Precise global collision detection in multi-axis NC-machining

We introduce a new approach to the problem of collision detection in multi-axis NC-machining. Due to the directional nature (tool axis) of multi-axis NC-machining, space subdivision techniques are adopted from ray-tracing algorithms and are extended to suit the peculiarities of the problem in hand. We exploit the axial symmetry inherent in the tool's rotational motion to derive a highly precise polygon/surface-tool intersection algorithms that, combined with the proper data structure, also yields efficient computation times. Other advantages of the proposed method are the separation of the entire computation into a preprocessing stage that is executed only once, allowing more than one toolpath to be efficiently verified thereafter, and the introduced ability to test for collisions against arbitrary shaped tools such as flat-end or ball-end, or even test for interference with the tool holder or other parts of the NC-machine.