Shape Preservation of Ternary 4-point Non-Stationary Interpolating Subdivision Scheme

Abstract

The paper suggests conditions for preserving the shape properties of the original data using the ternary 4-point non-stationary interpolating subdivision scheme. Sufficient conditions with a suitable selection of the starting tension parameter are determined, which guarantee to retain the properties of positivity, monotonicity and convexity from the initial data to the curves generated for a limited number of iterations. The obtained results are significantly extended in the limiting case for maintaining such shape properties in the limit functions. The geometric interpretation of results is depicted through different numerical examples.