A constructive approach has been adopted to build interpolatory and freeform cubic spline curves with a more general continuity than Beta-continuity. This method provides not only a large variety of very interesting shape controls like biased, point and interval tensions but, as a special, also recovers a number of spline methods like Nu-splines of Nielson ,Beta-splines ,Gamma-splines of Boehm and weighted Nu-splines . A discussion, for the conversion of complex continuity constraints into simple ones, has also been made for the practical implementation point of view.