A Non Uniform Non-stationary Mixed Trigonometric and Hyperbolic Subdivision Scheme with Variables Parameters

This study proposes a new family of non-uniform subdivision schemes with one shape parameter and two sets of tension parameters. The scheme enables effective and hierarchical curve generation. The asymptotic equivalence approach and property A are used to analyze the convergence and regularity of the suggested schemes. They produce very encouragingly numerical results. Moreover, by taking into account instances that show how the shape parameter is assigned with sets of tension parameters and control points to replicate such well-controlled curves, the effectiveness of our approach has been demonstrated in this context.