Generalized Bezier Curves Based on Lupaş q-Analogue of the Bernstein Operator

In this thesis, we study the Bezier curves and their properties. Bezier curves are one of the most important curves in Computer-Aided Geometric Design (CAGD). Bernstein functions are the basis of the Bezier curves. Therefore, we investigate the Lupaş 𝑞���- analogue of Bernstein functions, their properties and corresponding Lupaş 𝑞���-Bezier curves and their useful properties. Finally, we have studied the de Casteljau algorithms of Lupaş 𝑞���-Bezier curve and the upgrade procedure. Keywords: Bernstein polynomials, Bezier curve, de Casteljau algorithms, degree elevation, Lupaş 𝑞���-Bezier curve, Lupaş 𝑞���-Bezier surface, Lupaş q-analogue of Bernstein operator