A numerically controlled machine tool, and method for control thereof, to display virtual two-dimensional future positions to be adopted by a workpiece and by the machine tool in a pre-set predictive time window. The system and method calculate target coordinate values defining positions of the tool along axes of the machine tool on the basis of a machining program. While machining is in progress, a processor receives the calculated target coordinate values to generate and display image data on the basis of the target coordinate values and of stored mathematical models of the machine, of the workpiece, and of the tool.