Quartic Bézier curves and surfaces with shape parameters

A new polynomial base function of 4th degree with shape parameters is presented which includes the common quartic Bernstein basis function. Properties of this new base function are analyzed and the corresponding polynomial curve and surface with shape parameters are defined. They inherit the most properties of quartic Bezier curves and surfaces and degenerate to them when shape parameters are 1. Moreover the shape of the curve and surface can be adjusted entirely or locally through changing the values of the shape parameters when the control points are maintained. Examples illustrate that this method of constructing curves and surfaces is useful in CAGD.