简介:Inthispaper,thesmoothconnectionbetweentwoB-splinesurfacesisdiscussed.First,abriefproofofsomesimplesufficientconditionsofG~0andG~1continuityisgiven.Onthisbasis,anovelmethodforG~0orG~1connectionbetweentwoadjacentB-splinesurfacesispresented.Areparameterizationstepisfirstlytakenforoneofthesurfacessuchthattheyhavethesameparameterizationinvdirection,then,adjusttheirboundarycontrolverticestomakethemG~0orG~1connected.TheG~1connectionparameterisdeterminedbyanoptimizationproblem.Comparedwiththeexistedmethods,ourmethodissimpleandeasytobeusedinpractice.
简介:TheexplicitexpressionoftheG~3basisfunctionispresentedinthispaper.ItisderivedbyconstructingtheconversionmatrixbetweenG~3basisfunctionandBézierrepresentation.Afterthematrixdecomposition,equationsforconstructingG~3splinescanbepresentedindependentlyofgeometricshapeparameters’values.Itmakestheequation’ssolvingeasier.ItisalsoknownthatthegeneralformoftheG~3splinebasisfunctionisgiveninthefirsttime.Itsgeometricconstructionmethodispresented.