中文摘要：

文章基于一类广义Bernstein基函数定义了圆域有理q-Bezier曲线，通过改变参数q的取值，可以得到一类有理q-Bezier曲线簇，并研究了该类曲线的基本性质及De Casteljau型算法，用二次有理q-Bezier曲线可精确表示圆锥曲线。该方法比现有方法更加灵活，且表示范围更大。数值实例表明，圆域有理q-Bezier曲线的研究具有一定的理论意义与应用价值。

英文摘要：

Disk rational q-Bezier curves are presented using a class of generalized Bernstein basis. A family of disk rational q-Bezier curves can be obtained by changing the value of parameter q. The basic properties of this kind of rational curves are discussed. De Casteljau type algorithm of disk rational q- Bezier curves is also considered. The quadratic disk rational q-Bezier curve can be used to represent conic section accurately. The proposed method is more flexible than the existing methods, and it indi- cates a larger range. Some numerical examples demonstrate that the study of disk rational q-Bezier curves is of theoretical importance and practical significance.