q-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q-$$\end{document}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.