Contents I. Introduction
As is well known, the classical Bernstein polynomials of order n for f ∈ C[0,1] is defined as , x ∈ [0,1], where \begin{equation*}b_k^n(x) = {\binom n k }{x^k}{(1 - x)^{n - k}},\quad n,k \geq 0,\tag{1}\end{equation*} are called the Bernstein basis functions. Due to the Bernstein polynomials possess many remarkable properties, such as shape-preserving properties, they play important roles not only in approximation theory, but also in CAGD. As we know, the famous Bézier curves and surfaces are based on these Bernstein basis functions. Nowadays, the study of Bézier curves and surfaces is still in the ascendant, some methods of generating triangular patch were presented by using shape parameters, we mention some of them as [1]–[5].
