Techniques are described for machining flat workpieces, such as metal sheets, or three-dimensional workpieces on a processing machine, such as a machine tool or laser cutting machine, including capturing a live image of a workpiece to be machined with an image capturing device for capturing two-dimensional images; displaying at least one workpiece machining operation to be performed in the live image of the workpiece by a predetermined forward transformation of the workpiece machining operation from the three-dimensional machine coordinate system into the two-dimensional live-image coordinate system; repositioning the workpiece machining operation to be performed in the live image of the workpiece; and performing the workpiece machining operation on the workpiece by a predetermined inverse transformation of the repositioned workpiece machining operation from the two-dimensional live-image coordinate system into the three-dimensional machine coordinate system.