Abstract: A set of cubic polynomial function with two shape parameters was presented as an extension of cubic DP basis functions. The properties of the new basis were analyzed. The generalized cubic DP curve with two shape parameters was defined using the new basis. The new curve not only retains many properties of cubic DP curve,but also can adjust the shape by moderating shape parameters or u. Based on the some given condition, the two section curves can be G^2 or C^2-continuous between adjacent generalized cubic DP curves,which is useful for free curve and surface design.

Key words: Cubic DP curve, Shape parameter, Geometric continuous, Parameter continuous