An Improved B-Spline Fitting Method with Arc-Length Parameterization, G2-continuous Blending, and Quality Refinement

Abstract

In computer numerical control machining, tool paths are typically represented with piecewise linear segments (GO1s), which lack G1 and G2 continuity and cause fluctuation of feed rate and acceleration. To improve the continuity of tool paths, some method, e.g., B-spline tool path fitting, is preferred. However, none of the currently B-spline fitting method satisfies all tool-path fitting requirements of arc-length parameterization, G2 continuity and smoothness across the whole path. The aim of this research is to derive an industrial-strength method for B-spline tool path fitting, satisfying all of the named requirements. The improvements cover the arc-length based parameterization, G2 continuity as well as numerically measure to improve the quality of B-spline tool paths. To achieve arc-length parameterization, a preliminary fitting is added to evaluate arc-length and guide the parameterization (i.e., knot vector assignment); for joint G2-continuity, a five-control-point B-spline which satisfies chord error and shape-preserving constraints is constructed to blend adjacent B-splines; and a method based on the Hausdorff distance between the fitted B-splines and the original polylines is used to evaluate the fitting quality, and an additional refinement procedure is employed when the evaluation finds any disqualification. Simulation and experiment results prove that the proposed methods are effective.