A 3D display device with controllable device for tracking visibility regions is disclosed, and includes a controllable device for tracking a visibility region, generated by way of superposition of light source images, in a observer plane of the display device. In preferred embodiments, the cladding of a waveguide comprises at least one material with optical properties of an anisotropic liquid, or at least two materials with optical properties of an isotropic liquid; a matrix arrangement of control electrodes defines multiple positions to be generated for local exit points in the cladding of the waveguide at which the total reflection is locally cancelled; and a system controller modifies positions of the output coupling points for superposing the output-coupled light through the lens array to the visibility region by displacing an output coupling point, or by switching off one output coupling point and switching on another one.