Surface Modeling by Using a New Ternary Interpolatory Subdivision Scheme Based on Arbitrary Triangular Control Mesh

A ternary subdivision scheme based on arbitrary triangular control mesh is proposed and analyzed in this paper.The sufficient conditions of the convergence property and G¹continuity property of the new subdivision scheme are obtained and proved.In comparison with the existing ternary interpolatory subdivision schemes of surface,the presented subdivision scheme is simple and has a better local property；the corresponding smooth subdivision surfaces can also be generated quickly.