有理q-Bernstein-Bzier曲线的构造及其应用  

Construction and application of rational q-Bernstein-Bézier curves

作　　者：黄日朋[1] 

机构地区：[1]滁州学院数学系,安徽滁州239000

出　　处：《计算机应用》2010年第5期1359-1362,共4页journal of Computer Applications

基　　金：滁州学院科研基金资助项目(2008kj014B)

摘　　要：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.

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 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]