AnewmethodisproposedforsurfaceconstructiononirregularquadmeshesasextensionstouniformB-splinesurfaces.Givenanumberofcontrolpoints,whichformaregularorirregularquadmesh,aweightfunctionisconstructedforeachcontrolpoint.TheweightfunctionisdefinedonalocaldomainandisC1continuous.Thenthewholesurfaceisconstructedbytheweightedcombinationofallthecontrolpoints.ThepropertyofthenewmethodisthatthesurfaceisdefinedbypiecewiseC1bi-cubicrationalparametricpolynomialwitheachquadface.ItisanextensiontouniformB-splinesurfacesinthesensethatitsdefinitionisananalogyoftheB-splinesurface,anditproducesauniformbi-cubicB-splinesurfaceifthecontrolmeshisaregularquadmesh.Examplesproducedbythenewmethodarealsoincluded.
