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

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