On the Size of the 3D Visibility Skeleton: Experimental Results

The 3D visibility skeleton is a data structure used to encode global visibility information about a set of objects. Previous theoretical results have shown that for k convex polytopes with n edges in total, the worst case size complexity of this data structure is Θ(n2k2) [Brönnimann et al. 07]; whereas for k uniformly distributed unit spheres, the expected size is Θ(k) [Devillers et al. 03]. In this paper, we study the size of the visibility skeleton experimentally. Our results indicate that the size of the 3D visibility skeleton, in our setting, is C k √ nk, where C varies with the scene density but remains small. This is the first experimentally determined asymptotic estimate of the size of the 3D visibility skeleton for reasonably large n and expressed in terms of both n and k. We suggest theoretical explanations for the experimental results we obtained. Our experiments also indicate that the running time of our implementation is O(n3/2k logk), while its worst-case running time complexity is O(n2k2 logk).