A method of cutting openings in flat, concave, convex, and converging surfaces, in which the geometry of the outline of the element to be welded into the workpiece is measured, while subsequently an electronic control unit of the device uses the measurement data to plot the path of the cutting tool, and the IMCM device is placed onto the work surface, where the geometry of the work surface is measured using a scanning system, cutting parameters are automatically entered into the control unit based on the measurement results, the surface is heated and cut along the selected path, the cut-out part of the surface is removed, and the edges of the cut-out opening are grinded.