$$q-$$Bézier Curves with Shifted Nodes

This article explores the applications of q-calculus in polynomial basis functions and curve modeling. We define the properties of q-Bernstein Cholodowsky basis polynomials. A novel approach to Bézier curves is introduced, utilizing basis polynomials to create generalized curves with shape-preserving properties. Additionally, the article presents degree elevation and De Casteljau algorithms tailored for these curves.