A Novel Approximation Method for Noncircular Curves Based on Hausdorff Distance

Parts with conic boundaries are commonly used in aerospace, mold, and gear industries. However, after tool radius compensation, the resulting curve often differs from the original parametric equations. Conventional computer numerical control (CNC) systems typically support only linear and arc interpolation. Therefore, computer-aided manufacturing (CAM) systems use short line segments to approximate the curve boundaries for machining code generation. This approach requires a large number of short line segments to achieve the desired accuracy, resulting in numerous G01 codes with very short machining lengths. For conventional machine tools lacking look-ahead functionality or velocity planning, this can lead to reduced processing efficiency and increased machine impacts. To tackle this challenge, this chapter introduces a high-accuracy approximation method called Hausdorff distance-based approximation (HDBA). This method first selects the appropriate type of approximate curve based on the geometric characteristics of discrete points. Next, it adapts the approximate curve length according to the Hausdorff distance between the original and approximate curves. The performance of HDBA is evaluated against typical tasks and compared with other methods. Results show that HDBA achieves a shorter approximation curve length and minimizes approximation error, improving surface quality in wire electrical discharge machining (WEDM) and enhancing efficiency in die-sinking EDM processes.