Innovations in reconstruction and rendering of panoramic video are described, including the use of a platform rendering engine to provide a screen projection based on a view direction specified for an application through an interface. For example, based at least in part on the view direction specified for the application, at least a section of panoramic video in an input projection is identified. At least some of sample values of the at least a section of the picture of panoramic video in the input projection are mapped to a screen projection. The screen projection is output for display to a buffer for the application. Thus, an application may use panoramic video, including updating a view direction, without itself having to render a screen projection for the panoramic video.