简介:OneofthecentralquestionsinCAGE^[1]isblendingsurfaceswhichprovidesthetheoreticalbasisforthedesigntechnologyofspacesurfaces.Wewilldiscussthegeneraltheoriesandalgorithmsformultivariatehyperfiniteinterpolationandtheirapplicationtotheblendingofimplicitalgebraicsurfaces,andinvestigatetheexistenceconditionsofhyperfiniteinterpolation.BasedonWu'stheoryonblendingimplicitalgebraicsurfaces,theproblemofblendingtwoquadricsurfacesisstudied.TheconditionsforthecoefficientofgiunderwhichthereexiststhecubicblendingsurfaceS(f)(thelowestdegree)areobtainedandtheconcreteexpressionsoffarepresentedistheyexist.TheseresultscanbeapplieddirectlytoCAGD.