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Article: Computation of rotation minimizing frames

TitleComputation of rotation minimizing frames
Authors
KeywordsCurve
Differential Geometry
Motion
Motion Design
Rotation Minimizing Frame
Sweep Surface
Issue Date2008
Citation
ACM Transactions On Graphics, 2008, v. 27 n. 1, article no. 2 How to Cite?
AbstractDue to its minimal twist, the rotation minimizing frame (RMF) is widely used in computer graphics, including sweep or blending surface modeling, motion design and control in computer animation and robotics, streamline visualization, and tool path planning in CAD/CAM. We present a novel simple and efficient method for accurate and stable computation of RMF of a curve in 3D. This method, called the double reflection method, uses two reflections to compute each frame from its preceding one to yield a sequence of frames to approximate an exact RMF. The double reflection method has the fourth order global approximation error, thus it is much more accurate than the two currently prevailing methods with the second order approximation error - -the projection method by Klok and the rotation method by Bloomenthal, while all these methods have nearly the same per-frame computational cost. Furthermore, the double reflection method is much simpler and faster than using the standard fourth order Runge-Kutta method to integrate the defining ODE of the RMF, though they have the same accuracy. We also investigate further properties and extensions of the double reflection method, and discuss the variational principles in design moving frames with boundary conditions, based on RMF. © 2008 ACM.
Persistent Identifierhttp://hdl.handle.net/10722/152386
ISSN
2015 Impact Factor: 4.218
2015 SCImago Journal Rankings: 2.552
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorWang, Wen_US
dc.contributor.authorJüttler, Ben_US
dc.contributor.authorZheng, Den_US
dc.contributor.authorLiu, Yen_US
dc.date.accessioned2012-06-26T06:37:50Z-
dc.date.available2012-06-26T06:37:50Z-
dc.date.issued2008en_US
dc.identifier.citationACM Transactions On Graphics, 2008, v. 27 n. 1, article no. 2en_US
dc.identifier.issn0730-0301en_US
dc.identifier.urihttp://hdl.handle.net/10722/152386-
dc.description.abstractDue to its minimal twist, the rotation minimizing frame (RMF) is widely used in computer graphics, including sweep or blending surface modeling, motion design and control in computer animation and robotics, streamline visualization, and tool path planning in CAD/CAM. We present a novel simple and efficient method for accurate and stable computation of RMF of a curve in 3D. This method, called the double reflection method, uses two reflections to compute each frame from its preceding one to yield a sequence of frames to approximate an exact RMF. The double reflection method has the fourth order global approximation error, thus it is much more accurate than the two currently prevailing methods with the second order approximation error - -the projection method by Klok and the rotation method by Bloomenthal, while all these methods have nearly the same per-frame computational cost. Furthermore, the double reflection method is much simpler and faster than using the standard fourth order Runge-Kutta method to integrate the defining ODE of the RMF, though they have the same accuracy. We also investigate further properties and extensions of the double reflection method, and discuss the variational principles in design moving frames with boundary conditions, based on RMF. © 2008 ACM.en_US
dc.languageengen_US
dc.relation.ispartofACM Transactions on Graphicsen_US
dc.subjectCurveen_US
dc.subjectDifferential Geometryen_US
dc.subjectMotionen_US
dc.subjectMotion Designen_US
dc.subjectRotation Minimizing Frameen_US
dc.subjectSweep Surfaceen_US
dc.titleComputation of rotation minimizing framesen_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.doi10.1145/1330511.1330513en_US
dc.identifier.scopuseid_2-s2.0-41349092142en_US
dc.identifier.hkuros141108-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-41349092142&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume27en_US
dc.identifier.issue1en_US
dc.identifier.spagearticle no. 2-
dc.identifier.epagearticle no. 2-
dc.identifier.eissn1557-7368-
dc.identifier.isiWOS:000255121300002-
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridWang, W=35147101600en_US
dc.identifier.scopusauthoridJüttler, B=6701753933en_US
dc.identifier.scopusauthoridZheng, D=23988277100en_US
dc.identifier.scopusauthoridLiu, Y=36066740000en_US
dc.identifier.citeulike2633767-

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