There is presented a system for determining a placement of a virtual object in a performance space according to a performance by a real-time performer. The disclosed system comprises a projection module including a polarizing filter, the projection module configured to generate a polarized visible image corresponding to the virtual object. The system includes a surface for displaying the polarized visible image to the real-time performer. The system also includes 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. The system further comprises a mapping module configured for mapping a location of each input 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 inputs to the surface by the real-time performer.