One embodiment of the present invention provides a system that facilitates manipulating a 2D window within a three-dimensional (3D) display model. During operation, the system receives an input from a 2D pointing device, wherein the input specifies a 2D offset within a 2D display, and wherein the 2D display provides a view into the 3D display model. Next, the system uses the 2D offset to move a cursor to a position in the 2D display, and then determines if the cursor overlaps a window within the 3D display model. If so, the system determines a 2D position of the cursor with respect to a 2D coordinate system for the window, and communicates this 2D position to an application associated with the window. This enables a user of the 2D pointing device to interact with the application.