广义Ball基函数的对偶基及其应用

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1、合肥工业大学硕士学位论文广义Ball基函数的对偶基及其应用姓名：江平申请学位级别：硕士专业：计算机辅助几何设计指导教师：邬弘毅;檀结庆2003.3.1广义Ball基函数的对偶基及其鹿用摘要本文筵分为鞠章。第一章赍绍Said．Ball趣线靛定义及其性质。剥惩Said。Ball基鼹数豹对援(泛函)基。得到幂撩函数在Said-Ball基下的Marsden恒等式，及从B6zier曲线到Said-Ball曲线的转换．并给出Said．Ball曲线的降阶赋值算法．筹=肇套缨Wang-Ball錾线熬定义及瞧震，鞋及Wang-Ball麴线静遂

2、鼷求藿算法胙者在

3、这里荫次给出Wang-Bail基函数的对偶泛函，并由此导出从Bemstein基到Wang-Ball基的显式表示．第三搴奔绍Said-Bdzicr壅广义Ball麴线(楚稼为SBGB鍪莹线)定义，这类曲线包括Said-Ball越线、Bdzier鼬线及若们的递归算法，SBGB基函数的对偶泛函，鏊函数转换公式．就多}，还讨论了sBGB髓线豹毽络及细势算瘘、／√第蹬辈奔缨Wang—Said型广义Ball曲线(WSGB夔线)戆定义，憩类鏖骞线雹据Wang-Bail曲线、Said-Bail曲线及另外若千条中间曲线。以及它们的递归算法．棒者在醋数的转按公式．

4、2．构造出WSGB基函数的对偶泛函，并应用WsGB褥弱另一耱方法实现WSGB整线麓B6zier魏线静甄籀转化要结果：WSGB基的对偶泛函，关键词：Bgzier曲线，Said-Bail曲线，Wang-Ball曲线，SBGB曲线，WSGB曲线，对偶蘩DualbasisfunctionsforgeneralizedBallbasisanditsapplicationsAbstractThethesisiscomposedoffourchapters，InChapteronetheauthorgivesthedefinitionoftheSaid-B

5、allcurvesandtheirproperties．Bymeansofthedual(functional)ofSaid-Bailbasis，theMagsdenidentityisgotintermsofSaid-Ballbasis，andadegreereductionalgorithmforSaid-Ballcurvesispresented妞onghthetransformfromBgfiercurves协Said-Bailcurves，ChaptertwoisfocusedontheWang-BaitcBl-ves，includ

6、ingdefinition，propertiesandrecursionalgorithms．TheauthorderivesthedualfunctionaloftheWang-BallbasisforthefirsttimeandthenobtainstheexplicitexpressionofWang-BallbasisintermsoftheBemsteinbasis．TheemphasisofChapterthreeislaiduponthegeneralizedBallellivesofSaid-Beziertype(SBGBC

7、lLrves)whichincludesSaid·Ballcurves，B6ziercurvesandsomeoftheirintermediatecurvesasspecialCases．Thecontentsinvolvethereeursionalgorithms。thedualfunctionalofSBGBbasisandthetransformationformulabetweenSBGBbasisandBemsteinbasis．羽耱coBvexhuIlofSBGBandsubdivisionaigorithmsarealSOd

8、iscussed．Lastbutnotleast，generalizedBallcurvesoftheWang-SaidtypeCVVSGBcurves)ale{ntroducedinChapterfour．ItlspointedoutthatWang-Ballcurves。Said-Bailcurvesandsomeotherintermedlatecurvesarea11membersoftheWSGBfamily．Bymaking鑫thoroughstudyofWSGBcurves,theauthoracquirestwomainres

9、ults,i．e。，the衄ansfOrmationformulafromBemsteinbasistoWSGBbasisandtheconstructionoft