Abstract: A class of quasi-quartic trigonometric polynomial Bézier curves with two shape parameters of λ1 and λ2 is presented. The trigonometric polynomial curves have the same featurs with traditional quartic Bézier curves, and it can represent exactly some quadratic curves such as the arc of a circle, an ellipse, or a parabola and some transcendental curves such as circular helix without using rational form. Its shape can be adjusted locally or totally through changing the value of the two parameters, and it can approach to the given control polygon from both sides. The G2 and C4 continuity condition of two pieces of curves is discussed. Examples are given to illustrate the new curve in model design.

Key words: Bézier curves, trigonometric polynomial, quasi-quartic, shape parameter, continuity