The 3D visibility complex
Frédo Durand, George Drettakis, Claude P. Puech · ACM Transactions on Graphics · 2002
Visibility problems are central to many computer graphics applications. The most common examples include hidden-part removal for view computation, shadow boundaries, mutual visibility of objects for lighting simulation. In this paper, we present a theoretical study of 3D visibility properties for scenes of smooth convex objects. We work in the space of light rays, or more precisely, ofmaximal free segments. We group segments that "see" the same object; this defines the3D visibility complex. The boundaries of these groups of segments correspond to thevisual eventsof the scene (limits of shadows, disappearance of an object when the viewpoint is moved, etc.). We provide a worst case analysis of the complexity of the visibility complex of 3D scenes, as well as a probabilistic study under a simple assumption for "normal" scenes. We extend the visibility complex to handle temporal visibility. We give an output-sensitive construction algorithm and present applications of our approach.