C-Bézier曲线降阶的B网扰动和约束优化法

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次次C-Bézier曲线的条件.在满足退化条件的约束下,使n次C-Bézier曲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.

Degree reduction of C-B(e)zier curves based on disturbance of B netand constrained optimization

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.