A device for monitoring, in particular for regulating, a cutting process on a workpiece, comprising: a focusing element for focusing a high-energy beam, in particular a laser beam, onto the workpiece, an image capture apparatus for capturing a region at the workpiece to be monitored, said region comprising an interaction region of the high-energy beam with the workpiece, and an evaluation apparatus embodied to determine at least one characteristic variable (α) of the cutting process, in particular of a kerf formed during the cutting process, on the basis of the captured interaction region, wherein the evaluation apparatus is embodied to determine a cutting front angle (α) of the kerf and/or an overshoot and/or undershoot of a predetermined cutting front angle (α G) of the kerf as characteristic variable(s) of the cutting process on the basis of the captured interaction region, and wherein the device further comprises: a control apparatus for regulating the cutting front angle (α) to a predetermined constant value (α G) by influencing at least one control parameter (v, P) of the cutting process, characterized in that the control apparatus is embodied to select the control parameter (v, P) for regulating the cutting front angle (α) in a manner dependent on a contour (31, 34) to be cut into the workpiece wherein the control apparatus is embodied to influence the advance speed (v) between the high-energy beam and the workpiece as a control parameter for regulating the cutting front angle (α) if the advance speed (v) is restricted to a maximum value (v MAX) by the material and the thickness of the workpiece and is not restricted to a maximum value (v MAX) by the geometry of a contour to be cut into the workpiece, and wherein the control apparatus is embodied to influence the power of the high-energy beam as a control parameter for regulating the cutting front angle (α) if the advance speed (v) between the high-energy beam and the workpiece is restricted to a maximum value (v MAX) by the geometry of a contour to be cut into the workpiece. a focusing element for focusing a high-energy beam, in particular a laser beam, onto the workpiece, an image capture apparatus for capturing a region at the workpiece to be monitored, said region comprising an interaction region of the high-energy beam with the workpiece, and an evaluation apparatus embodied to determine at least one characteristic variable (α) of the cutting process, in particular of a kerf formed during the cutting process, on the basis of the captured interaction region, wherein the evaluation apparatus is embodied to determine a cutting front angle (α) of the kerf and/or an overshoot and/or undershoot of a predetermined cutting front angle (α G) of the kerf as characteristic variable(s) of the cutting process on the basis of the captured interaction region, and wherein the device further comprises: a control apparatus for regulating the cutting front angle (α) to a predetermined constant value (α G) by influencing at least one control parameter (v, P) of the cutting process, characterized in that the control apparatus is embodied to select the control parameter (v, P) for regulating the cutting front angle (α) in a manner dependent on a contour (31, 34) to be cut into the workpiece wherein the control apparatus is embodied to influence the advance speed (v) between the high-energy beam and the workpiece as a control parameter for regulating the cutting front angle (α) if the advance speed (v) is restricted to a maximum value (v MAX) by the material and the thickness of the workpiece and is not restricted to a maximum value (v MAX) by the geometry of a contour to be cut into the workpiece, and wherein the control apparatus is embodied to influence the power of the high-energy beam as a control parameter for regulating the cutting front angle (α) if the advance speed (v) between the high-energy beam and the workpiece is restricted to a maximum value (v MAX) by the geometry of a contour to be cut into the workpiece.