Abstract: This paper studies the technique of smooth connections between cubic TC-Bézier curves and surfaces with two shape parameters and cubic H-Bézier curves and surfaces.Based on a study of their basis functions,endpoint properties and shape analysis,we present G¹ continuity connection conditions between TC-Bézier and H-Bézier curves and surfaces,as well as G² continuity connection condition between TC-Bézier and H-Bézier curves at a special case.Experimental examples show that smooth connections between the curves and surfaces can be effectively applied in complicated curve and surface design by adjusting the shapes of the curves and surfaces through selecting parameters reasonably.