数控加工中NURBS曲线的小线段离散方法

针对将NURBS曲线离散成连续小线段轨迹问题，提出局部等弦长、等弦差、偏转角可控的离散算法.分别对等弦长、等弦差离散算法进行仿真，验证这两种算法的优缺点；结合弦长、弦差和偏转角之间的耦合关系，提出对NURBS曲线进行区域分割，实现离散后的小线段轨迹局部等弦长、等弦差，轨迹相对光顺.利用平面光栅进行实验验证，实验结果表明：利用该算法，离散后的小线段轨迹可以很好地逼近原NURBS曲线，并且保证轨迹相对光顺.
A new method is proposed to solve the problem of NURBS curve separation. Firstly, both of the equal chord length and the equal error separation algorithms are simulated to verify the advantages and disadvantages. Given the relationships among chord length, error and deflection angle, the separation of the NURBS curve is proposed. The algorithm guarantees the chord length and error remaining unchanged, and the deflection angle stays in a feasible range. Then some simulations are carried out to test the correctness of the algorithm. At last, the plane grating is used to make an experience to verify the algorithm. Experimental results indicate that the continuous line segments can approach the NURBS curve with the proposed algorithm accurately and the fitting location is smooth. The proposed approach can discrete the NURBS curve into the continuous line segments effectively.