Methods and apparatus to render 3D content within a moveable region of a display screen. An example apparatus includes a projection system controller adapted to be coupled to a light source and to be optically coupled to a screen panel, the projection system controller configured to determine a location of a region within a viewing area of the screen panel to display content. The region is to be smaller than the viewing area. The location of the region is to move within the viewing area to track a motion path, the content including different stereoscopic views. The projection system controller configured to activate the light source to project light corresponding to the content toward the region. The screen panel includes a light redirecting surface to produce a 3D light field associated with the different stereoscopic views.