A Simple Point-based Iso-Scallop Tool Path Planning Method for Noisy Point Clouds with High Robustness and Controlled Errors

Abstract

With the rapid advances in 3D scanning and vision technologies, point clouds have seen a significant increase in their application to CNC machining. As an important way to generate tool paths from point clouds, point-based direct planning methods are, however, now restricted to high-quality point clouds. Most existing methods would have robustness issues if a noisy point cloud is given due to their reliance on the noise-sensitive estimation of differential properties from point clouds. Error control under noisy point clouds is also rarely considered. This paper presents a robust and error-controlled point-based iso-scallop tool path planning method for CNC machining with ball-nosed cutters. It casts the problem of searching for scallop/CL points to another problem of finding circle-sphere intersection points and the maximum/minimum among them. Both circle-sphere intersections and max/min comparisons are easy to implement and robust. It has also been theoretically proved that the intersections and comparisons can ensure an error bound of 2ϵ on the final results if two conditions called ϵ-sampling and ϵ-covering are met. The effectiveness of the method has been demonstrated by a series of examples and comparisons.