Innovations in reconstruction and rendering of panoramic video are described. For example, a view-dependent operation controller of a panoramic video playback system receives an indication of a view direction for an application and, based at least in part on the view direction, identifies a section of a picture of panoramic video in an input projection. The view-dependent operation controller limits operations of a color converter, video decoder, and/or streaming controller to the identified section. In this way, the panoramic video playback system can avoid performing operations to reconstruct sections of the picture of panoramic video that will not be viewed. As another example, a mapper of a panoramic video playback system re-projects at least some sample values in an input flat projection towards a center location for a view direction, producing an output flat projection, which an application can use to generate one or more screen projections.