Bézier curves and surfaces with multiple shape parameters

In this paper,a class of quartic polynomial basis functions with multiple shape parameters is constructed.It is the extension of quadric Bernstein basis functions.The properties of this class of basis functions are analyzed and a polynomial curve with multiple parameters is defined based on it.The defined curve not only inherits the properties of Bezier curves,but it is also adjustable in the shape with different parameters under the same controlling vertex and fits close to the control polygon.And the classical quadratic Bezier curve and the curves in the related literature are the special cases of this paper.Moreover,the tensor product method is used to extend the curve to surface.Some examples show that the curve and surface defined in this paper provide an effective method for designing curves and surfaces.