In exemplary implementations of this invention, a handheld, collapsible input device (CID) may be employed by a user to input and manipulate 3D information. The CID telescopes in length. As a user presses the CID against a display screen, the physical length of the CID shortens, and the display screen displays a virtual end of the CID that appears to project through the screen into the virtual 3D space behind the screen. The total apparent length of the CID, comprised of a physical portion and a virtual portion, remains the same (after taking into account foreshortening). Thus, the user experience is that, as the user holds the physical CID and pushes it against the display screen, the end of the CID appears to be pushed through the display screen into the virtual 3D space beyond it. The CID housing may include a push button for user input.