A class of quasiquartic trigonometric polynomial Bézier curves with a shape
parameter is presented. The curve is controlled by five points, and it has a lot of similar
characteristics with the traditional quartic Bézier curve, and its shape can be adjusted by a
parameter, which makes the curve feature more powerful expression ability. The shape
parameter affects the property of geometry, the larger is the parameter, and the more of the
curve approaches the control polygon, therefore, the trigonometric polynomial curve with the
shape parameter can be close to the given control polygon than the quartic Bézier curve. The
new curve can represent exactly the arc of circle, arc of ellipse, arc of parabola and other
quadratic curves without using a rational form. For designing free curves, the G2 and C3
continuity condition of twopiece curves are also discussed. The modeling examples illustrate
that the new curve has a high application value for computer aided geometric design.