五次C-曲线的细分

Subdivision for C-curves of degree five

五次C-曲线是定义在空间Ω=span{1,t,t2,t3,sint,cost}上的一类曲线,它可以表示自由形式的曲线,例如圆.给出了五次C-曲线的细分公式,并且证明了细分过程产生的控制多边形序列收敛于原曲线.在收敛性的基础上,还证明了五次C-曲线的一些重要性质,例如变差缩减性和保凸性.

C-curves of degree five are defined over the space Ω=span {1,t,t^2,t^3,sin t, cos t}.They can deal with some free-form curves,such as circles.An effective subdivision formula for C-curves of degree five is presented.Furthermore,it is proved that the control polygons generated by the subdivision converge to the original C-curve of degree five.Some important properties are proved for C-curves of degree five,such as convexity preserving and the variation diminishing (V-D) properties.