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=鹽壘墅鑒叁塾望險塑壘墜搓盤絲盈壅培養(yǎng)單位逝姿盤堂鏊莖莖學科(專業(yè))座周塑鱟作者姓名左垡焦指導教師汪國昭檻二零零六年五月浙江大學碩士學位論文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