<contributor.author>Li, X</contributor.author>
<date.accessioned>2012-06-26T06:39:26Z</date.accessioned>
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<description.abstract>There 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&apos;s method, which do not possess quadratic precision. &#169; 2011 Elsevier Ltd. All rights reserved.</description.abstract>
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<subject>Interpolation</subject>
<subject>Knots</subject>
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Author Affiliations
  1. Shandong University
  2. The University of Hong Kong
  3. Shandong Economics University