A surface navigation device for a computer or similar graphical display and methods for implementing its operation. The device moves sensitively and precisely over a surface such as a desktop and operator generated changes in its position relative to targetable objects on that desktop arranged about the circumference of a pseudo-circle are described in terms of a lumped motion vector. The motion vector is decomposed into a translational and rotational part by metrical and topological methods. The device communicates each part of the decomposed motion quickly and accurately to a computer screen or other display where it may implement the motion of a cursor or it may be used to manipulate objects having a 3D character by providing them with translational and rotational motions. The rotational parameter generated by the device may also be used independently to trigger some computer action.