There is described a method with which, on the basis of a three-dimensional recording of a component to be reworked, its surface configuration can be determined and stored temporarily so that, after it has been coated, it can be produced in its original surface form, or in its surface form then required, in certain regions, i.e. locally in the area of film-cooling openings. An especially precise and quick three-dimensional recording can be achieved by the use of the triangulation method. In this case, a reference pattern depicted on the component by a projector is recorded by two camera arranged at an angle. From the images from the cameras, the coordinates describing the surface three-dimensionally can then be determined by a control system using the triangulation method.