Visibility map for global illumination in point clouds

Point-sampled geometry has gained significant interest due to their simplicity. The lack of connectivity touted as a plus, however, creates difficulties in many operations like generating global illumination effects. This becomes especially true when we have a complex scene consisting of several models. The data is often hard to segment as individual models and hence not suitable for surface reconstruction. Inter-reflections in such complex scenes requires knowledge of visibility between point pairs. Computing visibility for point models is all the more difficult (than for polygonal models), since we do not have any surface or object information. We present in this paper a novel, hierarchical, fast and memory efficient algorithm to compute a description of mutual visibility in the form of a visibility map. Ray shooting and visibility queries can be answered in sub-linear time using this data structure. We evaluate our scheme analytically, qualitatively, and quantitatively and conclude that these maps are desirable.