基于PCHIP与G 1连续的离散点曲线重构方法研究

Discrete point curve reconstruction methodbased on PCHIP and G1 continuous

为了更加充分地使用现有海绵切割数控系统中的圆弧插补功能,保证加工曲线的顺滑性,提出了双圆弧逼近分段三次Hermite插值多项式(PCHIP)拟合的样条曲线的重构方法。使用PCHIP拟合的海绵加工坐标文件中符合要求样条区间的离散点,建立了基于最小误差的双圆弧几何模型与误差模型,基于设计余量等分与整体递增分割逼近方案,借助Python数据处理模块,获得了组成样条曲线的圆弧,最后对两种方案的圆弧段数与逼近误差进行了对比。研究结果表明:重构的曲线最大程度地还原了设计曲线;在设定的误差范围之内,曲线分段较少,圆弧间光滑连接,可实现平稳加工。

In order to made full use of the circular interpolation function in the existing sponge cutting CNC system,and ensured the smoothness of the processing curve,a method of approximating the spline curve fitted by piecewise cubic Hermite interpolation polynomial(PCHIP)with biarc was proposed.The discrete points in the spline interval that met the requirements in the sponge processing coordinate file were fitted by PCHIP fitting,the biarc geometric model and error model based on the minimum error were established.Approximation schemes of margin equalization and global incremental segmentation were designed.With the help of the Python data processing module,the arc of the composed spline curve was obtained,and the numbers of arc segments and approximating error between the two schemes were compared.The results indicate that the reconstructed curve restores the design curve to the greatest extent.Within the set error range,the curve has fewer segments and the arcs are smoothly connected,which can realize stable machining.