A head-up display and techniques for operating a head-up display for a motor vehicle. An assignment is obtained of at least one virtual object that can be displayed to a part of the environment. The head-up display may be operated in a normal display mode when the object assigned to the part of the environment is within a field of view for the head-up display. The head-up display is then operated in an alternative display mode when the object assigned to the part of the environment is not, or not entirely, contained within the field of view for the head-up display, wherein a virtual display is generated in the alternative display mode.