Abstract: A method for dividing a workpiece into elements includes: a pulsed laser beam of an ultrashort pulse laser is directed onto a workpiece composed of brittle-hard material; instances of filamentary damage are introduced next to one another along a path. The distance between the instances of filamentary damage at least in one portion of the path is selected such that one of the following conditions is met: (i) the difference in terms of magnitude between the characteristic fracture strengths of the element upon bending in opposite directions in this portion is at most 10 MPa; (ii) the difference in terms of magnitude between the characteristic fracture strengths of the element upon bending in opposite directions in this portion is at least 30 MPa; and (iii) the difference in terms of magnitude between the fracture strengths upon bending of the element in opposite directions is at least 30 MPa*d[mm]*?/3.

Abstract: A method for controlling a tool, including the steps: providing a reference matrix including reference points and a centering matrix including centering points in a material processing plane; imaging the material processing plane through a camera as a camera image in a size of a camera image field; de-skewing the camera image of the material processing plane by aligning with the reference matrix; scaling a pixel size of the camera image through aligning with the reference matrix; centering the camera image through aligning with the centering points; projecting a processing contour onto the de-skewed and scaled camera image of a workpiece; and aligning the processing contour on the camera image of the work piece and starting the processing, wherein the processing of the work piece is performed though the tool along the processing contour.