三次B样条曲线用于二维激光切割

The Application of Third Order B Spline Interpolation to Two Dimensional Laser Cutting

采用计算几何中的高次曲线样条插补的方法解决光滑程度要求高，且加工速度快的二维激光切割问题．推导了三次B样条曲线的矩阵形式，从理论上证明了三次B样条曲线具有二阶连续性．如果插入一个点，只影响局部曲线，不影响整条曲线，因此有利于工程实现与应用．上述结论已在实际系统中进行了推广．

The high order curvilinear spline interpolation method derived from computational geometry has been applied to the two dimensional laser cutting to meet the requirement of strict smoothness and high speed. The matrix formation of third order B spline curve is derived. It is proved that there is second order continuity in third order B spline curve. An inserted dot only affects the local curve,not the whole curve. This will make the method easily to be realized and applied in engineering processing. The conclusion has been applied in a real cutting system.