A method and system are provided for drawing or writing using an input device in computer systems. The system provides an absolute-coordinate drawing mode, in which the user may draw written strokes to which the computer system display is responsive, and a relative-coordinate repositioning mode, in which the user may figuratively “pick up the pen” and reposition the beginning of a following written stroke. The system enters the drawing mode in response to a user command, and remains in the drawing mode in response to continued written strokes. The system enters the cursor mode after a selected time period occurs with no written strokes, or in response to other user commands. In the drawing mode, a coordinate system for the touchpad is mapped to a coordinate system for a selected window on the display. The mapping is selected so that an initial position of a written stroke in the window corresponds to a final position selected during the cursor mode, so that the user is able to reposition the input device when it has (or is about to) “run off the edge” of an input tablet which is relatively smaller than the display. The system uses either a resistive touchpad input tablet, or a capacitive touchpad input tablet in conjunction with a passive stylus input device having a flexible conductive writing tip. The system alternatively provides a signature mode, in which the user is able to make a simple drawing, such as a handwritten signature.