1. A system for determining a placement of a virtual object in a performance space according to a performance by a real-time performer, the system comprising: a projection module including a polarizing filter, the projection module configured to generate a polarized visible image corresponding to the virtual object; a surface for displaying the polarized visible image, the surface viewable by the real-time performer; a detection module for detecting touch inputs to the surface, wherein the touch inputs are provided by the real-time performer based on a location of the polarized visible image on the surface; and a mapping module configured for mapping a location of each of the touch inputs to the surface to a corresponding point in the performance space, for the placement of the virtual object in the performance space according to the locations of the touch inputs to the surface by the real-time performer; a reverse-polarizing filter, the reverse-polarizing filter configured to reverse-polarize images of the performance by the real-time performer and the polarized visible image displayed on the surface to produce reverse-polarized images; and wherein the reverse-polarizing filter is further configured to block the polarized visible image from a viewer of the performance.