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1、-iv--万方数据摘要Bézier曲线是计算机辅助几何设计的重要研究内容之一,也是曲线曲面造型设计的重要工具之一,其采用逼近原理来模仿曲线、曲面的设计过程,同时供程序设计员使用.但是,对于给定的控制多边形,Bézier曲线的位置是确定的,而实际应用中设计的线和面的形状繁复多变,很难用单一的曲线曲面去描述.因此,第二章中函数引入了形状参数,通过改变参数值以调整曲线形状.此外,通过曲线间的光滑拼接以达到更好表达复杂组合曲线.首先,将四次Bézier曲线的基函数进行拓展,定义了带三个形状参数的类四次Bernstein基函数,讨论它的基本
2、性质.再基于该组基函数定义了三个形状参数的类四次Bézier曲线.该曲线和四次Bézier曲线有类似性质,并给出了曲线间的光滑拼接.通过实例表明该方法在设计曲线曲面时十分有效.其次,利用B样条曲线的Bézier构造方法以及应用Bézier曲线拼接技术,实现均匀B样条曲线和Bézier曲012线间的G、G、G拼接.再次,利用NURBS曲线与有理Bézier曲线相互转化的方法,将二次Bézier曲线与三次非均匀B样条曲线的拼接转化为二次Bézier曲线与三次Bézier曲线的拼接问题,从而得出拼接定理.最后,论文进行总结以及对今后研究
3、工作的展望.关键词：Bézier曲线;类四次Bézier曲线;B样条曲线;NURBS曲线;光滑拼接;-1--万方数据AbstractTheBéziercurveisoneoftheimportantcomponentsforcomputeraidedgeometricdesignandtoolsfortheCurveSurfaceModelingDesign,itsapproximationprincipleisusedtoimitatethedesignprocessofcurveandsurface,atthesametime
4、fortheuseofprogrammer.Foragivencontrolpolygon,theBéziercurve’spositionisdetermined,whilethesecurve’sshapeiscomplicatedandvariableinthepracticalapplicationitisdifficulttodescribewithasinglecurveorsurface.Therefore,byquotingtheshapeparameterinthecurve’sfunctioninthechap
5、tertwo,andchangingtheparametervaluetoadjustthecurveshape.Inaddition,throughthesmoothconnectionbetweenthecurvestoachieveabetterexpressionforthecomplexcombinationcurves.Firstofall,aclassofquarticBernsteinbasisfunctionwiththreeparametersispresentedasanextensionofthequart
6、icBernstein.PropertiesareanalyzedandthequasiBézierwiththreeshapeparametersisdefinedbasedonit.ThecurveinheritingtheoutstandingpropertiesofquarticBéziercurve,andthesmoothconnectionbetweencurvesareanalyzed.Someexamplesillustratethatthedefinedcurveprovidesaneffectivemetho
7、dfordesigningcurvesandsurfaces.Secondly,usingtheBézierb-splinecurve‘sconstructingmethodandapplyingtheBéziercurvesplicing012technology,thesmoothG、G、GconnectionbetweenuniformBsplinecurveandBeziercurvecometrue.Thirdly,usingthemutualtransformationbetweentheNURBScurveandra
8、tionalBeziercurve,transformingtheconnectionbetweenquadraticBeziercurveandcubicnon-uniformb-splinecurveintoaquadraticBeziercu
