三點(diǎn)三次三角樣條函數(shù)與曲線的研究.pdf

1、中南工業(yè)大學(xué)碩士學(xué)位論文三點(diǎn)三次三角樣條函數(shù)與曲線的研究姓名：吳曉勤申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：韓旭里2000THESTUDYOFCUBICTR隊(duì)NGUALSPLINEFUNCTIoNANDCURVEWITHTHREEDoTSAbstract：PolynomialsareusuallyusedasthebasicfunctionforthefittingofcurvesandsurfacesinCAGD，Inthispap

2、er，Weproposeamethodoffitting／interpolationwhichbasesontriangualfunctions，Thesebasicfunctionsarecalled耳(￡)(，=0，1，2；0≤t≤詈)，Weusethemconstractcurveiscalled“IS—carve，constructfunetioniScalledTSfunctionTscurvenotonlycontmnspr

3、opertyofendpointthatconicB—splineCurvehas，butalsocon—rainsthepropertyofC3_continuity，andmoveitcontainsthepropertyofconvexhull、VDandSOonBesides，ThesegmentofTS—curveisonlyrelatedtothreecontrolVertexIfwedealwithcontrolVerte

4、x，Itwillgeneratescusp，linesegment，closedcurve，andwecaninterpolatewithIS—curveWecandeveloptheTSCUlWetoTSsurfacewiththetensorproductmethod，ThesesurfacecontmnC3continuityTS—functionissurpefiortocubicmoguangsplinefunctionTS—

5、curve／surfavcewhichweproposeisfitfordesignoffreeCUlTeSandsurfacesEspecilly，Intheeaseoflocalcontinuitymustbehighorder，ItisagoodmethodTSfunctionownssoombetterpropertiesinthefittingofpreservingInthispaper，TheFirstchapterist

6、hesummariesofrefmnces。whichelaboratethestudyofB—splineandtrangualsplineatpresent；InthesecondchapterweintmduceTs—curve(surface)’sdefonitionanddiscuss“IScurve(surface)’spropertiesAtlastwedisCUSSthepropertiesof“IS—functiona