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Article: Using signature sequences to classify intersection curves of two quadrics

TitleUsing signature sequences to classify intersection curves of two quadrics
Authors
KeywordsExact computation
Index function
Intersection curves
Morphology classification
Quadric surfaces
Signature sequence
Issue Date2009
PublisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/cagd
Citation
Computer Aided Geometric Design, 2009, v. 26 n. 3, p. 317-335 How to Cite?
AbstractWe present a method that uses signature sequences to classify the intersection curve of two quadrics (QSIC) or, equivalently, quadric pencils in PR3 (3D real projective space), in terms of the shape, topological properties, and algebraic properties of the QSIC. Specifically, for a QSIC we consider its singularity, reducibility, the number of its components, and the degree of each irreducible component, etc. There are in total 35 different types of non-degenerate quadric pencils. For each of the 35 types of QSICs given by these non-degenerate pencils, through a detailed study of the eigenvalue curve and the index function jump we establish a characterizing algebraic condition expressed in terms of the Segre characteristics and the signature sequence of the quadric pencil. We show how to compute a signature sequence with rational arithmetic and use it to determine the type of the intersection curve of any two quadrics which form a non-degenerate pencil. As an example of application, we discuss how to apply our results to collision detection of cones in 3D affine space. © 2008.
Persistent Identifierhttp://hdl.handle.net/10722/60629
ISSN
2015 Impact Factor: 1.092
2015 SCImago Journal Rankings: 1.024
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorTu, Cen_HK
dc.contributor.authorWang, Wen_HK
dc.contributor.authorMourrain, Ben_HK
dc.contributor.authorWang, Jen_HK
dc.date.accessioned2010-05-31T04:15:17Z-
dc.date.available2010-05-31T04:15:17Z-
dc.date.issued2009en_HK
dc.identifier.citationComputer Aided Geometric Design, 2009, v. 26 n. 3, p. 317-335en_HK
dc.identifier.issn0167-8396en_HK
dc.identifier.urihttp://hdl.handle.net/10722/60629-
dc.description.abstractWe present a method that uses signature sequences to classify the intersection curve of two quadrics (QSIC) or, equivalently, quadric pencils in PR3 (3D real projective space), in terms of the shape, topological properties, and algebraic properties of the QSIC. Specifically, for a QSIC we consider its singularity, reducibility, the number of its components, and the degree of each irreducible component, etc. There are in total 35 different types of non-degenerate quadric pencils. For each of the 35 types of QSICs given by these non-degenerate pencils, through a detailed study of the eigenvalue curve and the index function jump we establish a characterizing algebraic condition expressed in terms of the Segre characteristics and the signature sequence of the quadric pencil. We show how to compute a signature sequence with rational arithmetic and use it to determine the type of the intersection curve of any two quadrics which form a non-degenerate pencil. As an example of application, we discuss how to apply our results to collision detection of cones in 3D affine space. © 2008.en_HK
dc.languageengen_HK
dc.publisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/cagden_HK
dc.relation.ispartofComputer Aided Geometric Designen_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in <Computer Aided Geometric Design>. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in PUBLICATION, [VOL 16, ISSUE 3, (MAR 2009)] DOI 10.1016/j.cagd.2008.08.004-
dc.subjectExact computationen_HK
dc.subjectIndex functionen_HK
dc.subjectIntersection curvesen_HK
dc.subjectMorphology classificationen_HK
dc.subjectQuadric surfacesen_HK
dc.subjectSignature sequenceen_HK
dc.titleUsing signature sequences to classify intersection curves of two quadricsen_HK
dc.typeArticleen_HK
dc.identifier.emailWang, W:wenping@cs.hku.hken_HK
dc.identifier.authorityWang, W=rp00186en_HK
dc.description.naturepreprint-
dc.identifier.doi10.1016/j.cagd.2008.08.004en_HK
dc.identifier.scopuseid_2-s2.0-58849160794en_HK
dc.identifier.hkuros160928en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-58849160794&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume26en_HK
dc.identifier.issue3en_HK
dc.identifier.spage317en_HK
dc.identifier.epage335en_HK
dc.identifier.isiWOS:000263631900006-
dc.publisher.placeNetherlandsen_HK
dc.identifier.scopusauthoridTu, C=7402578832en_HK
dc.identifier.scopusauthoridWang, W=35147101600en_HK
dc.identifier.scopusauthoridMourrain, B=7003436036en_HK
dc.identifier.scopusauthoridWang, J=8384548600en_HK

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