Trigonometric extension of quartic Bézier curves

A class of quasi-quartic trigonometric polynomial Bezier curves with two shape parameters is presented The trigonometric polynomial curves have the same characteristic with traditional quartic Bezier curves, and it can represent exactly some quadratic curves such as the arc of circle, arc of ellipse, arc of parabola without using rational form. Its shape can be adjusted locally or totally through changing the value of the two parameters, and approach to the given control polygon from both sides. The G² and C³ continuity condition of two pieces of curves is discussed. Examples are given to illustrate that the new curve has high applied value in model design.