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 inputs to the surface, wherein the 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 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 inputs to the surface by the real-time performer.