Abstract: Rational Bernstein-Bézier curve has been applied widely in computer-aided design and computer graphics. To construct a kind of rational q-Bernstein-Bézier curves based on classical Bernstein-Bézier curves, de Casteljau algorithm and q-Bernstein polynomials were studied. Some properties, the algorithm for computing curves, the technique concerning subdivision and degree elevation of curves were also discussed. A family of rational Bernstein-Bézier curves could be obtained by changing the value of q. The results indicate that the rational curves have strong flexibility. At last, the generalization of rational q- Bernstein-Bézier curves was proved to be effective by conic curve and representation digital image interpolation.

Key words: rational curve, de Casteljau algorithm, curve subdivision, curve degree elevation, conic curve, image interpolation

摘要： 有理Bernstein-Bézier曲线在计算机辅助设计和计算机图形学上具有广泛的应用。在研究了经典的Bernstein-Bézier曲线及de Casteljau算法的基础上，结合q-Bernstein多项式，给出了有理q-Bernstein-Bézier曲线的构造方法、性质和计算有理曲线的de Casteljau算法，并讨论了曲线的细分和升阶的方法，通过改变q的取值，可以获得有理曲线族，在曲线造型上具有较强的灵活性。最后通过表示圆锥曲线和数字图像插值证明有理q-Bernstein-Bézier曲线的推广是有效的。

关键词: 有理曲线, de Casteljau算法, 曲线细分, 曲线升阶, 圆锥曲线, 图像插值