The 3D Visibility Complex

Frédo Durand 1, 2 George Drettakis 1, 3 Claude Puech 1
1 iMAGIS - Models, Algorithms and Geometry for Computer Generated Image Graphics
GRAVIR - IMAG - Graphisme, Vision et Robotique, Inria Grenoble - Rhône-Alpes
3 REVES - Rendering and virtual environments with sound
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : 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, of maximal free segments. We group segments that "see" the same object; this defines the 3D visibility complex. The boundaries of these groups of segments correspond to the visual events of 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.
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Frédo Durand, George Drettakis, Claude Puech. The 3D Visibility Complex. ACM Transactions on Graphics, Association for Computing Machinery, 2002, 21 (2), pp.176-206. ⟨10.1145/508357.508362⟩. ⟨inria-00606717⟩

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