A system that includes a flat panel display that can change three-dimensional orientation in a continuous way, such as when the display is horizontally rotated on a turntable. Position or orientation of the display relative to a reference orientation is sensed by orientation sensors coupled to the display. A computer compares the orientation of the display to a fixed reference orientation. When the orientation of the display has changed from the reference, the computer maps the orientation of a user interface onto the display in such a way as to maintain the same orientation of the interface with respect to the reference. User input through an overlaid input device correlates to the oriented user interface. In this way if the display is rotated into, for example, a sideways or upside-down orientation, the user interface elements will still be displayed in a normal upright orientation for the user and the user inputs in a normal manner. When multiple users interact with the display, the orientation of each user with respect to the reference is tracked by the computer and the particular user's interface orientation is maintained constant with respect to the particular user's reference.