Machining system (10) comprising a facility comprising: - a real tool (12);- actuators (14) for displacing the real tool (12); - sensors (15) for generating positioning data (16) for the real tool (12); - a memory (17) for storing correction data in respect of the geometry (20) of the real tool (12); - a physical controller (18) for executing a machining program (19) and commanding the actuators (14), as a function of the data for correction of geometry (20), to displace the real tool (12) with respect 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), means for displaying images (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.