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#### Article: Revisiting the μ-basis of a rational ruled surface

Title Revisiting the μ-basis of a rational ruled surface Chen, FWang, W Μ-BasisImplicitizationModuleMoving PlaneRational Ruled Surface 2003 Academic Press. The Journal's web site is located at http://www.elsevier.com/locate/jsc Journal Of Symbolic Computation, 2003, v. 36 n. 5, p. 699-716 How to Cite? The μ-basis of a rational ruled surface P(s, t) = P0(s +tP1 (s) is defined in Chen et al. (Comput. Aided Geom. Design 18 (2001) 61) to consist of two polynomials p(x, y, z, s) and q(x, y, z, s) that are linear in x, y, z. It is shown there that the resultant of p and q with respect to s gives the implicit equation of the rational ruled surface; however, the parametric equation P(s, t) of the rational ruled surface cannot be recovered from p and q. Furthermore, the μ-basis thus defined for a rational ruled surface does not possess many nice properties that hold for the μ-basis of a rational planar curve (Comput. Aided Geom. Design 18 (1998) 803). In this paper, we introduce another polynomial r(x, y, z, s, t) that is linear in x, y, z and t such that p, q, r can be used to recover the parametric equation P(s, t) of the rational ruled surface; hence, we redefine the μ-basis to consist of the three polynomials p, q, r. We present an efficient algorithm for computing the newly-defined μ-basis, and derive some of its properties. In particular, we show that the new μ-basis serves as a basis for both the moving plane module and the moving plane ideal corresponding to the rational ruled surface. © 2003 Elsevier Ltd. All rights reserved. http://hdl.handle.net/10722/152304 0747-71712017 Impact Factor: 0.7552015 SCImago Journal Rankings: 0.979 WOS:000186484500002 References in Scopus

DC FieldValueLanguage
dc.contributor.authorChen, Fen_US
dc.contributor.authorWang, Wen_US
dc.date.accessioned2012-06-26T06:37:04Z-
dc.date.available2012-06-26T06:37:04Z-
dc.date.issued2003en_US
dc.identifier.citationJournal Of Symbolic Computation, 2003, v. 36 n. 5, p. 699-716en_US
dc.identifier.issn0747-7171en_US
dc.identifier.urihttp://hdl.handle.net/10722/152304-
dc.description.abstractThe μ-basis of a rational ruled surface P(s, t) = P0(s +tP1 (s) is defined in Chen et al. (Comput. Aided Geom. Design 18 (2001) 61) to consist of two polynomials p(x, y, z, s) and q(x, y, z, s) that are linear in x, y, z. It is shown there that the resultant of p and q with respect to s gives the implicit equation of the rational ruled surface; however, the parametric equation P(s, t) of the rational ruled surface cannot be recovered from p and q. Furthermore, the μ-basis thus defined for a rational ruled surface does not possess many nice properties that hold for the μ-basis of a rational planar curve (Comput. Aided Geom. Design 18 (1998) 803). In this paper, we introduce another polynomial r(x, y, z, s, t) that is linear in x, y, z and t such that p, q, r can be used to recover the parametric equation P(s, t) of the rational ruled surface; hence, we redefine the μ-basis to consist of the three polynomials p, q, r. We present an efficient algorithm for computing the newly-defined μ-basis, and derive some of its properties. In particular, we show that the new μ-basis serves as a basis for both the moving plane module and the moving plane ideal corresponding to the rational ruled surface. © 2003 Elsevier Ltd. All rights reserved.en_US
dc.languageengen_US
dc.publisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jscen_US
dc.relation.ispartofJournal of Symbolic Computationen_US
dc.subjectΜ-Basisen_US
dc.subjectImplicitizationen_US
dc.subjectModuleen_US
dc.subjectMoving Planeen_US
dc.subjectRational Ruled Surfaceen_US
dc.titleRevisiting the μ-basis of a rational ruled surfaceen_US
dc.typeArticleen_US
dc.identifier.emailWang, W:wenping@cs.hku.hken_US
dc.identifier.authorityWang, W=rp00186en_US
dc.identifier.doi10.1016/S0747-7171(03)00064-6en_US
dc.identifier.scopuseid_2-s2.0-0242593248en_US
dc.identifier.hkuros95099-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0242593248&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume36en_US
dc.identifier.issue5en_US
dc.identifier.spage699en_US
dc.identifier.epage716en_US
dc.identifier.isiWOS:000186484500002-
dc.publisher.placeUnited Kingdomen_US
dc.identifier.scopusauthoridChen, F=7404908180en_US
dc.identifier.scopusauthoridWang, W=35147101600en_US