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This study presents a generalized approach to Bézier curves and surfaces by utilizing the blending (α , λ , s) -Bernstein basis. The (α , λ , s) -Bernstein basis introduces shape parameters α , λ , and s, which allow for more flexibility and control over the curve's shape compared to the classical Bernstein basis. The paper explores the properties of these generalized curves and surfaces, demonstrating their ability to maintain essential geometric characteristics, such as convex hull containment and endpoint interpolation, while providing enhanced control over the shape. This work aims to contribute to the fields of computer-aided geometric design and related applications by offering a robust tool for curve and surface modeling. [ABSTRACT FROM AUTHOR]