一種多形狀參數(shù)四階均勻B樣條的研究.pdf

1、洳。≥≥j碩士畢業(yè)論文⑧論文題目=鹽壘墅鑒叁塾望險(xiǎn)塑壘墜搓盤(pán)絲盈壅培養(yǎng)單位逝姿盤(pán)堂鏊莖莖學(xué)科(專(zhuān)業(yè))座周塑鱟作者姓名左垡焦指導(dǎo)教師汪國(guó)昭檻二零零六年五月浙江大學(xué)碩士學(xué)位論文⑧AbstractCompmeraidedgeome缸cdesign(CAGD)servesthetechniqueofcomputeraideddesign(CAD)andisapowerfultooltoprovidemathematicmodelsforthed

2、esignofCADThesplinetheoriesandmemodshavebeentheimportantbasictheoriesandcentralcontentsofthetechniqueofCAGDInthispaperwegiveakindofunifolmBsplinebasisfunctionoffourorderwithtwoindependentandthreeindependentshapeparameter

3、sandmakealotofresearchesonthiskindofuniformB—splineFirstlyweintroducethedevelopmenthistoryandbackgoundofparametercurvesandsurfacesmodelingwithshapeparameterandthepmpeItiesofthecubicuniformB—splinefunctionThecubicuniformB

4、—splineC1Lrvehassomegoodpropertiesingeometricmodeling，suchassimpleshape，flexibilityandwideapplicationinmanyfieldsThenwegiveaclassofuniformBsplineof4orderand5degreewimmultiparameterinshapeinthethirdchapterandthefo曲chapter

5、wegivethedefinitionsoftheuniformB—splinefunctionoffourorderbasedontwoindependentshapeparametersandtheuniformB—splinefunctionoffourorderinthreeindependentshapeparametersWeprovetheseuniformBsplinebasisfunctionswiththreeorf

6、ourshapeparametersarepositiveinsomecasesandthecubicuniformB—splinebasisisaspecialkindofthesemulti—shapeparameterfunctionsThentheuniformBsplinecurvesoffourorderwiththreeorfourshapeparameterspossesstheSalnegeometricpropert

7、iesandterminalpointpropertiesofthecubicuniformB—splinecurve，WecallalsoprovethatthegeneratedcurvesareC2continuousandG2continuousBychangingthe砌ueoftheparameterwecangetdifferentcurvesindifferentshapesandlocationsSothemethod

8、sofdesigningcurveswillbemoreflexibleandvariousItisdifficulttodesignsurfacewimtheseuniformB—splinefunctionsoffourorderwithmultishapeparameterHowtouseparametersmoreeffectivelywillbeanotherimportantproblemtostudyinthefuture