File Download

There are no files associated with this item.

  Links for fulltext
     (May Require Subscription)
Supplementary

Article: Using invariants to extract geometric characteristics of conic sections from rational quadratic parameterizations

TitleUsing invariants to extract geometric characteristics of conic sections from rational quadratic parameterizations
Authors
KeywordsConic Section
Invariant
Quadratic Parameterization
Issue Date2004
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, 2004, v. 14 n. 3, p. 161-187 How to Cite?
AbstractExtracting the geometric characteristics of conic sections, such as their center, axes and foci, from their defining equations is required for various applications in computer graphics and geometric modeling. Although there exist standard techniques for computing the geometric characteristics for conics in implicit form, in shape modeling applications conic sections are often represented by rational quadratic parameterizations. Here we present closed formulas for computing the geometric characteristics of conics directly from their quadratic parameterizations without resorting to implicitization procedures. Our approach uses the invariants of rational quadratic parameterizations under rational linear reparameterizations. These invariants are also used to give a complete characterization of degenerate conics represented by rational quadratic parameterizations.
Persistent Identifierhttp://hdl.handle.net/10722/152422
ISSN
2013 Impact Factor: 0.082
2015 SCImago Journal Rankings: 0.988
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorGoldman, Ren_US
dc.contributor.authorWang, Wen_US
dc.date.accessioned2012-06-26T06:38:21Z-
dc.date.available2012-06-26T06:38:21Z-
dc.date.issued2004en_US
dc.identifier.citationInternational Journal Of Computational Geometry And Applications, 2004, v. 14 n. 3, p. 161-187en_US
dc.identifier.issn0218-1959en_US
dc.identifier.urihttp://hdl.handle.net/10722/152422-
dc.description.abstractExtracting the geometric characteristics of conic sections, such as their center, axes and foci, from their defining equations is required for various applications in computer graphics and geometric modeling. Although there exist standard techniques for computing the geometric characteristics for conics in implicit form, in shape modeling applications conic sections are often represented by rational quadratic parameterizations. Here we present closed formulas for computing the geometric characteristics of conics directly from their quadratic parameterizations without resorting to implicitization procedures. Our approach uses the invariants of rational quadratic parameterizations under rational linear reparameterizations. These invariants are also used to give a complete characterization of degenerate conics represented by rational quadratic parameterizations.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.subjectConic Sectionen_US
dc.subjectInvarianten_US
dc.subjectQuadratic Parameterizationen_US
dc.titleUsing invariants to extract geometric characteristics of conic sections from rational quadratic parameterizationsen_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.doi10.1142/S021819590400141Xen_US
dc.identifier.scopuseid_2-s2.0-7244227666en_US
dc.identifier.hkuros95120-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-7244227666&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume14en_US
dc.identifier.issue3en_US
dc.identifier.spage161en_US
dc.identifier.epage187en_US
dc.identifier.isiWOS:000223439300002-
dc.publisher.placeSingaporeen_US
dc.identifier.scopusauthoridGoldman, R=7402001143en_US
dc.identifier.scopusauthoridWang, W=35147101600en_US

Export via OAI-PMH Interface in XML Formats


OR


Export to Other Non-XML Formats