A machining system (10) comprising a machine comprising: real tool (12); actuators (14) for moving the real tool (12); sensors (15) for generating positioning data (16) for the real tool (12); a memory (17) for storing shape correction data (20) for the real tool (12); and a physical controller (18) for executing a machining program (19) and for controlling the actuators (14) as a function of the shape correction data (20), so as to move the real tool (12) relative to the real blank (13). On the basis of said data (22) representative of the positions of the real tool (12) and of the real blank (13), image display means (24) generate a reconstituted image (25) representative: of the shape of the real blank (13); and of the position of the real tool (12) at a given instant.