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

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.