Discrete point curve reconstruction method based on PCHIP and G1 continuous

LIU Yu, ZHU Zhi-song, ZHAO Xu, ZHANG Zi-li
（School of Mechanical Engineering, Nantong University, Nantong 226019, China）

Abstract: 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.

Key words: piecewise cubic Hermite interpolation polynomial (PCHIP); biarc; sponge cutting; discrete point reconstruction