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1、合肥工業(yè)大學(xué)碩士學(xué)位論文廣義Ball基函數(shù)的對偶基及其應(yīng)用姓名：江平申請學(xué)位級別：碩士專業(yè)：計算機輔助幾何設(shè)計指導(dǎo)教師：鄔弘毅;檀結(jié)慶2003.3.1廣義Ball基函數(shù)的對偶基及其鹿用摘要本文筵分為鞠章。第一章赍紹Said．Ball趣線靛定義及其性質(zhì)。剝懲Said。Ball基鼴數(shù)豹對援(泛函)基。得到冪撩函數(shù)在Said-Ball基下的Marsden恒等式，及從B6zier曲線到Said-Ball曲線的轉(zhuǎn)換．并給出Said．Ball曲線的降階賦值算法．籌=肇套纓Wang-Ball鏨線熬定義及瞧震，鞋及Wang-Ball麴線靜遂
2、鼷求藿算法胙者在
3、這里蔭次給出Wang-Bail基函數(shù)的對偶泛函，并由此導(dǎo)出從Bemstein基到Wang-Ball基的顯式表示．第三搴奔紹Said-Bdzicr壅廣義Ball麴線(楚稼為SBGB鍪瑩線)定義，這類曲線包括Said-Ball越線、Bdzier鼬線及若們的遞歸算法，SBGB基函數(shù)的對偶泛函，鏊函數(shù)轉(zhuǎn)換公式．就多}，還討論了sBGB髓線豹毽絡(luò)及細(xì)勢算瘺、／√第蹬輩奔纓Wang—Said型廣義Ball曲線(WSGB夔線)戇定義，憩類鏖騫線雹據(jù)Wang-Bail曲線、Said-Bail曲線及另外若千條中間曲線。以及它們的遞歸算法．棒者在醋數(shù)的轉(zhuǎn)按公式．
4、2．構(gòu)造出WSGB基函數(shù)的對偶泛函，并應(yīng)用WsGB褥弱另一耱方法實現(xiàn)WSGB整線麓B6zier魏線靜甄籀轉(zhuǎn)化要結(jié)果：WSGB基的對偶泛函，關(guān)鍵詞：Bgzier曲線，Said-Bail曲線，Wang-Ball曲線，SBGB曲線，WSGB曲線，對偶蘩DualbasisfunctionsforgeneralizedBallbasisanditsapplicationsAbstractThethesisiscomposedoffourchapters，InChapteronetheauthorgivesthedefinitionoftheSaid-B
5、allcurvesandtheirproperties．Bymeansofthedual(functional)ofSaid-Bailbasis，theMagsdenidentityisgotintermsofSaid-Ballbasis，andadegreereductionalgorithmforSaid-Ballcurvesispresented妞onghthetransformfromBgfiercurves協(xié)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
