Recently, projector camera systems have been used actively for image synthesis and for 3D reconstruction. For using the projector camera systems in these applications, it is very important to compute the geometry between projectors and cameras accurately. Recently, it has been shown that by using the mutual projection of cameras, multiple cameras are calibrated quite accurately. However, this property cannot be used for projector camera systems, since projectors are light-emitting devices and the projection of cameras cannot be obtained in projector images. In this paper, we show that by using the shadow of cameras and the shadow of projectors generated by projector light, we can generate virtual mutual projections between projectors and cameras, and projectors and projectors. These virtual mutual projections can be used for calibrating projector-camera systems quite accurately. Furthermore, the calibration can be achieved without using any 3D points unlike the existing calibration methods. The accuracy of the proposed method is evaluated by using real and synthetic images