A Family of 5-Point Nonlinear Ternary Interpolating Subdivision Schemes with C-2 Smoothness

The occurrence of the Gibbs phenomenon near irregular initial data points is a widely known fact in curve generation by interpolating subdivision schemes. In this article, we propose a family of 5-point nonlinear ternary interpolating subdivision schemes. We provide the convergence analysis and prove that this family of subdivision schemes is C-2 continuous. Numerical results are presented to show that nonlinear schemes reduce the Gibbs phenomenon significantly while keeping the same order of smoothness.