简介:AmethodconstructinqC~1Piecewisequinticpolynomialoveratriangulargridtointerpo-latefunctionvaluesandpartialderivativesatverticesispresentedinthispaper.Thesetofprecisepoly-nomialsofthismethodisdiscussed.
简介:AnewmethodisproposedforsurfaceconstructiononirregularquadmeshesasextensionstouniformB-splinesurfaces.Givenanumberofcontrolpoints,whichformaregularorirregularquadmesh,aweightfunctionisconstructedforeachcontrolpoint.TheweightfunctionisdefinedonalocaldomainandisC1continuous.Thenthewholesurfaceisconstructedbytheweightedcombinationofallthecontrolpoints.ThepropertyofthenewmethodisthatthesurfaceisdefinedbypiecewiseC1bi-cubicrationalparametricpolynomialwitheachquadface.ItisanextensiontouniformB-splinesurfacesinthesensethatitsdefinitionisananalogyoftheB-splinesurface,anditproducesauniformbi-cubicB-splinesurfaceifthecontrolmeshisaregularquadmesh.Examplesproducedbythenewmethodarealsoincluded.
简介:Afamilyofpiecewiserationalquinticinterpolationispresented.Eachinterpolationofthefamily,whichisidentifieduniquelybythevalueofaparameterαi,isofC2continuitywithoutsolvingasystemofconsistencyequationsforthederivativevaluesattheknots,andcanbeexpressedbythebasisfunctions.InterpolantisofO(hr)accuracywhenf(x)?Cr[a,b],andtheerrorshaveonlyasmallfloatingforabigchangeoftheparameterαi,itmeanstheinterpolationisstablefortheparameter.Theinterpolationcanpreservetheshapepropertiesofthegivendata,suchasmonotonicityandconvexity,andaproperchoiceofparameterαiisgiven.
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