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Article: Rational quadratic parameterizations of quadrics

TitleRational quadratic parameterizations of quadrics
Authors
KeywordsComputer Aided Geometric Design
Intersection Of Quadrics
Quadric
Rational Quadratic Parameterization
Reparameterization
Issue Date1997
PublisherWorld Scientific Publishing Co Pte Ltd. The Journal's web site is located at http://www.worldscinet.com/ijcga/ijcga.shtml
Citation
International Journal Of Computational Geometry And Applications, 1997, v. 7 n. 6, p. 599-619 How to Cite?
AbstractEvery irreducible quadric in E3 has infinitely many different rational quadratic parameterizations. These parameterizations and the relationships between them are investigated. It is shown that every faithful rational quadratic parameterization of a quadric can be generated by a stereographic projection from a point on the quadric, called the center of projection (COP). Two such parameterizations for the same quadric are related by a rational linear reparameterization if they have the same COP; otherwise they are related by a rational quadratic reparameterization. We also consider unfaithful parameterizations for which, in general, a one-to-one correspondence between points on the surface and parameters in the plane does not exist. It is shown that all unfaithful rational quadratic parameterizations of a properly degenerate quadric can be characterized by a simple canonical form, and there exist no unfaithful rational quadratic parameterizations for a nondegenerate quadric. In addition, given a faithful rational quadratic parameterization of a quadric, a new technique is presented to compute its base points and inversion formula. These results are applied to solve the problems of parameterizing the intersection of two quadrics and reparameterizing a given quadric parameterization with respect to a different COP without implicitization.
Persistent Identifierhttp://hdl.handle.net/10722/152265
ISSN
2013 Impact Factor: 0.082
2015 SCImago Journal Rankings: 0.988
References

 

DC FieldValueLanguage
dc.contributor.authorWang, Wen_US
dc.contributor.authorJoe, Ben_US
dc.contributor.authorGoldman, Ren_US
dc.date.accessioned2012-06-26T06:36:50Z-
dc.date.available2012-06-26T06:36:50Z-
dc.date.issued1997en_US
dc.identifier.citationInternational Journal Of Computational Geometry And Applications, 1997, v. 7 n. 6, p. 599-619en_US
dc.identifier.issn0218-1959en_US
dc.identifier.urihttp://hdl.handle.net/10722/152265-
dc.description.abstractEvery irreducible quadric in E3 has infinitely many different rational quadratic parameterizations. These parameterizations and the relationships between them are investigated. It is shown that every faithful rational quadratic parameterization of a quadric can be generated by a stereographic projection from a point on the quadric, called the center of projection (COP). Two such parameterizations for the same quadric are related by a rational linear reparameterization if they have the same COP; otherwise they are related by a rational quadratic reparameterization. We also consider unfaithful parameterizations for which, in general, a one-to-one correspondence between points on the surface and parameters in the plane does not exist. It is shown that all unfaithful rational quadratic parameterizations of a properly degenerate quadric can be characterized by a simple canonical form, and there exist no unfaithful rational quadratic parameterizations for a nondegenerate quadric. In addition, given a faithful rational quadratic parameterization of a quadric, a new technique is presented to compute its base points and inversion formula. These results are applied to solve the problems of parameterizing the intersection of two quadrics and reparameterizing a given quadric parameterization with respect to a different COP without implicitization.en_US
dc.languageengen_US
dc.publisherWorld Scientific Publishing Co Pte Ltd. The Journal's web site is located at http://www.worldscinet.com/ijcga/ijcga.shtmlen_US
dc.relation.ispartofInternational Journal of Computational Geometry and Applicationsen_US
dc.subjectComputer Aided Geometric Designen_US
dc.subjectIntersection Of Quadricsen_US
dc.subjectQuadricen_US
dc.subjectRational Quadratic Parameterizationen_US
dc.subjectReparameterizationen_US
dc.titleRational quadratic parameterizations of quadricsen_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.scopuseid_2-s2.0-0031313757en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0031313757&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume7en_US
dc.identifier.issue6en_US
dc.identifier.spage599en_US
dc.identifier.epage619en_US
dc.publisher.placeSingaporeen_US
dc.identifier.scopusauthoridWang, W=35147101600en_US
dc.identifier.scopusauthoridJoe, B=7005294816en_US
dc.identifier.scopusauthoridGoldman, R=7402001143en_US

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