Curve Fitting of NURBS Curve for CNC Motion Controller

Abstract

This paper proposes a real-time coplanar Non-Uniform Rational B-Spline (NURBS) curve fitting in a CAD/CAM system to improve fitting quality and reduce calculation effort. Curve segmentation is applied to filter the line segments and reshape the different NURBS curve segments. Both position errors and the first derivative are considered to avoid over fitting of the NURBS curve. After the fitted NURBS curve is obtained, the corresponding interpolation for each interpolated time is further processed to obtain the motion command for each axis. The real-time NURBS curve fitting process consists of (1) discrete points import, (2) linear segment filter, (3) curve reshaping, (4) curve fitting considering both the position errors and the first derivative. Simulation results show the proposed approach effectively improves the fitting quality and calculation efficiency.