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Article: Control point adjustment for B-spline curve approximation

TitleControl point adjustment for B-spline curve approximation
Authors
KeywordsB-spline curve
Optimization
Shape approximation
Squared distance
Issue Date2004
PublisherElsevier Ltd. The Journal's web site is located at http://www.elsevier.com/locate/cad
Citation
Cad Computer Aided Design, 2004, v. 36 n. 7, p. 639-652 How to Cite?
AbstractPottmann et al. propose an iterative optimization scheme for approximating a target curve with a B-spline curve based on square distance minimization, or SDM. The main advantage of SDM is that it does not need a parameterization of data points on the target curve. Starting with an initial B-spline curve, this scheme makes an active B-spline curve converge faster towards the target curve and produces a better approximating B-spline curve than existing methods relying on data point parameterization. However, SDM is sensitive to the initial B-spline curve due to its local nature of optimization. To address this, we integrate SDM with procedures for automatically adjusting both the number and locations of the control points of the active spline curve. This leads to a method that is more robust and applicable than SDM used alone. Furthermore, it is observed that the most time consuming part of SDM is the repeated computation of the foot-point on the target curve of a sample point on the active B-spline curve. In our implementation, we speed up the foot-point computation by pre-computing the distance field of the target curve using the Fast Marching Method. Experimental examples are presented to demonstrate the effectiveness of our method. Problems for further research are discussed. © 2003 Elsevier Ltd. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/48429
ISSN
2015 Impact Factor: 2.149
2015 SCImago Journal Rankings: 1.078
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorYang, Hen_HK
dc.contributor.authorWang, Wen_HK
dc.contributor.authorSun, Jen_HK
dc.date.accessioned2008-05-22T04:12:46Z-
dc.date.available2008-05-22T04:12:46Z-
dc.date.issued2004en_HK
dc.identifier.citationCad Computer Aided Design, 2004, v. 36 n. 7, p. 639-652en_HK
dc.identifier.issn0010-4485en_HK
dc.identifier.urihttp://hdl.handle.net/10722/48429-
dc.description.abstractPottmann et al. propose an iterative optimization scheme for approximating a target curve with a B-spline curve based on square distance minimization, or SDM. The main advantage of SDM is that it does not need a parameterization of data points on the target curve. Starting with an initial B-spline curve, this scheme makes an active B-spline curve converge faster towards the target curve and produces a better approximating B-spline curve than existing methods relying on data point parameterization. However, SDM is sensitive to the initial B-spline curve due to its local nature of optimization. To address this, we integrate SDM with procedures for automatically adjusting both the number and locations of the control points of the active spline curve. This leads to a method that is more robust and applicable than SDM used alone. Furthermore, it is observed that the most time consuming part of SDM is the repeated computation of the foot-point on the target curve of a sample point on the active B-spline curve. In our implementation, we speed up the foot-point computation by pre-computing the distance field of the target curve using the Fast Marching Method. Experimental examples are presented to demonstrate the effectiveness of our method. Problems for further research are discussed. © 2003 Elsevier Ltd. All rights reserved.en_HK
dc.format.extent1544960 bytes-
dc.format.extent89087 bytes-
dc.format.mimetypeapplication/pdf-
dc.format.mimetypeapplication/pdf-
dc.languageengen_HK
dc.publisherElsevier Ltd. The Journal's web site is located at http://www.elsevier.com/locate/caden_HK
dc.relation.ispartofCAD Computer Aided Designen_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectB-spline curveen_HK
dc.subjectOptimizationen_HK
dc.subjectShape approximationen_HK
dc.subjectSquared distanceen_HK
dc.titleControl point adjustment for B-spline curve approximationen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0010-4485&volume=36&issue=7&spage=639&epage=652&date=2004&atitle=Control+point+adjustment+for+B-spline+curve+approximation+en_HK
dc.identifier.emailWang, W:wenping@cs.hku.hken_HK
dc.identifier.authorityWang, W=rp00186en_HK
dc.description.naturepostprinten_HK
dc.identifier.doi10.1016/S0010-4485(03)00140-4en_HK
dc.identifier.scopuseid_2-s2.0-1842832051en_HK
dc.identifier.hkuros95104-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-1842832051&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume36en_HK
dc.identifier.issue7en_HK
dc.identifier.spage639en_HK
dc.identifier.epage652en_HK
dc.identifier.isiWOS:000221213200006-
dc.publisher.placeUnited Kingdomen_HK
dc.identifier.scopusauthoridYang, H=15137870100en_HK
dc.identifier.scopusauthoridWang, W=35147101600en_HK
dc.identifier.scopusauthoridSun, J=37071294700en_HK
dc.identifier.citeulike7751387-

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