The 3D Visibility Complex: A New Approach to the Problems of Accurate Visibility

Visibility computations are central in any computer graphics application. The most common way to reduce this expense is the use of approximate approaches using spatial subdivision. More recently analytic approaches efficiently encoding visibility have appeared for 2D (the visibility complex) and for certain limited cases in 3D (aspect graph, discontinuity meshes). In this paper we propose a new way of describing and studying the visibility of 3D space by a dual space of the 3D lines, such that all the visibility events are described. A new data-structure is defined, called the 3D visibility complex, which encapsulates all visibility events. This structure is global and complete since it encodes all visibility relations in 3D, and is spatially coherent allowing efficient visibility queries such as view extraction, aspect graph, discontinuity mesh, or form factor computation. A construction algorithm and suitable data structures are sketched.