廣義Ball基的全正性及三角域與矩形域上曲面片的轉(zhuǎn)化.pdf

1、合肥工業(yè)大學(xué)碩士學(xué)位論文廣義Ball基的全正性及三角域與矩形域上曲面片的轉(zhuǎn)化姓名：汪峻萍申請學(xué)位級別：碩士專業(yè)：計算數(shù)學(xué)指導(dǎo)教師：鄔弘毅20040501TotalPositivityofGeneralizedBallBases&ConversionbetweenTriangularandRectangularSBGBPatchesAbstractThethesislscomposedoffourchaptersThefirsttwoch

2、aptersarefocusedontheSaid—BallandWang—Ballcurves，includingtheirdefinitions，propertiesandexplicitconversionformulastotheB6zierrepresentation，theauthoralsopointsoutthattheSaidBallbasisisNTPTheemphasisofthenexttwochaptersar

3、elaiduponthetwonewfamiliesofthegeneralizedBallbaseswhichareintroducedbyWuHongYi，ie，Said—B6ziertypegeneralizedBall(SBGB)basesandWangSaidtypegeneralizedBall(WSGB)bases，thecurvesconstructedonthesebasesincludetheB6ziercurve，

4、theSaid—Ballcurve，theWall—BallcurveandsomeintermediatecurvesThesecurveshavemanythepropertiessimilartotheonesoftheB6ziercurveBymakingafurtherstudyofSBGBcurves，theauthoracquirestwomainresultsnamely：1Usingacorner—cuttingalg

5、orithm，thisthesisshowsthattheSBGBbasesarenormalizedtotallypositive(TNP)，andtheWSGBbasesarenotTNP2ThisthesisalsopresentsanexplicitformulathatconvertsatriangularSBGBpatchofdegree月toadegeneraterectangularSBGBpatchofdegreenH