Continuity and Error Estimate of 4-Point Ternary Stationary Subdivision Scheme

In 2002,Dr.Hassan presented a novel approach named for 4-point ternary stationary subdivision scheme.Compared with Dyn’s 4-point scheme,the limit curve generated by Hassan’s approach reaches C² continuity.We studied the same topic with great care and worked out the necessary conditions and sufficient conditions for the C⁰,C¹,C² situations of limit curve.During the derivation,we obtained the explicit expression of the first and second order derivative for limit curve at vertex and mid-point.As the scheme can reproduce polynomials of degree≤2,so it has an error of order O（h³）.