The rise of Unmanned Aerial Vehicles and their increasing use in the cinema industry calls for the creation of dedicated tools. Though there is a range of techniques to automatically control drones for a variety of applications, none have considered the problem of producing cinematographic camera motion in real-time for shooting purposes. In this paper we present our approach to UAV navigation for autonomous cinematography. The contributions of this research are twofold: (i) we adapt virtual camera control techniques to UAV navigation; (ii) we introduce a drone-independent platform for high-level user interactions that integrates cinematographic knowledge. The results presented in this paper demonstrate the capacities of our tool to capture live movie scenes involving one or two moving actors.