Interval Extension of Bézier Curve

By extending definition interval of the classical Bernstein basis functions to be dynamic, a class of Bernstein basis functions with a shape parameter is constructed in this work. The new basis functions are simple extension of the classical Bernstein basis functions. Then the corresponding Bezier-like curve is generated on base of the introduced basis functions. The new curve not only has most properties of the classical Bezier curve, but also can be adjusted by altering value of the shape parameter when the control points are fixed. Because the proposed curve is a polynomial model of the same degree and having most properties of the classical Bezier curve, it has more advantages than some existing similar models.