C-Bézier曲线降阶逼近

Degree reduction of C-Bézier curves

给出了基于L2范数下用m次(m≤n)C-Bzier曲线最小平方逼近n+1次C-Bzier曲线的方法,同时也考虑了C0和C1约束条件下的最小平方降阶逼近.通过解线性方程组可得到新的降阶逼近曲线的控制顶点,降阶逼近曲线的误差也可计算.

A method for constructing an approximative C-Bezier curve of degree m （m≤n） to a C-Bezier curve of degree n＋1 by L2-norm is provided. At the same time, the problems of least squares degree reduction of C-Bezier curves in C^0 and C^2 constraint condition are analysized. The new control points of approximation C-Bezier curve can be confirmed by solving linear equations and the error can also be computed.