2D NURBS Curve discretization method with double constraints of area and chord error and contour accuracy prediction modeling

Abstract

The short segment discretization algorithm for complex curves is one of the critical factors in improving the quality and efficiency of economical CNC machine tools. However, traditional single constraint methods such as equal error and equal chord length algorithms cannot achieve the requirements of both quality and efficiency, and intelligent methods with high algorithmic complexity are unsuitable for traditional machining. To this end, a simple and effective method for generating short segment trajectories called area-chord error double constraint is presented in this paper. The area enclosed by the trace of the short line segment and the original curve is defined as area error, and the semicircle with chord length as the diameter is defined as constrained area. By controlling the ratio of the area error to the constrained area, short line segment separation with variable chord length and error can be achieved according to the curvature characteristics. The influence mechanism of short line segmentation on curves is investigated and the contour accuracy prediction model is established through 70 irregular curves from simple to complex. The experimental results show that this method can retain more geometric features of the original curve on the premise of fewer feature points so as to achieve both processing precision and efficiency.