Abstract: The invention relates to machines and methods for the separative machining of a plate-shaped workpieces. The machine includes a first movement device for moving the workpiece in a first direction (X), a second movement device for moving a machining head, which directs the machining beam onto the workpiece, along a second direction (Y), Between workpiece bearing faces there is formed a gap for the passage of the machining beam. In the machine, mutually facing side edges of at least two of the workpiece bearing faces are oriented non-perpendicularly and non-parallel with respect to the first direction (X).

Abstract: 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.