A novel Bézier curve with a shape parameter of the same degree

In this paper, we construct a class of Bernstein basis functions with a shape parameter of the same degree by extending definition interval of the classical Bernstein basis functions to be dynamic. Then, we define the corresponding Bézier curve based on the introduced basis functions. The new curve not only has most properties of the classical Bézier curve, but also can be adjusted in shape by altering the value of the shape parameter when the control points are remained unchanged. The proposed curve is simpler than some existing similar models, which is a novel extension of the Bézier curve.