Abstract: Two new classes of curves with shape parameters are defined. The first class of curve contains the quintic Wang-Ball and Said-Ball curves and the curves located between them. The second class of curve contains the quintic Said-Ball and Bézier curves and the curves located between them. By analyzing the relationship between the new curves and the quintic Bézier curve, the geometric meaning of shape parameters are obtained, and the geometrical drawing method of the new curves are given.

Key words: Wang-Ball basis function, Said-Ball basis function, Bernstein basis function, Ball curve, shape parameter