A computer mouse for providing commands to create both two-dimensional (2D) and three-dimensional (3D) movements and manipulations of objects as projected on a 3D display. The computer mouse comprises an input device including conventional button/wheel and trackball controllers and a mode switch for toggling between 2D operation and 3D operation. The computer mouse also includes an external processor responsive to the command signals and mode signal from the input device, and functions to translate the received signals into cursor actions on an associated 3D display.