有理q-Bernstein-Bzier曲线的构造及其应用

Construction and application of rational q-Bernstein-Bézier curves

有理Bernstein-Bzier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-Bzier曲线及deCasteljau算法的基础上,结合q-Bernstein多项式,给出了有理q-Bernstein-Bzier曲线的构造方法、性质和计算有理曲线的deCasteljau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-Bzier曲线的推广是有效的。

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.