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Article: Enhancing Levin's method for computing quadric-surface intersections

TitleEnhancing Levin's method for computing quadric-surface intersections
Authors
KeywordsIntersection
Quadric Surface
Stereographic Projection
Issue Date2003
PublisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/cagd
Citation
Computer Aided Geometric Design, 2003, v. 20 n. 7, p. 401-422 How to Cite?
AbstractLevin's method produces a parameterization of the intersection curve of two quadrics in the form p(u) = a(u) ± d(u)√s(u), where a(u) and d(u) are vector valued polynomials, and s(u) is a quartic polynomial. This method, however, is incapable of classifying the morphology of the intersection curve, in terms of reducibility, singularity, and the number of connected components, which is critical structural information required by solid modeling applications. We study the theoretical foundation of Levin's method, as well as the parameterization p(u) it produces. The following contributions are presented in this paper: (1) It is shown how the roots of s(u) can be used to classify the morphology of an irreducible intersection curve of two quadric surfaces. (2) An enhanced version of Levin's method is proposed that, besides classifying the morphology of the intersection curve of two quadrics, produces a rational parameterization of the curve if the curve is singular. (3) A simple geometric proof is given for the existence of a real ruled quadric in any quadric pencil, which is the key result on which Levin's method is based. These results enhance the capability of Levin's method in processing the intersection curve of two general quadrics within its own self-contained framework. © 2003 Published by Elsevier B.V.
Persistent Identifierhttp://hdl.handle.net/10722/152301
ISSN
2015 Impact Factor: 1.092
2015 SCImago Journal Rankings: 1.024
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorWang, Wen_US
dc.contributor.authorGoldman, Ren_US
dc.contributor.authorTu, Cen_US
dc.date.accessioned2012-06-26T06:37:01Z-
dc.date.available2012-06-26T06:37:01Z-
dc.date.issued2003en_US
dc.identifier.citationComputer Aided Geometric Design, 2003, v. 20 n. 7, p. 401-422en_US
dc.identifier.issn0167-8396en_US
dc.identifier.urihttp://hdl.handle.net/10722/152301-
dc.description.abstractLevin's method produces a parameterization of the intersection curve of two quadrics in the form p(u) = a(u) ± d(u)√s(u), where a(u) and d(u) are vector valued polynomials, and s(u) is a quartic polynomial. This method, however, is incapable of classifying the morphology of the intersection curve, in terms of reducibility, singularity, and the number of connected components, which is critical structural information required by solid modeling applications. We study the theoretical foundation of Levin's method, as well as the parameterization p(u) it produces. The following contributions are presented in this paper: (1) It is shown how the roots of s(u) can be used to classify the morphology of an irreducible intersection curve of two quadric surfaces. (2) An enhanced version of Levin's method is proposed that, besides classifying the morphology of the intersection curve of two quadrics, produces a rational parameterization of the curve if the curve is singular. (3) A simple geometric proof is given for the existence of a real ruled quadric in any quadric pencil, which is the key result on which Levin's method is based. These results enhance the capability of Levin's method in processing the intersection curve of two general quadrics within its own self-contained framework. © 2003 Published by Elsevier B.V.en_US
dc.languageengen_US
dc.publisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/cagden_US
dc.relation.ispartofComputer Aided Geometric Designen_US
dc.rightsComputer-Aided Geometric Design. Copyright © Elsevier BV.-
dc.subjectIntersectionen_US
dc.subjectQuadric Surfaceen_US
dc.subjectStereographic Projectionen_US
dc.titleEnhancing Levin's method for computing quadric-surface intersectionsen_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/S0167-8396(03)00081-5en_US
dc.identifier.scopuseid_2-s2.0-0141844586en_US
dc.identifier.hkuros95095-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0141844586&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume20en_US
dc.identifier.issue7en_US
dc.identifier.spage401en_US
dc.identifier.epage422en_US
dc.identifier.isiWOS:000185999900002-
dc.publisher.placeNetherlandsen_US
dc.identifier.scopusauthoridWang, W=35147101600en_US
dc.identifier.scopusauthoridGoldman, R=7402001143en_US
dc.identifier.scopusauthoridTu, C=7402578832en_US

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