The present disclosure discloses a three dimensional (3D) display apparatus and a control method for the 3D display apparatus, the 3D display apparatus comprising: a liquid crystal optical grating located on a liquid crystal display module, wherein the liquid crystal optical grating is provided with a respective probe terminal on each of the four corners of an electrode layer thereof, for detection of an electric current value; and a controller signally connected with the four probe terminals, wherein the controller is used for calculation of a touch point position of a touch object on the 3D display apparatus based on the electric current values detected at the four probe terminals. The 3D display apparatus has both a 3D display function and a touch screen function.