Abstract: A set of cubic trigonometric polynomial function with two parameters is presented as an extension of cubic Bernstein basis functions.The quality of the new basis is analyzed.Based on the new basis，the trigonometric polynomial curve with two shape parameters is defined.The new curve not only holds many applied geometrical qualities of Bézier curve，but also can rectify the shape.When the control polygon is fixed，different approximation to the control polygon with the changing of shape parameters α and β are given.The circle and ellipse is represented with this curve accurately.G1 and G2 condition of cubic TC- Bézier curves and examples in surface model are presented，which is more useful in free curve and surface design.

Key words: TC-Bézier curve, shape control parameters, continuity, curve design

摘要： 给出一组含有两个参数的二次三角多项式基函数，它是三次Bernstein基函数的扩展；分析了这组基函数的性质。定义了带有两个形状参数的三角多项式曲线，它不仅具有 Bézier 曲线的一些实用的几何特性，而且具有形状的可调性。在控制多边形不变的情况下，通过改变参数α和β，可以生成不同的逼近该控制多边形的曲线，并可以精确表示圆弧、椭圆弧等。由于带有两个参数，所以具有更加灵活的形状控制能力。给出了曲线间的G₁、G₂拼接条件以及在曲线造型中的应用实例，为自由曲线设计提供了一种有效的方法。

关键词: TC-Bézier曲线, 形状参数, 拼接, 曲面造型