Tool path planning on triangular mesh surfaces based on the shortest boundary path graph

In this paper, a new method is developed for tool path planning on triangular mesh surfaces with consideration of the scallop height restriction and the path smoothness. This method first maps the triangular mesh surface into a unit disk region by using a harmonic map algorithm, and then the shortest boundary path graph (SBPG) is constructed on the unit disk region to describe the shortest geodesic distance from each mesh vertex to the surface boundary. The tool path is then obtained by inversely mapping the contours of SBPG from the harmonic mapped region to the physical space of mesh surface. During this process, a subdivision method is used to boost the computing efficiency and a smoothing treatment is conducted on the SBPG to improve the path smoothness. The tool path planning is performed starting from the surface boundary in an iteration process. Taking the level difference of SBPG contours as the initial path interval and being supplemented by a correction process, the maximal step distance between any two paths, which meets the requirement of scallop height restriction, can be determined efficiently. Typical simulation cases and experiments are carried out to illustrate the effectiveness of the proposed method.