Geometric simulation of locally optimal tool paths in three-axis milling
  The most important aim in tool path generation methods is to increase the machining efficiency by minimizing the total length of tool paths while the error is kept under a prescribed tolerance. This can be achieved by determining the moving direction of the cutting tool such that the machined stripe is the widest. From a technical point of view it is recommended that the angle between the tool axis and the surface normal does not change too much along the tool path in order to ensure even abrasion of the tool. In this paper a mathematical method for tool path generation in 3-axis milling is presented, which considers these requirements by combining the features of isophotic curves and principal curvatures. It calculates the proposed moving direction of the tool at each point of the surface. The proposed direction depends on the measurement of the tool and on the curvature values of the surface. For triangulated surfaces a new local offset computation method is presented, which is suitable also for detecting tool collision with the target surface and self intersection in the offset mesh. 
M\'arta Szilv\'asi-Nagy, Gyula M\'aty\'asi, Szilvia B\'ela
cs.CG cs.CE math.NA