资源描述：
《rational offset approximation of rational bézier curves》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。
1、Chengetal./JZhejiangUnivSCIENCEA20067(9):1561-15651561JournalofZhejiangUniversitySCIENCEAISSN1009-3095(Print);ISSN1862-1775(Online)www.zju.edu.cn/jzus;www.springerlink.comE-mail:jzus@zju.edu.cn*RationaloffsetapproximationofrationalBéziercurves1,2†‡1CHENGMin,WANGGuo-jin1(DepartmentofMathematics,
2、ZhejiangUniversity,Hangzhou310027,China)2(DepartmentofMathematics,ZhejiangUniversityofTechnology,Hangzhou310032,China)†E-mail:gjwang@hzcnc.comReceivedMar.20,2006;revisionacceptedMay21,2006Abstract:Theproblemofparametricspeedapproximationofarationalcurveisraisedinthispaper.Offsetcurvesarewidelyu
3、sedinvariousapplications.Asforthereasonthatinmostcasestheoffsetcurvesdonotpreservethesamepolynomialorrationalpolynomialrepresentations,itarousesdifficultyinapplications.Thusapproximationmethodshavebeenintroducedtosolvethisproblem.Inthispaper,ithasbeenpointedoutthatthecruxofoffsetcurveapproximat
4、ionliesintheapproximationofparametricspeed.BasedontheJacobipolynomialapproximationtheorywithendpointsinterpolation,analgebraicrationalapproximationalgorithmofoffsetcurve,whichpreservesthedirectionofnormal,ispresented.Keywords:RationalBéziercurve,Parametricspeed,Offset,Rationalapproximationdoi:1
5、0.1631/jzus.2006.A1561Documentcode:ACLCnumber:TP391INTRODUCTIONhereN(t)representstheidentitynormalofthecurveC(t).Offsetcurves/surfaces,alsocalledparallelResearchonoffsetcurves/surfaceshasgraduallycurves/surfaces,aredefinedasthelocusofthepointsbecomeahottopic,asoffsetsarewidelyusedinwhichareatco
6、nstantdistancealongthenormalfromvariousapplicationsincomputergraphicsandnu-thegeneratorcurves/surfaces.Asforaplanargen-mericalcontrolmachining.Forexample,intheareaeratorcurveΓ:C(t)=(x(t),y(t)),theparametricspeedofaccesspathdesigninroboticsandin3Dnumericalanditsnormσ(t)aredefinedrespectivelyas(F
7、arouki,controlmachininggeneration,offsetcalculationsare1992)widelyused(Maekawa,1999).Fromtherepresentationofoffset,itcanbeeasilyseenthatapartfromsomecertaincurves/surfaces22C′′′()tx=((),()),tytσ()tx=+′′()ty().t(1)(suchasline,circl
