A New Ternary Interpolatory Subdivision Scheme for Polyhedral Meshes with Arbitrary Topology

interpolation using ternary subdivision is an attractive characteristic in geometric modeling due to its advantage over commonly used binary subdivision. In this paper, a new ternary interpolatory subdivision scheme with one parameter based on arbitrarily triangular meshes is proposed. It can be used to any polyhedral meshes with arbitrary topology. The sufficient conditions of the convergence and the tangent plane continuity of the presented subdivision scheme are obtained using geometric methods and algebraic manipulations. It is simple, fast and has a better local property in comparison with the existing ternary interpolatory surface subdivision schemes.