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

Authors  
Issue Date  1995 
Publisher  Elsevier 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. 469489 How to Cite? 
Abstract  Given 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 Identifier  http://hdl.handle.net/10722/152194 
ISSN  2015 Impact Factor: 1.092 2015 SCImago Journal Rankings: 1.024 
DC Field  Value  Language 

dc.contributor.author  Wenping Wang  en_US 
dc.contributor.author  Joe, B  en_US 
dc.date.accessioned  20120626T06:36:26Z   
dc.date.available  20120626T06:36:26Z   
dc.date.issued  1995  en_US 
dc.identifier.citation  Computer Aided Geometric Design, 1995, v. 12 n. 5, p. 469489  en_US 
dc.identifier.issn  01678396  en_US 
dc.identifier.uri  http://hdl.handle.net/10722/152194   
dc.description.abstract  Given 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.language  eng  en_US 
dc.publisher  Elsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/cagd  en_US 
dc.relation.ispartof  Computer Aided Geometric Design  en_US 
dc.title  The geometric interpretation of inversion formulae for rational plane curves  en_US 
dc.type  Article  en_US 
dc.identifier.email  Wenping Wang:wenping@cs.hku.hk  en_US 
dc.identifier.authority  Wenping Wang=rp00186  en_US 
dc.description.nature  link_to_subscribed_fulltext  en_US 
dc.identifier.scopus  eid_2s2.00008455833  en_US 
dc.identifier.volume  12  en_US 
dc.identifier.issue  5  en_US 
dc.identifier.spage  469  en_US 
dc.identifier.epage  489  en_US 
dc.publisher.place  Netherlands  en_US 
dc.identifier.scopusauthorid  Wenping Wang=35147101600  en_US 
dc.identifier.scopusauthorid  Joe, B=7005294816  en_US 