This paper deals with the autocalibration of a system that consists of a planar screen, multiple projectors, and a camera. In the system, either multiple projectors or a single moving projector projects patterns on a screen while a stationary camera placed in front of the screen takes images of the patterns. We treat the case in which the patterns that the projectors project toward space are assumed to be known (i.e., the projectors are calibrated), whereas poses of the projectors are unknown. Under these conditions, we consider the problem of estimating screen-to-camera homography from the images alone. This is intended for cases where there is no clue on the screen surface that enables direct estimation of the screen-to-camera homography. One application is a 6DOF input device; poses of a multi-beam projector freely moving in space are computed from the images of beam spots on the screen. The primary contribution of the paper is theoretical results on the uniqueness of solutions and a noniterative algorithm for the problem. The effectiveness of the method is shown by experimental results on synthetic as well as on real images.