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Article: Robust computation of the rotation minimizing frame for sweep surface modeling

TitleRobust computation of the rotation minimizing frame for sweep surface modeling
Authors
KeywordsBiarc
Moving Frame
Nurbs
Surface Modeling
Sweep Surface
Issue Date1997
PublisherElsevier Ltd. The Journal's web site is located at http://www.elsevier.com/locate/cad
Citation
Cad Computer Aided Design, 1997, v. 29 n. 5, p. 379-391 How to Cite?
AbstractThe rotation minimizing frame is superior to the Frenet frame for modeling sweep surfaces [F. Klok, Computer Aided Geometric Design 3, 217-229 (1986)]. However, the existing techniques for computing the rotation minimizing frame either have low approximation degree or are unrobust numerically. We present a method to compute an approximate rotation minimizing frame in a robust and efficient manner. The following problem is studied. Given an axial curve A(u) in space and a 2D cross-section curve C(v), generate a sweep surface S(u, v) = A(u) + F(u)C(v), where F(u) is a rotation minimizing frame defined on A(u). Our method works by approximating A(u) with a Gl circular-arc spline curve and then sweeping C(v) with a rotation minimizing frame along the approximating circular-arc spline curve; the sweep surface thus generated is an approximation of S(u, v). The advantages of this method are: (1) the approximate rotation minimizing frame is computed robustly, with its error being much smaller than would be obtained by Klok's linear method with the same number of segmentations; (2) the sweep surface generated is a NURBS surface if the cross-section curve is a NURBS curve; (3) the method is easily adapted to generating a smooth and closed sweep surface when A(u) is a closed smooth curve. © 1997 Elsevier Science Ltd. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/152191
ISSN
2015 Impact Factor: 2.149
2015 SCImago Journal Rankings: 1.078
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorWang, Wen_US
dc.contributor.authorJoe, Ben_US
dc.date.accessioned2012-06-26T06:36:25Z-
dc.date.available2012-06-26T06:36:25Z-
dc.date.issued1997en_US
dc.identifier.citationCad Computer Aided Design, 1997, v. 29 n. 5, p. 379-391en_US
dc.identifier.issn0010-4485en_US
dc.identifier.urihttp://hdl.handle.net/10722/152191-
dc.description.abstractThe rotation minimizing frame is superior to the Frenet frame for modeling sweep surfaces [F. Klok, Computer Aided Geometric Design 3, 217-229 (1986)]. However, the existing techniques for computing the rotation minimizing frame either have low approximation degree or are unrobust numerically. We present a method to compute an approximate rotation minimizing frame in a robust and efficient manner. The following problem is studied. Given an axial curve A(u) in space and a 2D cross-section curve C(v), generate a sweep surface S(u, v) = A(u) + F(u)C(v), where F(u) is a rotation minimizing frame defined on A(u). Our method works by approximating A(u) with a Gl circular-arc spline curve and then sweeping C(v) with a rotation minimizing frame along the approximating circular-arc spline curve; the sweep surface thus generated is an approximation of S(u, v). The advantages of this method are: (1) the approximate rotation minimizing frame is computed robustly, with its error being much smaller than would be obtained by Klok's linear method with the same number of segmentations; (2) the sweep surface generated is a NURBS surface if the cross-section curve is a NURBS curve; (3) the method is easily adapted to generating a smooth and closed sweep surface when A(u) is a closed smooth curve. © 1997 Elsevier Science 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.subjectBiarcen_US
dc.subjectMoving Frameen_US
dc.subjectNurbsen_US
dc.subjectSurface Modelingen_US
dc.subjectSweep Surfaceen_US
dc.titleRobust computation of the rotation minimizing frame for sweep surface modelingen_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/S0010-4485(96)00077-2-
dc.identifier.scopuseid_2-s2.0-0001288152en_US
dc.identifier.hkuros27250-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0001288152&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume29en_US
dc.identifier.issue5en_US
dc.identifier.spage379en_US
dc.identifier.epage391en_US
dc.identifier.isiWOS:A1997WN56200005-
dc.publisher.placeUnited Kingdomen_US
dc.identifier.scopusauthoridWang, W=35147101600en_US
dc.identifier.scopusauthoridJoe, B=7005294816en_US

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