C-Bézier曲线降阶的B网扰动和约束优化法  

Degree reduction of C-Bézier curves based on disturbance of B net and constrained optimization

作　　者：王文涛[1] 

机构地区：[1]嘉兴学院数学与信息工程学院,浙江嘉兴314001

出　　处：《高校应用数学学报（A辑）》2009年第4期418-424,共7页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：浙江省教育厅青年教师资助项目(00505163);浙江省教育厅科研项目(20070602)

摘　　要：基于B网扰动和约束优化方法,对n次C-Bézier曲线控制多边形顶点进行扰动,并找到其退化为n-1次C-Bézier曲线的条件。在满足退化条件的约束下,使n次C-Bézier线控制多边形顶点扰动量最小,由此找到降阶为n-1次的C-Bézier曲线,同时也研究了在C^0,C^1连续条件下对n次C-Bézier曲线降阶的B网扰动和约束优化方法,给出了扰动显示格式计算方法和降阶逼近的误差估计式。Based on disturbance of B net and constrained optimization, the control polygon vertexes of n degree C-Bézier curve are disturbed and the condition of its degenerating n - 1 degree C-Bézier curve is found. With the degeneracy condition minimizing the disturbance of control polygon vertexes of n degree C-Bézier curve, the n - 1 degree reduction of C-Bézier curve can be gained. Moreover, the problems of degree reduction of C-Bézier curve under C^0 and C^1 constraint conditions are also studied. The disturbances of control polygon vertexes can be computed exactly and the error estimate of the degree reduction approximation is provided.

关 键 词：降阶 C-BÉZIER曲线 约束优化 扰动 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]