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The visual hull is a geometric entity that relates the shape of an object to its silhouettes or shadows. This paper develops the theory of the visual hull of generic smooth objects. We show that the visual hull can be constructed using surfaces which partition the viewpoint space of the aspect graph of the object. The surfaces are those generated by the visual events tangent crossing and triple point. An analysis based on the shape of the object at the tangency points of these surfaces allows pruning away many surfaces and patches not relevant to the construction. An algorithm for computing the visual hull is outlined.