The reaction between designer, and design needs modified methods to control the
design. This paper presents modified mathematical technique for controlling the
generation of the 2D designs of third degree, by using modified Gallier of Bezier
curves. The paper discuses a polynomial in terms, of polar forms, with respect to the
parameter. The modified method has resulted in good starting point, to generate
which 2D design, algorithm which allows the designer to produce a design in
combinational way allows him to get the shape that he has in his mind keeping the
four control points for 2D design. The method shows a great flexibility in 2D design
controlling area with changing. There is no need to change the control points of the
design; moreover efficiency in designs is obtained in comparison with that needed for
conventional methods.
Keywords: Gallier of Bezier curves, B-Spline Curves.