A virtual reality or augmented reality experience may be presented for a viewer through the use of input including only three degrees of freedom. The input may include orientation data indicative of a viewer orientation at which a head of the viewer is oriented. The viewer orientation may be mapped to an estimated viewer location. Viewpoint video may be generated of a scene as viewed from a virtual viewpoint with a virtual location corresponding to the estimated viewer location, from along the viewer orientation. The viewpoint video may be displayed for the viewer. In some embodiments, mapping may be carried out by defining a ray at the viewer orientation, locating an intersection of the ray with a three-dimensional shape, and, based on a location of the intersection, generating the estimated viewer location. The shape may be generated via calibration with a device that receives input including six degrees of freedom.