Convexity preservation of the interpolating four-point C2 ternary stationary subdivision scheme

Since subdivision schemes can generate curves and surfaces rapidly, they are widely used in the curve and surface modeling. Such topic is one of the important research fields in computer aided geometric design. The convexity preserving properties of the interpolating four-point ternary subdivision scheme are discussed in this paper. The conditions on the parameter of the scheme to preserve convexity are given. The parameter locates in the interval , thus the limit curve generated by the scheme is C2.