Abstract: A process for graphically representing a simulated workpiece as processed by a numerically-controlled machine tool. Stored data defining the workpiece and the tool as well as program data defining relative movement therebetween are used to generate polygons which represent the workpiece and the tool and the path of movement of the tool. These polygons are hierarchically ordered and liked. Corresponding to the hierarchic order of the polygons, intersection point calculations in the linkage are made only for the workpiece polygons which overlap the tool polygon. The image of the processed workpiece is generated successively through the continuous superposition of the changing workpiece polygons with the processing polygons corresponding to the tool and its path. Workpiece edges which drop out are erased, and invisible workpiece edges are nto represented.