Properties of ($\lambda, q$)-Bézier Curves and Surfaces

In this paper, we introduce a new type q-Bernstein basis functions with shape parameter λ, named ( λ, q)-Bernstein bases, we give a practical algorithm of curve modeling by these basis functions. We also give some geometric properties of the basis functions and the corresponding ( λ, q)-Bézier curves. Furthermore, we construct the corresponding tensor product surfaces over the rectangular domain and study the properties of the surfaces.