Abstract: Two classes of polynomial basis of 3th and 4th degree are presented. They are extensions of cubic Ball basis. Based on these two bases, two polynomial curves with shape parameters are defined. They not only inherit the outstanding properties of the cubic Ball curve, but also are adjustable in shape and fit closer to the control polygon than the cubic Ball curve. The geometrical meaning of shape parameters is discovered by analyzing the connection of the new curves and the Bézier curve. Meanwhile, the geometrical drawing method of the extension curves is given out.

Key words: computer application, curve design, Ball curve, shape parameter