A depth camera and an optional visual camera are used in conjunction with a computing device and projector to display a presentation and automatically correct the geometry of the projected presentation. Interaction with the presentation (switching slides, pointing, etc.) is achieved by utilizing gesture recognition/human tracking based on the output of the depth camera and (optionally) the visual camera. Additionally, the output of the depth camera and/or visual camera can be used to detect occlusions between the projector and the screen (or other target area) in order to adjust the presentation to not project on the occlusion and, optionally, reorganize the presentation to avoid the occlusion.