五次C-Bézier曲线的生成及其性质

Generation and properties about quintic C-Bézier curves

以sint,cost,t3,t2,t,1为基底构造了一组类似于Bernstein多项式的基函数,它们依赖于参数a,用这组基函数表示的自由曲线称为五次C-Bézier曲线,它不仅具有一般五次Bézier曲线所具有的各种几何性质,同时又可以精确地表示一些圆锥曲线,例如圆弧甚至整圆.

In this paper,a group of basis functions similar to the Bernstein polynomials are generated on the bases of sint,cost,t^3,t^2,t,1,and the curves represented by these basis functions are called quintic C-Bézier curves.They not only have almost every property of ordinary quintic Bézier curves,but can give the exact representation of conic sections as well.