Subdivision Algorithm of A Type aß-Bezier Curve

Splines with shape parameters have stronger expression ability than the traditional splines. In this paper, a alpha ss-Bezier curve with shape parameters are studied. A necessary condition for obtaining subdivision algorithms based on De Casteljau algorithm for general parameter curves is given. Under this condition, it was verified that the alpha ss-Bezier curve cannot calculate the control points of the subdivided sub-curves through De Casteljau algorithm. The alpha ss-Bezier curve subdivision algorithm was provided by the mutual transformation relationship between the alpha ss-Bezier curve and the classical Bezier curve. The two sub-curves are defined by the two sets of control points obtained through the subdivision algorithm and alpha ss-Bezier basis functions. The algorithm is simple, intuitive, and easy to operate. Calculation examples also demonstrate the feasibility and effectiveness of the algorithm.