DefinePK

Abstract

In this study, we explore the interaction of two Laurent polynomials to generate a new polynomial through multiplication. Introducing a parameter allows us to adjust the number of factors within this polynomial, thereby facilitating the creation of a diverse family of non-stationary subdivision schemes. Each distinct value of the parameter corresponds to a unique member of this scheme family. Additionally, leveraging the concept of asymptotic equivalence, we derive a separate family of stationary schemes. Following the derivation of stationary schemes, we proceed to analyze their key characteristics and practical applications. This includes detailed examination of properties such as convergence behavior, polynomial generation degree, reproduction capabilities, continuity, and the structure of limit stencils. Furthermore, we explore the practical applications of these schemes in generating smooth curves.