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Article: The geometric interpretation of inversion formulae for rational plane curves

TitleThe geometric interpretation of inversion formulae for rational plane curves
Authors
Issue Date1995
PublisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/cagd
Citation
Computer Aided Geometric Design, 1995, v. 12 n. 5, p. 469-489 How to Cite?
AbstractGiven a faithful parameterization P(t) of a rational plane curve, an inversion formula t = f(x,y) gives the parameter value corresponding to a point (x,y) on the curve, where f is a rational function in x and y. We investigate the relationship between a point (x*,y*) not on the curve and the corresponding point P(t*) on the curve, where t* = f(x*,y*). It is shown that for a rational quadratic plane curve, P(t*) is the projection of (x*,y*) from a point which may be any point on the curve; for a rational cubic plane curve, P(t*) is the projection of (x*,y*) from the double point of the curve. Applications of these results are discussed and a generalized result is proved for rational plane curves of higher degree. © 1995.
Persistent Identifierhttp://hdl.handle.net/10722/152194
ISSN
2015 Impact Factor: 1.092
2015 SCImago Journal Rankings: 1.024

 

DC FieldValueLanguage
dc.contributor.authorWenping Wangen_US
dc.contributor.authorJoe, Ben_US
dc.date.accessioned2012-06-26T06:36:26Z-
dc.date.available2012-06-26T06:36:26Z-
dc.date.issued1995en_US
dc.identifier.citationComputer Aided Geometric Design, 1995, v. 12 n. 5, p. 469-489en_US
dc.identifier.issn0167-8396en_US
dc.identifier.urihttp://hdl.handle.net/10722/152194-
dc.description.abstractGiven a faithful parameterization P(t) of a rational plane curve, an inversion formula t = f(x,y) gives the parameter value corresponding to a point (x,y) on the curve, where f is a rational function in x and y. We investigate the relationship between a point (x*,y*) not on the curve and the corresponding point P(t*) on the curve, where t* = f(x*,y*). It is shown that for a rational quadratic plane curve, P(t*) is the projection of (x*,y*) from a point which may be any point on the curve; for a rational cubic plane curve, P(t*) is the projection of (x*,y*) from the double point of the curve. Applications of these results are discussed and a generalized result is proved for rational plane curves of higher degree. © 1995.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.titleThe geometric interpretation of inversion formulae for rational plane curvesen_US
dc.typeArticleen_US
dc.identifier.emailWenping Wang:wenping@cs.hku.hken_US
dc.identifier.authorityWenping Wang=rp00186en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.scopuseid_2-s2.0-0008455833en_US
dc.identifier.volume12en_US
dc.identifier.issue5en_US
dc.identifier.spage469en_US
dc.identifier.epage489en_US
dc.publisher.placeNetherlandsen_US
dc.identifier.scopusauthoridWenping Wang=35147101600en_US
dc.identifier.scopusauthoridJoe, B=7005294816en_US

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