A new type of the generalized Bézier curves

In this paper, we improve the generalized Bernstein basis functions introduced by Han, et al. The new basis functions not only inherit the most properties of the classical Bernstein basis functions, but also reserve the shape parameters that are similar to the shape parameters of the generalized Bernstein basis functions. The degree elevation algorithm and the conversion formulae between the new basis functions and the classical Bernstein basis functions are obtained. Also the new Q-Bézier curve and surface...